The Effect of Drop (Bubble) Size on Advancing and Receding Contact Angles for Heterogeneous and Rough Solid Surfaces as Observed with Sessile-Drop and Captive-Bubble Techniques

c. ,.o,~ "c,. ,

JOURNALOFCOU.DID AND INfERFACESCIENCE 179, 37-50 (1996) \ARTICLE NO. 0186 ,\'

The Effect of Drop (Bubble) Size on Advancing and Receding ContactAngles for Heterogeneous and Rough Solid Surfaces as Observed

with Sessile-Drop and Captive-Bubble "'Cechniques

JAROSLAW DRELICH,*,I JAN D. MILLER,* AND ROBERT J. Gooot

* Department of Metallurgical Engineering, University of Utah. WBB 412, Salt Lake City, Utah 84112; and t Department of Chemical Engineering,

State University of New York at Buffalo, 506 Furnas Hall, Buffalo, New York 14260

Received February 17, 1995; accepted October 25, 1995

the three interfaces, solid/liquid, solid/vapor, and liquid/vapor,SessiJe-drop and captive-bubble tec~ques were ~ for COD- and by the solid topography ( 1 ). The angle between the tangent

tact angle measurements. The advancmg and recedmg contact to the liquid surface and the tangent to the solid surface ( contactangles were measured for water and ethylene glycol at self-assem- I ) h te . tI' te f th three h te .

.ang e , a c arac ns c parnme roe -p ase sys m. ISbled monolayer surfaces of dodecanethiol, for water at methylated used to describe the I 0 hobicll hiIic ro rties of the solidquartz surfaces, and for water at roughened polyethylene and poly- ..Y P yop P pe ,tetraOuoroethylene surfaces. It was found that for each technique surface ~d Its quality. ~easurements of .contact angles usmgused, sessiJe-drop and captive-bubble, different advancing contact the sessIle-drop and captIve-bubble techniques are among theangles and different receding contact angles were frequently ob- most popular methods used in surface chemistry laboratoriestamed for nonideal systems with rough and heterogeneous solid for this purpose, especially due to their simplicity and smallsurfaces. The disagreement between contact angles, as measured amount of liquid and solid sample required ( I ). It is not alwayswith the two different techniques, increased with increasing imper- well recognized that these two techniques can provide quitefection of the solid surface. Also, it was observed that solid surface different contact angle data depending on the quality of theroughness and heterogeneity affected a variation of the advancing solid surface and the drop (bubble) size used in such contactand receding contact angles with drop (bubble) size. No contact angle measurements,angle change .Mth respect to drop (bubble) size (in the range 1- The eff~t of drop (bubble) size on contact angle was ob-7 rom base dIameter) was observed when smooth and homoge- ed d gnized (2 4) b t .gnifi t...serv an reco many years ago -u no SI canneous solId surfaces were well prepared. It IS possIble that metasta- mad ard the d din f thi phble states, which are responsible for the contact angle hysteresis, progress was .e tow un ers~ g 0 s ~n~me-also affect the contact angle/drop (bubble) size relationship. These non, and the varIety of sampl.es exammed was rather limited.three-phase systems with sessile drop and captive bubble at hetero- Mack (2) observed changes m contact angle from about 50"geneous and/or rough solid surfaces are complex because solid to 90" for water drops placed on the surface of apple wax whensurface heterogeneity and roughness cause contortions in the shape the drop volume was changed from 3.65 to 0.4 ILl; and theof the three-phase contact line and the drop (bubble) surface in contact angle remained constant at gso -90" for small dropsthe vicinity of the three-phase contact line. These contortions may with a volume of 0.1-0.4 ILl. He believed that this eff~t wasaffect a variation of the internal free energy of the liquid drop stimulated by the gravitational force. Also, Leja and Poling (4)(gas bubble). It is shown that a S~ght variation ~ the advancing followed a similar concept. However, the hypothesis of the~ntact angle value over a few m;illimeter:s change In drop (bubble) particular effect of gravity on equilibrium contact angle wasdiameter does not guarantee a high-ijuality surface state. Measure- . ted b raI th (5 - 9) Also '-"'nt contact angle.. d :_r. reJ~ Y seve au ors ., ments of the recedmg contact angles proVl e more llllonnation on ti raI .th Ii .ds f .dthe quality of the solid surface and they should always be included ~easurements or seve s~s~~ WI .b q~ 0 ;;::ng ~n-with the measurements of advancing contact angles. C 1996 Academk Sity demonstrated the neg gt e contn utIon ? ~V1~-Press, lDC. tional force to the contact angle/ drop (bubble) Size relatIonship

Key Words: contact angle; contact angle hysteresis; self-assem- for rigid solids (10).bled monolayer; gold; quartz; line tension; wettability. Vesselovsky and Pertzov (3) reported the effect of bubble

size on contact angle for the air bubble/aqueous phase/par-INTRODUCTION affin sys~m, and ~mporta~tIy, the! pr~posed (prob~bly for

the first tIme) the Ime tensIon modificatIon of Young s equa-The shape of a liquid drop or gas bubble placed at a homoge- tion as (3)

noons, rigid solid surface is controlled by the free energy of"YSLV [1]"YSV -"YSL = "YLVCOS e + -.

I To whom correspondence should be addressed. r

37 0021-9797196 $18.00Copyright C 1996 by Academic Press. loc.

All rights of reproduction in any form reservat.

i

! ;;.~j

38 DRELICH, MILLER, AND GOOD.-'YLY, 'YSY, and 'YSL are the interfacial tensions, the L, S, and was more evident at reduced pressures for the water/copperV subscripts corresponding to liquid, solid, and vapor, re- system (25-27). Also, they demonstrated that the equilib-spectively; e is the contact angle; 'YSLY is the line tension: rium film pressure has a negligible effect on the contactthe excess free energy in the region of the triple interface angle and the contact angle/drop size relationship for water/(II). Equation [I] is applicable for homogeneous, rigid, flat, (argon: saturated with water or organic solvent)/PTFE sys-horiz?ntal, and smooth solid surfaces. tern (28). Further, it was found that the contact angle/drop

UsIng Eq. [I], Vesselovsky and Pertzov (3) calculated size relationship depends on the temperature of the experi-the line tension to be from -1.3 X 10-6 to -14 X 10-6 J/ ment (28). When the temperature of the system was 25-m. (The negative line tension indicates that the contact angle 75°C the contact angle decreased with decreasing water dropas measured for the aqueous phase increased with increasing volume for a polymer (PTFE) surface as well as for metalbubble size.) Unfortunately, as they correctly discussed (3), surfaces (stainless steel, gold, copper). This correlationthe line tension values determined were much larger than changed at the boiling point of water and the contact anglethose that would be expected from intermolecular interac- decreased with increasing drop volume in these circum-tions. stances. Even though Ponter and co-workers (25-29) pro-

The modified Young's equation [1] was also used by Neu- vided several useful examples of the effect of drop size onmann et at. (12, 13) for the interpretation of the contact contact angle, they did not propose any rational explanationangle/drop size relationships. The line tension values were for this phenomenon. There are also a few additional exam-calculated to be 2 X 10-6 to 3 X 10-6 J/m for alkane/Teflon pIes of the contact angle/drop (bubble) size relationship in(FEP) system (12) and 2 X 10-6 to 6 X 10-6 J/m for the literature with limited discussion of the factors whichdodecane/FC-721, dodecane/Zonyl FSC, and ethylene gly- account for this relationship (30-32).col/dimethyldioctadecylammonium syste91s (13). Good and Koo (15) measured the advancing and the re-

Also based on Eq. [1], Janczuk and Bialopiotrowicz (14) ceding contact angles for water, ethylene glycol, and decaneanalyzed the contact angle change for water drops placed on Teflon FEP, and for water on PMMA. They observed aon Teflon during water evaporation. They calculated that the decrease in contact angle with decreasing drop volume forline tension can reach a value of about -16 X 10-6 J/m at both the water/FEP and the water/PMMA systems. Therethe end of evaporation process. was no change in the advancing contact angle for the ethyl-

The hypothesis that the contact angle/drop (bubble) size ene glycol/FEP system and no change in either the advanc-relationship can be explained based on the modified Young's ing or the receding contact angle for the decane/FEP system.equation [1] was rejected (10,15-17) for most of the sys- Good and Koo (15) proposed that surface heterogeneityterns examined. It must be recognized that the modified could be the reason for the contact angle/drop size relation-Young's equation [1] is limited to ideal three-phase systems ship observed. They suggested that local patches of varyingwith pure liquids and homogeneous, smooth, isotropic, ~gid polarity make the three-phase contact line corrugated andsolid surfaces, inert to fluids, which are exceedingly difficult that such a contortion causes the contact angle variation withto prepare. A linear correlation of the cosine of the contact drop size. The concept of the effect of surface heterogeneityangle vs reciprocal of the drop (bubble) base radius, as on the contact angle/drop (bubble) size relationship wasrequired by Eq. [I], was demonstrated experimentally over mentioned previously by other researchers (3, 30) but wasa wide range of drop (bubble) volumes for only a few three- not discussed to any great extent. This hypothesis on thephase systems, in which pure single-component liquids and particular role of surface heterogeneity in the relationshipfreshly prepared clean solid surfaces were used (10, 17). between contact angle and drop (bubble) size has now beenFor such systems the values of the line tension on the order of supported experimentally (17, 33. 34). Further, Good and10-9-10-8 J/m were calculated from experimental contact Koo (15) also proposed a new term, "pseudo-line tension,"angle data (10, 17). These experimental values are much which can be used to describe the correlation between thesmaller than those presented in previous contributions, cosine of the contact angle and the radius of drop base for10-6-10-5 J/m (3,12-14). Also, as expected, these values nonideal systems instead of the line tension which describesare closer, by an order of magnitude, to the line tensions the excess free energy associated with the three-phase con-predicted theoretically, 10-12-10-10 J/m (II, 18-20), or tact line and which may only be determined from contactdetermined experimentally using other experimental tech- angle/drop (bubble) size relationship for ideal systems, i.e.,niques, 10-11-10-9 J/m (21-24). , for systems which comply with the modified Young's equa-

The effect of liquid (water or organic solvent) drop size tion [1]. The pseudo line tension values were calculated foron contact angle for polymers (polytetrafluoroethylene several nonideal three-phase systems and it was found that(PTFE), polymethylmethacrylate (PMMA» and metals these values are close to the values attributed previously to(copper, stainless steel, gold) was examined by Ponter et the line tension (10,16,34).at. (25-29). They found that the drop size effect is evident Further, an important hypothesis, which was consideredfor drop base diameters less than 0.5-1 cm, and this effect in the literature (25, 35), but unfortunately not discussed in

--~

'-.

~,

CONTACT ANGLE MEASUREMENTS 39 I.

detail, is that the surface roughness may be responsible for technique. In this way, contact angle differences betweenthe variation of contact angle with drop size. The first experi- the three techniques are demonstrated.mental support for this concept was provided quite recently( 17, 34). Also, the effect of solid surface roughness on EXPERIMENTAL PROCEDUREScontact angle/drop (bubble) size relationship was consid-ered theoretically to a certain extent and a modification of Reagents and Materialsthe Wenzel equation including the line tension term was ., ..d .d (17 34) , , Four dIfferent SOlId surfaces were used m the expenments:

en:e .'. ..(i) a polyethylene (PE) film on a glass slide or an aluminium~mally, It .should ?~ ~mphaslzed. that. def~rmatIon of a plate prepared by coatin'k the slide/plate with low-density

solId surfac~ m ~e vlcmlty o~ the triple Junct~on due to ~e polyethylene (Scientific Polymer Products, Inc.) in tolueneeffect of solId stram can be an ImPOrt.ant factor m t.he analysIs solution and evaporation of the solvent, (ii) a PTFE plateof the co~tact a~gle/drop (bubble) SIze data, partlcul~ly for received from Utah Regional Supply, Inc., (iii) optical-gradethose so!Ids WhICh are deforma~le and have ~n ela~tIc su~- quartz plates (Minarad Scientific Inc.) hydrophobized withface. ThIS phenomenon was consIdered theoretically m detaIl a solution of chlorotrimethylsilane in cyclohexane, and (iv)by several researchers (see Refs. 36-38 and literature cited a gold film, which was vapor deposited onto a silicon wafer,therein). However, there is still no experimental work to and covered with a thiol self-assembled monolayer of do de-evaluate the significance of solid surface deformation on canethiol.the relationship between contact angle and drop (bubble) The chemicals used in the experiments were as follows:volume. distilled and Milli-Q deionized water with pH 5.8 :t 0.1,

The effect of solid surface heterogeneity and roughness specific conductivity < 10-6 S / cm, and surface tension 72.6on the contact angle/drop (bubble) size relationship has :t 0.2 mN/m at 20°C; ethylene glycol with purity greaterrecently been demonstrated for several systems (10, 17,33, than 99.5% (Mallinckrodt, Inc.) and surface tension 47.8 :t34) using a dynamic captive-bubble technique. However, 0.2 mN /m (20°C); spectrograde cyclohexane, toluene, andour understanding of the contact angle variation with drop acetone (Mallinckrodt, Inc.); chlorotrimethylsilane with pu-(bubble) volume is still incomplete. Both experimental and rity greater than 98% (Mallinckrodt, Inc.); I-dodecanethioltheoretical examinations of the relationship between contact with 98% purity (Aldrich Chemical Co.); dehydrated ethylangle and drop (bubble) size for a variety of solid surfaces alcohol (Quantum Chemical Co.); and chromic-sulfuricand under different experimental conditions are required. cleaning solution (Manostat).

The dynamic captive-bubble (drop) technique was incor-porated in our previous studies for examination of the contact Solid Surface Preparationangle/drop (bubble) size relationship (10, 17,33,34). In Granulated low-density polyethylene (PE) was dissolvedthis technique the gas bubbles or liquid droplets ar.e injected in toluene at a temperature of 60- 70°C (0.2-1 wt% concen-beneath the surface and are transported to the solId surface tration). The microscopic glass slide or aluminium plate wasdue to buoyant force (see Experimental Procedures for fur- covered by the fE-toluene solution and kept in a cleanther details). The important advantage of the dynamic cap- vacuum oven several hours at a temperature of 60-65°C.tive-bubble (drop) method is the ability to examine the con- The toluene was evaporated and the remaining polyethylenetact angle/bubble ( drop) size relationship over a wide range formed a film.of bubble (drop) volumes, from several micrometers to sev- The PTFE plate was used as received after washing theeral milimeters in diameter (16,17). A disadvantage of this surface with chromic-sulfuric solution and distilled water.technique is that the "equilibrium" contact angle cannot be In a second experiment, the same PTFE plate was rougheneduniquely defined, and the receding contact angle and the by polishing with 600-grit paper.intermediate contact angle (contact angle between the reced- The quartz plates were methylated as in previous studiesing and advancing) were observed for nonideal systems. ( 17, 33). Carefully prepared, dry quartz plates were im-

In this contribution, two standard techniques for contact mersed into a solution of chlorotrimethylsilane (TMCS) inangle measurements, the static sessile-drop technique and cyclohexane. The concentration of TMCS in cyclohexanethe static captive-bubble technique, were adopted in order was 1 X 10-6 -5 X 10-6 M and the time of immersionto demonstrate the effect of solid surface heterogeneity and was 5-30 min. Hydrophobized plates were washed withroughness on the contact angle/drop (bubble) size relation- cyclohexane to remove unbounded residual TMCS and wereship for advancing and receding contact angles. Addition- then heated in the oven for 2 h at 110-115°C.ally, based on these experiments, the advancing and receding A 200-nm gold film supported on a silicon wafer, pre-contact angle data obtained with the static sessile-drop tech- coated with titanium to improve adhesion of the gold film,nique and static captive-bubble technique are compared with was used as a substrate to prepare a model homogene~uscontact angle data obtained with the dynamic captive-bubble surface composed of a self-assembled monolayer of thlOl.

c,.".,"

,,

.' 40 DRELICH, MILLER, AND GOOD

recedin, or intermediate contact anile

b C'~ ~~(!f advanclnc lntennediate recedinca j t contact anIle contact anIle contact anIle --gas -Q ~ as A V 'gas ~ lillid- ' ..q buoyancy

liqUid.. lIquid -""'- = ro~ce --

ad~ancinc intennediate recedinc I t --contact anIle contact anIle contact anile t -..pressure air

A.a. 1. Illus~atjon of the three methods used for contact angle measurements. (a) Sessile-drop technique (static); (b) captive-bubble technique(static); (c) captive bubble technique (dynamic).

Ij The same substrate which was prepared in the previous con- paraffin; 0.5 mm diameter) remained in contact with the

tribution (39) was reused after cleaning the gold surface for drop. Precautions were taken in the measurements to avoidf removal of the organic monolayer and organic and inorganic distortion of the drop shape by the needle. First, the outer

cont~n~ts. The .gold su~ace ",:a~ cleaned with chromic- surface of the needle was made hydrophobic by coating, s~lfuric acl.d cleanmg sol~tion, dlsti~led water, and ethanol. with a paraffin film. This coating inhibited the liquid from1 Fmal cleanIng from orgaruc contarrunants and the adsorbed climbing up the needle and protected against the formation

~iol monolayer was conducted in a Tegal Co. plasma chem- of a concave meniscus. Climbing of the liquid may cause aIStry reactor (Plasmod model). The substrate was treated distortion of the circular shape of the drop and affect the

t with argon plasma for 60 min. Such a freshly cleaned gold contact angle measurements, particularly for small dropssurface was immediately immersed for about 30 min into (bubbles). In such cases, an intermediate contact angle can

i the 1 mM ethanol solution of l-dodecanethiol (thiol forms frequently be observed instead of the advancing or recedingself-assembled monolayer on the gold surface through gold- contact angle. Second, the tip of the needle was alwayssul~ur bound with the hydrocarbon chain oriented into the kept at the top of the sessile drop (captive bubble). AnyenvIronment (40-42)). After removal from the adsorbate immersion of the needle into the liquid drop (gas bubble)solution, slides were washed with ethanol and then dried in and any pulling of the liquid (gas) with the needle wasa stream of argon. avoided and thus there was no distortion of a shape of the

: liquid drop (gas bubble).Contact Angle Measurements Th thr h ...e ee-p ase contact hne of the hquld drop was made

Three different contact angle measurement techniques to advance or retreat by adding or withdrawing a small vol-were used in these studies, as follows (see Fig. 1): (i) static ume of liquid (see Fig. la) and the advancing and recedingsessile-drop technique (Fig. la), (ii) static captive-bubble contact angles, respectively, were measured in 30-45 s ontechnique (Fig. Ib), and (iii) dynamic captive-bubble both sides of the drop (the average values are reported).(drop) technique (Fig. lc). The 30-45 s were sufficient to take the contact angle mea-

The static sessile-drop (Fig. la) and captive-bubble (Fig. surements at both sides of the drop. The 20_40 of change in1 b ) techniques for contact angle measurements were adopted contact angles were observed in the first 5 -15 s after an

i from the literature ( 1, 43) using a NRL goniometer (Rame- increase or decrease of the drop volume, and contact anglesHart, Inc.). The optical system of the NRL goniometer has remained practically constant (~1°) in the next 1-2 min.independently rotatable crosshairs and internal protactor Importantly, the contact angle data as measured in 30-45 sreadout calibrated in 10 increments. The supporting stage of were reproducible for all systems examined.the instrument is calibrated on both horizontal and vertical In the captive-bubble technique, the solid sample wasaxes in 0.02-mm divisions and this allows for accurate mea- placed in the rectangular glass chamber on two stable sup-surements of the drop dimensions, i.e., drop (bubble) base ports with flat surfaces. The glass chamber with sample wasdiameter. , filled with liquid. A small air bubble was made at a tip of

In the sessile-drop technique, the solid sample examined the V-shaped needle using a microsyringe. The gas bubblewas placed in a controlled-atmosphere Rame- Hart chamber was attached to the solid surface. The three-phase contactwhich was partially filled with the liquid used for the contact line of the gas bubble was made to advance or retreat byangle experiments. The chamber with solid sample remained adding or withdrawing a small volume of air (Fig. 1 b), andclosed 0.5 -1 h to achieve equilibration between the phases. the receding and advancing contact angles (as measured forA liquid drop was introduced onto the solid surface through the liquid phase), respectively, were measured with the NRLa microsyringe, and the needle (stainless steel coated with goniometer in 30-45 s on both sides of the gas bubble

--

.""'".' .

CaNT ACf ANGLE MEASUREMENTS 41 \

(the average value is reported). The contact angles were 85

measured for varying bubble size. The needle remained in

a contact with the air bubble during all measurements but ~80 ~e~'~8'~Cb80e::>.

no distortion of the bubble shape by the needle was allowed ~75 .~~~~o~..cr.m~~to affect the contact angle measurements. a 0

As the third technique, the dynamic captive-bubble .?: 70

method (Fig. 1 c) has been used for examination of the effect Uof bubble size on contact angle (16, 17). The dynamic cap- ~ 65 .SD-Adv. 0 SD-Rec. 0 CB-Adl/. .CB-Rec. "V Dca

~ve-b~bble technique differs from the static one by the way <3 60 \

m whIch gas bubble attachment occurs at the solid surface.Air bubbles of varying size were generated in the liquid with 55

a syringe under the solid surface and allowed to release 0 1 2 3 4 .5 6 7

from the needle. Released bubbles were captured at the solid Drop (Bubble) Base Diameter [mm]

surface as a result ofbouyant transport and attachment. After FIG. 3. The effect of drop (bubble) size on advancing (Adv.) and

the air bubbles attached to the solid surface, both contact receding (Rec.) contact angles for the air/ethylene glycol/(dodecanethiolangle and bubble base diameter were measured with the on gold) system as obtained with the static sessile-drop (SO), static captive-

NRL goniometer. In contrast to the static techniques the bubble (CB), and dynamic captive-bubble (DCB) techniques.

contact angle is not always uniquely defined in the dynamic

technique, as presented in the next part of this paper. ,,'as the recedmg contact angle" (8R). The contact angle

hysteresis is the difference between the advancing and reced-

RESULTS AND DISCUSSION ing contact angles (~8 = 8A -8R). Elimination or at

H least minimization of the contact angle hysteresis is required

omogeneous and Smooth Solid Surface for accurate and reproducible wetting characterization of

Ideal solid surfaces with homogeneity and smoothness at solid surfaces, and this usually may be accomplished by

the atomic/molecular level are extremely difficult to prepare, caref~l solid surface ~reparation (polishing and cleaning),

and nearly all surfaces are heterogeneous and rough to an handlIng, and preservmg. The contact angle hysteresis does

appreciable extent (35). If this is the case, a liquid in contact not exceed a few degrees for well-prepared and stabilized

with such surfaces shows more than one contact angle. Two solid surfaces.

of these contact angles are of practical significance in the An effectively smooth and homogeneous surface was pre-

characterization of solids. The contact angle measured for pared for these studies using a silicon wafer with deposited

the liquid tending to advance is called the "advancing con- gold film having a roughness dimension of about 10 nm

tact angle" (8A) and it is larger than the contact angle (40) and coated with a self-assembled monolayer of l-dode-

measured for the liquid tending to recede which is known canethiol. It is believed that thiols form uniform and homo-

geneous self-assembled monolayers on the gold film (40-

42). The advancing and receding water contact angles, as

120 measured with the sessile-drop and static and dynamic cap-

tive-bubble techniques, are presented in Figs. 2 and 3.

'"C) 115 The monolayer of self-assembled alkyl thiols at the gold

~ 11 0 .~ ~~ ~~ o=~~'8.~ surface, as used in these studies, was found to be a good

~ 0 ~ ~~ ~ ..~ .-~~ example of a close-to-ideal surface. The contact angle hys-g>105 ~~~~ i!J [80 ~ !j teresis was very small, 5°-7°, for both water (8A = 110°-

~ 113° and 8R = 106°-108°, Fig. 2) and ethylene glycol (8A

~ 100 = 79°-82° and 8R = 75°-77°, Fig. 3) when the monolayer

5 was freshly prepared. Two different contact angle measure-

() 95 .SD-Adv. 0 SD-Rec. 0 CB-Adl/. .CB-Rec. "V Dca ment techniques, sessile-drop and captive-bubble methods,

provided the same contact angle data (see Figs. 2 and 3).

90 Both the advancing contact angle and the receding contact

0 1 2 3 4 5 6 7 8 angle remained constant over the range of drop (bubble)

Drop (Bubble) Base Diameter [mm] sizes examined, approximately 1-7 mm in base diameter

(Figs. 2 and 3). The contact angles as measured for the airFIG. 2. The effect of drop (bubble) size on advancing (Adv.) and ...

receding (Rec.) contact angles for the air/water/(dodecanethiol on gold) bubbles attach.ed to the monolayer WIth the dyn~c capuve-

system as obtained with the static sessile-<lrop (SO), static captive-bubble bubble techmque corresponded to the recedmg contact

(CB), and dynamic captive-bubble (OCB) techniques. angles (see Figs. 2 and 3; note that approximately the same

...42 DRELICH, MILLER, AND GOOD

30- to 45-s equilibration time for the three-phase system was 120maintained in all contact angle measurement techniques). 0 COO o~ ~ 0 ~<f,.i 0 ~ 0 cxxPo 0

The three-phase system with a homogeneous, smooth, and ~100 ..:- ~ .~

nondeformable solid surface is described by the modified EE ~""" "'ZS7Y . [1] .~..,w ..,"Vw~..,

j oung equation, which can also be expressed as Q) 8 rI-~'".c> 80 8-- -8 ~ ~~~rSJ: c: 0

« 0cos e = cos e~ -~ [2] "i:3 60 00

r'YLV ~ £:Ic:0

where () 40 0

, .SD-Adv. 0 SD-Aec. 0 CB-Adv. 8 CB-Aec. .., DCB

'\I -'\I 20, e ,SV ,SL..cos ~ = 0 1 2 3 4 5 6 7'YLV

DI rop (Bubble) Base Diameter [mm]e = e~ for r -+ 00.; FI~. S. The effect of drop (bubble) size on advancing (Adv.) and

I .." recedm~ (Rec:) contact ~gles for the air/water/polyethylene film system

Equation [2] sho.ws that there should be a linear relationship as obtatn~ WIth ~e statIC sessile-drop (SO), static captive-bubble (CB),

between the cosme of the contact angle (cos e) and the and dynarntc captIve-bubble (DCB) techniques. The polyethylene film was1 reciprocal of the drop (bubble) base radius (11 r)' i.e there formed on roughened.aluminum plate from polyethylene-toluene solution

h ld b .." after solvent evaporatIon.S ou e a change m contact angle With drop (bubble)size according to the contribution of the line tension ( 'YSLV ).. .Nevertheless, because of (i) the small line tension value size exanuned (-1-7 mm) proves that any distortion of the

f expected (from 10-12 to 10-9-10-8 JIm as determined for drop or bubble shape, as caused by the needle, was success-some systems (17)), (ii) large drops and bubbles used in fully avoided during contact angle measurements. It is ex-

, contact angle measurements, and (iii) the very narrow range pected that the contact angle will be affected by tip size onlyof drop (bubble) size examined in these studies (from 1 to for drops (bubbles) that are very close to the same size as7 mm in base diameter), the effect of line tension on contact the syringe tip (-0.5 mm in our systems). What looks likeangle could not be distinguished. The advancing and reced- a tip ~ize effect is g~nerally due to hysteresis. For a particularing contact angle values presented in Figs. 2 and 3 are con- location of the penmeter of the drop, on the solid, betweenstant for the range of the accuracy associated with these the locations for the advancing and receding of the drop

! contact angle measurements (1°-2°). front, and for a particular drop volume, the drop shape ad-Reproducibility of advancing and receding contact angles justs itself to minimize free energy, or to attain constant

(10-2°; Figs. 2 and 3) over the entire range of drop (bubble) Laplace. pressure across all the interface. The angle then canbe considered a dependent variable, and a continuous range

I of angles can exist. For a drop that is not on a syringe tip,120 if e is a true Young equilibrium angle on the solid (see Eq.

-[1]), then Young's equation acts as a boundary condition,"g> 1 00 ~ o~~'o~%~ ~... together with the Laplace curvature all over the surface, to:2. ~.;~ .,v~~ ~~ determine drop shape. If the drop is also attached to a syringe

j. ~ 80 0 or=- tip, then the three-phase line of attachment ( or of tangency)j ~ d:J acts as another boundary condition, but the contact angle on

"i:3 60 r:SJ the solid is not affected by it nor by the tip diameter. An~ D[IJ element of volume of the liquid, very near the three-phase8 40 0 contact line o~ the solid, is acted upon by the resultant of

0 the three tensions ('Ysv, 'YSL, and 'YLV) and the rigidity of.SD-Adv. 0 SO-ABC. 0 CB-Adv. 8 CB-Aec. .., DCB the solid; that resultant will be much greater than the net

20 '-- force due to 'YLV in the region of the tip.0 1 2 3 4 5 ~ 7 8 9

Drop (Bubble) Base Diameter [mm] Roughened Solid Surface

FI~. 4. The effect of drop (bubble) size on advancing (Adv.) and The contact angle I drop (bubble) size relationships forrecedIng (Rec.) contact angles for the air/water/polyethylene film system ..as obtained with the static sessile-drop (SO), static captive-bubble (CB), two dlfferen~ polymers, PE and PI'FE, With rough surfacesand dynamic captive-bubble (DCB) techniques. The polyethylene film was were deteTffilned by contact angle measurements. The exper-formed on microscope glass slide from polyethylene-toluene solution after imental results are presented in Figs. 4 and 5 for PE and insolvent evaporation. Figs. 6 and 7 for IYrFE.

--

I-

""""I

"

CONTACT ANGLE MEASUREMENTS 43 ~

140 The effect of surface roughness on contact angle hysteresisis commonly known and accepted (35, 43). It has been

120 extensively discussed in the literature that liquid in contactg> ~ ~~~~~ ~ .with a rough surface can adopt several metastable configura-

~ ..~ -: #l,~~~~ tions each with a different apparent contact angle, and that-g> 100 BOO [DJ:E):Jc.--~ the advancin.g. and receding contact angles ~orrespond ~~ ac{ ~ 0 different pOSItiOn of the three-phase contact lIne at aspentles

~ 80 r@I (43,45-49). The contact angle hysteresis for rough polymerc surfaces was found to ~e from several degrees to over 30°,0 .'\'() 60 and the hysteresIs was larger for rougher surfaces (compare

.SD,Adv. 0 SO-ABC. 0 CB-Adv. .CB-Aec. "'\7 DCB F. 4 .th F. 5 d F. 6 .th F.7)Ig. WI Ig. an Ig. WI Ig. .

40 It is believed that three phenomena, typical for systems0 1 2 3 4 5 6 7 8 with a rough solid surface, have to be considered in the

Drop (Bubble) Base Diameter [mm] discussion of the co~tact angle data presented in Fi~s. 4-::.They are: (i) contortIon of the three-phase contact lIne, (11)

FIG. 6. The effect of drop (bubbl~) size on advancing (Adv.).and free energy barriers acting against liquid movement (me-re~eding (R~.) co~tact angles for th~ aIr/~ater/PTFE system as obtaJn~d chanical barriers of rou hness features), and (iii) entrap-With the static sessile-drop (SD), static captive-bubble (CB), and dynamic g ...captive-bubble (DCB) techniques. ment of gas between aspentles of rough hydrophobIc sur-

faces.Contortion of the three-phase contact line. It was ob-

A PE film was deposited on a microscope slide and alu- served for all samples that the wetting line was located acrossminium plate by spreading the PE-toluene solution and a random array of asperities and that the three-phase contactevaporation of the solvent. The microscope glass slide was line was highly irregular (contorted) especially when theused as received, whereas the aluminium plate was slightly liquid boundary was made to recede. The three-phase contactroughened with 600-grit polishing paper. After solvent evap- line contortion phenomenon was proposed to explain theoration the remaining PE film had lustreless surface with a contact angle hysteresis (15, 45) and may also contribute toripple structure (see Ref. 44 for some examples of polymer the contact angle/drop (bubble) size relationship. A micro-surface images recorded with photon tunneling microscope). scopic convolution of the three-phase contact line due toAlso, two PTFE samples with rough surfaces were selected roughness could have the same qualitative result as that duefor contact angle measurements. The first plate was used as to microscopic patchwise heterogeneity (see Ref. 15 forreceived and the second was made even more rough with more details). Thus, we may consider the locally fluctuating600-grit polishing paper. All polymer surfaces prepared direction of the line tension vector, as the three-phase contactshowed rough features under an optical microscope but di- line "picks out" a contorted location that minimizes linearmensions of the surface irregularities were not defined.

The contact angle data shown in Figs. 4- 7 demonstratefive important features of rough solid surfaces: (i) conta~t 140 ~angle values are scattered; (ii) the contact angle hysteresIs 00 cP<8X2> ~is large; (iii) both advancing contact angles and receding 120 . .- ..~ ~ -..di th Q) ..-contact angles differ, for some systems, depen ng on e (!) 100 ~ --sz..;Q. V ~._. ~ .-.technique used, sessile-drop or captive-bubble; (IV) the con- (!) "'\7tact angle as obtained with the dynamic captive-bubble tech- "'6> 80 c}fD ocn]:D°nique corresponds to the receding contact angle or intermedi- ..?: 60 0 DOate contact angle (contact angle between receding and ad- ~ 0vancing); and, importantly for these studies, (v) the contact § 40 DOangle/ drop (bubble) size relationship is significantly af -()fected by the topographic features. 20 .SD-Adv. 0 SO-ABC. 0 CB-Adv. .CB-ABC. "'\7 DCB

The roughness geometry of the polymer surfaces used, 0PE and PTFE, was complex with poor reproducibility, and 0 1 2 3 4 5 6 7thus, a complete discussion of the experimental data is not Drop (Bubble) Base Diameter [mm]

possible. A goal of this contribution is to identify ~ssible FIG. 7. The effect of drop (bubble) size on advancing (Adv.) andfactors affecting the contact angle/drop (?ubble) SIze rela- receding (Rec.) contact angles for the air/water/PTFE system as obtain~tionship as well as to demonstrate the dIfference between with the static sessile-drop (SD), static captive-bubble (CB), and dynamiccontact angles when determined with different experimental captive-bubble (DCB). te.chniq~es. The same PTFE sample as in Fig. 6

techniques. after slight surface polishing With 6OO-gnt paper.

,.

, .44 DRELICH, MILLER, AND GOOD

ALv2 A LVI Fig. 8) is much larger than the radius of the local contortion>ASL2 = ASLI of the three-phase contact line (rL), rL ~ rl' In such a case,~ the macroscopic contact angle (81), as observed during con-

82 tact angle measurements, corresponds to a value which is

between two extreme contact angle values (8LI and 8L2),2r2 ~haracteristic for local contortions of the three-phase contact

211 line, 8L2 > 81 > 8LI .The situation changes with decreasing

e2 < e1 drop volume and the macroscopic contact angle for a small

drop ( 82) approaches the smallest local contact angle ( 8LI ) ,i.e., approaches the apparent contact angle which is observed~L at the extremeties of the contorted drop base, 82 -+ 8LI'

r2 In summary, contortion of the liquid drop (gas bubble)base has such an effect that the contact angle decreasesI rL-+r2 with drop (bubble) size (Fig. 8). Such contact angle/drop

(bubble) size relationships were observed in our systems,rL« I: which are particularly clear for receding contact angles1 (Figs. 4- 7). Nevertheless, mechanical barriers for a moving

j liquid at the rough solid surface should also be included in

.&.<e.<~ the discussion of the effect of drop (bubble) size on contact« angle. They may even change the contact angle/drop (bub-t ble) size relationship from a function which decreases with

decreasing drop (bubble) volume to one that increases, as! observed in some of our systems (Figs. 6 and 7). A short

discussion on this topic is presented in the forthcoming sec-tion.FIG. 8. A large drop and a small drop at rough solid surface. See text

for details and discussion. ALv and ASL are the interfacial areas; the L, S, Free energy barriers. We examined the edge of the dropand V subscripts correspond to liquid, solid, and vapor, respectively; e is or bubble microscopically and found that there were certainthe contact angle; r is the drop base radius; the I and 2 subscripts correspond three-phase contact line configurations, energetically favoredto a large and small drop, respectively. by the system, and spontaneous transition between them was

observed when the liquid phase boundary was advanced orfree energy, jointly with minimizing the area free energy receded (spontaneous jump of a portion of the three-phase(surface free energy) of the contorted surface near the solid. contact line from one surface site onto another). The me-When the envelope of the local, linear contour has a radius chanical barriers between metastable configurations mightthat is comparable to the local contortion of the three-phase be of particular importance for the correlation between dropline, the macroscopic contact angle will be a function of (bubble) size and contact angle. The internal free energydrop size (Fig. 8). When the envelope has a much larger of the entire liquid drop or gas bubble, which controls theradius, the contact angle will be independent of drop size. equilibration of the three-phase system, may, contrary to theHowever, the contact angle for infinite drop size will not, convolution effect, decrease with the volume of the sphericalin general, be exactly the contact angle for a smooth surface! drop or bubble. For example, a simplified theoretical modelThat could only be the case (sometimes) when the entire of Johnson and Dettre (46) for a spherical drop on a roughdrop size effect is due to heterogeneity in the form of patches homogeneous surface, composed of circularly symmetricalor bands having different surface free energy. sinusoidal-type asperities, predicts the total free energy of

Figure 8 presents a large drop and a small drop at a rough the system to besolid surface. The three-phase contact line is contorted forboth drops. This also affects a contortion of the drop surface 2 ( 2 )in the vicinity of the three-phase contact line. In some cases, F = 7rr "fLV I + cos cf> -x cos 8, [3 ]

the contortion of the drop surface may xxtend over the entiredrop surface, particularly for a small drop. For drops witha contorted surface, the ratio between the surface area for where cf> is the apparent contact angle experimentally ob-the liquid-gas (ALv) interface and the surface area for the served for the liquid drop on the rough surface; 8 is thesolid-liquid (ASL) interface may change with drop size and intrinsic contact angle; x = a/A is the roughness ratio (45,may lead to an increase in the excess energy of the entire 50, 51); a and A are the actual and apparent solid -liquiddrop per unit length of the three-phase contact line. interfacial area, respectively; and other nomenclature are the

The radius of the drop base for the large drop (rl) (see same as used in previous equations. It follows from this

--

.~..CONTACT ANGLE MEASUREMENTS 45 \

.'.theoretical relationship (Eq. [3]) that the liquid drop should For such systems, the contact angle is always larger than :\:

be able to reach the smaller contact angles with decreasing that for a smooth surface. For example, the advancing waterdrop volume, when the three-phase contact line is made to contact angle for PTFE is reported in the literature to berecede (the energy barriers are assumed to be the same over 108°-112° (56-59), whereas in this study the contact angle,the entire solid surface area). This concept would lead to the as measured with the captive-bubble technique on roughenedinterpretation of the receding contact angle data presented in PTFE, reached a value of 130°-140° (Fig. 7). Also, theFigs. 4-7. advancing water contact angle as measured with the same

The receding contact angles, as measured with the sessile- captive-bubble technique for the rough PE film, 112°-115°drop technique, decreased with drop size for all rough sur- (Fig. 5), is much lar~r than the values obtained by otherfaces examined (Figs. 4-7). On the other hand, a decrease researchers for "smooth" PE surfaces, 94°-103° (58-60).in the receding contact angle was not observed when the These data indicate that incomplete wetting must also becontact angle was measured with the captive-bubble tech- considered together with the specific position of the three-nique (Figs. 4-7). A difference might be expected in the phase contact line in order to explain the behavior of suchtotal free energy for sessile drop and captive bubble due to rough hydrophobic surfaces.a difference between the liquid-air surface area for the drop Line tension contribution. A linear relationship betweenand bubble with the same base diameter and contact angle the cosine of the contact angle and the reciprocal of the drop(contact angle different from 90°). It was not the case for (bubble) base radius for rough solid surfaces follows fromsystems presented in Fig. 4 and Fig. 7. The water-air surface the theoretical dependence proposed in our previous contri-area for large drops and bubbles were almost the same for butions (10, 34):these systems (Fig. 4 and Fig. 7: the receding contact anglesare cl~se to W). These experimental data indicate that inter- cos ar == X( cos a. -~ ) [4]pretation of the contact angle/ drop (bubble) size relation- r'YLVship for rough surfaces may fail if based on simplified mod-els. Further, if the interpretation of the contact angle data with roughness ratiofrom Figs. 4- 7 is based only on such a simplified theoreticalmodel as expressed by Eq. [3] the advancing contact angle x = ~ = ! ~ 1should also be observed to increase with decreasing drop A L '

(bubble) volume. Such was the case for the roughened PTFEsurface when the advancing contact angle was measured where a and A are the actual and apparent solid-liquid in-with the captive-bubble technique (Fig. 7). Inverse correla- terfacial area, respectively; I and L are the actual and appar-tiODS were observed for other rough surfaces (see Figs. 4 ent lengths of the three-phase contact line, respectively; andand 6) and the advancing contact angle slightly decreased subscripts r and s correspond to rough and smooth surface,with decreasing drop (bubble) size. These experimental data respectively. Equation [4] is a modification of the well-clearly show that the interpretation of the contact angle/ known Wenzel equation (45, 50, 51), by the line-tensiondrop (bubble) size relationship for rough surfaces requires term ('YSLV/r'YLV).analysis of more sophisticated models than that described The above dependence, Eq. [4], predicts a straight lineby Eq. [3], and contortion of the liquid drop (gas bubble) relationship between cos a and 1/ r with a slope of x'YsLvlbase needs also to be included in this analysis. 'YLV' However, because of the small value expected for the

line tension (1012-10-8 JIm, see previous section of thisEntrapped gas. Fu~~r, it is importan.t to recOgnize that paper), it cannot affect such significant variation in contact

the contact angle for a ltqUid at a rough soltd surface depends angles for large drops (bubbles) as observed in Figs. 4-not only. on the degree of r~ug~e~s but also ~~ the surface 7 (especially those changes demonstrated for the recedingtexture, i.e., the shape and distnbution of aspenties (35, 49). contact angles). Finally, Eq. [4] does not take into consider-It is well known that the water does not penetrate a space ation metastable states and cannot be applied for compositebetween asperities of hydrophobic material (43, 46, 52). systems when gas is entrapped between asperities under theThe result of this behavior is a composite solid/liquid inter- liquid phase (experimental contact angle data in Figs. 5 andface which causes an increase in contact angle (composite 7 indicate that such phenomena cannot be neglected in oursolid/liquid interfaces were examined theoretically and ex- systems). Also, Eq. [4] does not apply for systems withperi mentally by Cassie and Baxter (53, 54) and recently by liquid tending to spread between the asperities due to theHe and Laskowski (55». The polymers used in this study, action of capillary forces (wicking effect).PE and PTFE, are hydrophobic, and incomplete penetration .of liquid between surface asperities was observed micro- Heterogeneous Solid Suifacescopically. As a consequence of such behavior the liquid Methylated quartz plates were used as model heteroge-was in contact with both surface asperities and air cavities. neous surfaces. The roughness of these quartz plates was

.I

..

..46 ORELICH. MILLER, AND GOOO

60 range of 1-7 mm drop base diameter. This change can be

0 -0 "." 0.-: ~ ...even more pronounced for smaller bubbles. For example,'"g; 50 0 @o cSb.~8J Fig. 10, which was prepared based on the experimental data

~40 000 0 from Refs. (33,34), shows the water contact angle values

! ~ co ~ v vf;~ -z ~ for methylated quartz plates when the bubble bas~ diam~ter

~ 30 .9 ~,~ was reduced below 1 mm (note that the dynamIc captlve-! U 0 0 bubble technique was used in those studies). As is evident,

~ 20 0 DO db 000 D=b I2J 0 lID C§J the contact angle decreases with a decrease in bubble size

8 0 and the magnitude of the change depends on the extent of

10 quartz methylation (surface heterogeneity).

.SD-Adv. 0 SD-Rec. 0 CB-Adv. .CB-Rec. v DCB The surface distribution of trimethylsilyl groups is be-~ 0 0 1 2 3 4 5 6 lieved to be nonuniform at least for surfaces with incomplete

.Drop (Bubble) Base Diameter [mm] methylation (33). The distribution and size of polar (uncov-

ered quartz) and nonpolar (methylated part of the quartz~ FIG. 9. The effect of drop (bubble) size on advancing (Adv.) and surface) patches could not be determined for the methylated

j receding (Rec.) contact angles for the air/water/methylated quartz system quartz plates and a detailed discussion of the experimental

as obtained with the static sessile-drop (SO), static captive-bubble (CB),j and dynamic captive-bubble (DCB) techniques. Quartz surface was methyl- data IS not pos.sIble. .As m the case of samples wIth rough

ated with chlorotrimethylsilane (TMCS) using I -5 X 10-6 M TMCS surfaces, the dIScussIon of contact angle data for heteroge-

solution in cyclohexane. Exposure time of quartz plate to TMCS solution neous surfac~s is limited to the identification of .possible

was 5 Inln. factors affecting the contact angle value for varymg drop

(bubble) size rather than quantitative interpretation.

J found with atomic force microscope to be small, with asper- Free energy barriers. Free energy barriers caused by

ity heights of less than 50 nm. Chlorotrimethylsilane was patches of varying hydrophobicity and size, and contortion

used for methylation of the quartz surface. The contact angle of the three-phase contact line, seem to be of particular

.data for two hydrophobic samples are presented in Figs. 8 importance for the interpretation of the contact angle data, and 9 (different times of methylation, 5 and 30 min, respec- in Figs. 8-10. A theoretical analysis of the free energy for

1 tively, were used for each quartz plate which allowed for three-phase systems with model heterogeneous solid sur-

J the preparation of samples with different degrees of surface faces showed existence of multiple energy minima which

; hydrophobization; note that methylated quartz surface in Fig. are believed to be responsible for the contact angle hysteresis

9, for the longer methylation time, appears to be more homo- ( 43, 47, 61-64 ). The energy barriers between adjacent min-

.geneous than that in Fig. 8). Experimental contact angle ima might also influence the contact angle variation with

I data demonstrate that the surface heterogeneity accounts for drop (bubble) volume, at least to a certain extent. With

, not only: (i) scatter in experimental data and (ii) contact

i angle hysteresis, but also (iii) the difference between ad-

.vancing and receding contact angles as determined with dif -80

i ferent techniques (sessile-drop or captive-bubble) and (iv) 8' ~o~~o. _o~ ~~o~

j the variation of contact angle with drop (bubble) volume. -c; 70 0.. -=--0.. .~... .

1 A significant difference of approximately 100 existed be- ~

tween receding contact angles as determined with the sessile- ;60. SD-Adv. 0 SD-Rec. 0 CB-Adv. .CB-Rec. V DCB

drop technique and those determined with the captive-bubble g> 50

technique, in the range 1- 5 mm drop (bubble) base diame- ~ v ~ y v ~". ..

ter. This variation was slightly reduced to 70_80 for drops ~ 40 .;V~ -.~."'o

and bubbles with 5-7 rom base diameter (Figs. 8 and 9). a Vo 00 0 cPo 000000 cPoCi:Jj Examination of larger drops (bubbles) was not possible due Co) 30 0 0

, to the small diameter (1 cm) of the quartz plates used in

I h d .20t ese stu Ies. 0 1 2 3 4 5 6 7

t The contact angle as determmed wIth\he dynamIc captlve- Drop (Bubble) Base Diameter [mm]

t bubble technique corresponded to the receding contact angle

, values as determined with the static captive-bubble tech- FIG. 10. The effect of drop (bubble) size on advancing (Adv.) and

t nique (see Figs. 8 and 9). A significant decrease of the receding (Rec.) contact angles for the air/water/~ethyla~ed quartz system

f d. I .h d .b bbl. as obtained with the static sessile-drop (SO), static captive-bubble (CB),, a vancmg contact ang e WIt ~creasmg u e sIze was and dynamic captive-bubble (DCB) techniques. Quartz surface was methyl-

t observed for the first sample (FIg. 8, more heterogeneous ated with chlorotrimethylsilane (TMCS) using I -5 X 10-6 M TMCS

i sample). Further, a small change in the receding contact solution in cyclohexane. Exposure time of quartz plate to TMCS solution

~ angle was observed for both systems (Figs. 8 and 9) in the was 30 min.

j

i

~

l~

.~

CaNT ACT ANGLE MEASUREMENTS 47 i,

regard to this concept, it is expected that the system may hydrop~ilic portion of the three-phaseremain in a metastable state as long as the energy barrier to contaminant. contact line

a lower energy state is higher than the internal energy ofthe system (water drop or air bubble at methylated quartzin our case). The total free energy of the liquid drop or gasbubble decreases with decreasing drop or bubble volumeand energy barriers become important system features for ALvldecreasing drop (bubble) volumes. For example, see ASLIRefs.( 43, 61) for the theoretical relationship describing thetotal free energy of a liquid drop on a smooth and heteroge-neous surface composed of alternating circular bands of dif-ferent surface energy. In this model, the total free energy(F) of a liquid drop depends on the drop size (drop base 82 < 81

radius, r) such that F (X rz. Thus, in the case of a smoothheterogeneous surface, the receding contact angle is ex- ~pected to decrease with decreasing drop (bubble) size for ri;small drops (bubbles) in which the internal energy is compa- 2

rable to the energy barriers of the heterogeneous surface. The rL --r2advancing contact angle should also be affected by energybarriers and should increase for smaller drops (bubbles). rL« IiHowever, as is shown in Fig. 9, a slight trend of decrease,for smaller drops, between the advancing contact angle and ~ ...<81<~2 ~ ..",ez<8t.- bubble size was found with the static captive-bubble tech- 81 ~

nique for methylated quartz plates. The contortion of the ~~I ~~three-phase contact line, which always appears for liquid at' '

a heterogeneous surface, additionally complicates the inter-pretation of the contact angle/bubble size relationship. FIG. 11. A large drop and a small drop at heterogeneous and smooth

solid surface. See text for details and discussion. ALv and ASL are theContortion of the three-phase contact line. After visual interfacial areas; the L, S, and V subscripts corresP<1nding to liquid, solid,

observations of water drops or air bubbles at the methylated and vaP<1r, respectively; e is the contact angle; r is the drop base radius;quartz surface it was found that the wetting line was highly the I and 2 subscripts corresP<1nd to a large and small drop, respectively.

irregular (contorted), especially when water was made torecede (a photograph of the three-phase contact line for the entire drop (bubble) per unit length of the three-phasewater at methylated quartz surface has been presented in contact line (15).Ref. 33). Spo~taneous jum~s of a segment of the three- As proposed by Good and Koo (15), the macroscopicphase contact lIne from one sIte of the heterogeneous surface contact angle is a function of drop (bubble) size when theonto another site were observed, indicating the existence of drop (bubble) base radius is comparable to the local contor-energetic barriers in the system. A highly irregular shape of tion of the three-phase contact line. This is illustrated in Fig.the water drop or air bubble base, especially for small drops 11. Because the radius of the drop base for a large drop (rl)(bubbles), significantly affected the contortion of the water- is much larger than the radius of the local contortion of theair interface in the vicinity of the solid-liquid-air contact three-phase contact line (rL)' rL ~ rl, the macroscopic con-Iine. The concept is illustrated in Fig. 11 and is similar to tact angle (el) differs from any local contact angle, eLl >that discussed with regard to a rough solid surface (Fig. 8). el > eLI, i.e., the contact angle which characterizes theBoth the three-phase contact line and the drop surface in the hydrophobic substrate and hydrophilic contaminants in Fig.vicinity of the three-phase contact line are contorted for a 11. The situation changes with decreasing drop volume andlarge drop and a small drop (Fig. 11). Of course the same the macroscopic contact angle for a small drop (ez) ap-effect appears for gas bubbles at heterogeneous surfaces. In proaches the smallest local contact angle (eLl), i.e., ap-some systems, the contortion of the drop (bubble) surface proaches the contact angle for hydrophilic spots, ez -+ eLl.may extend over the entire drop (bubble) volume, particu- In summary, this analysis predicts that the contact anglelarly for a small drop (bubble). It is expected that the ratio should decrease with decreasing drop size. Such contactbetween surface area for the liquid-gas (ALv) interface and angle/drop (bubble) size relationships were observed in oursurface area for the solid-liquid (ASL) interface may change systems (Figs. 9,10, and 12). However, a recent theoreticalwith drop size when contortion of the drop surface takes approach regarding the effect of contortion of the three-place. This may lead to an increase in the excess energy of phase contact line on contact angle hysteresis for varying

.

..48 DRELICH, MILLER, AND GOOD

50 cos 0 = flcos 01 + hCOS O2

"-"40 ( 1)~ 0 --(fI'YSLVI/(\ -h'YSLV2/(2) , [5]~ 0 0 Cb 0 0 0 0 'YLV

0 0.§?30 O~O 0I 0) co 0c: 00 ..". .

f ~ 20 ~ o ~ .where fI is the area fraction of the surface methylated with~ --~ vv v vvvvv~ v v contact angle 0\ andh is the area fraction of the uncovered

, c: ~ v V -&.00 quartz sullace With contact angle 2; 'YSLVI and 'YSLV2 are

U 10 the line tensions for the hydrophobic (methylated part ofi quartz) and hydrophilic (uncovered quartz) portions of thef 0 surface, respectively; /(\ and /(2 are the geodesic curvaturesI 0.01 B bbl B O~. [] 1 of the three-phase contact line associated with the hydropho-t u ease lameter mm bic and hydrophilic regions, respectively: K = 1/ p for a

~ FIG. 12. The effect of bubble size on contact angle for the air!water! liquid drop or gas bubble located at a smooth solid surfacej methylated quartz systems as obtained with the dynamic captive-bubble where p is the radius of curvature of the three-phase contact

I technique. Quartz surfaces were methylated with chlorotrimethylsilane line. Equation [5] is a modification of the Cassie equation

(TMCS) using I X 10-6-1 X 10-4 M TMCS solution in cyclohexane. (67) . th 1E .f I TMCS I . 15 30 . Th ' to mcorporate e me tension contribution to the anal-xposure time 0 quartz p ate to so ution was -min. e. ..

experimental data are from Refs (33, 34). YSiS of the wettIng properties of heterogeneous surfaces.The theoretical relationship, Eq. [5], predicts the effect

of the wetting perimeter shape on contact angle, but doesI drop volumes indicates that contact angles may either in- not predict the correlation between contact angle and drop~ crease or decrease with decreasing drop size (65). This is (bubble) size. It is believed that a contortion of the three-

due to a strong dependence of the number of energy barriers phase contact line can change with drop (bubble) base diam-4 with the drop volume (65). eter ( 1O, 68); however, these changes, if any, should rather! Also, nonuniform movement of the drop (bubble) base occur in a range of much smaller drops (bubbles) than exarn-i on the heterogeneous surface caused contortion of the three- ined in this contribution.j, phase contact line and the liquid-surface characteristic of

'i' the system in the vicinity of the three-phase contact line (a CONCLUSIONSratio between polar and nonpolar sites of methylated quartz

f surface per unit of drop (bubble) perimeter) could be Wetting characteristics of uniform thiol monolayers atI changed, especially for small drops (bubbles). In general, smooth gold surfaces, methylated quartz surfaces, and.when the front of a polar liquid recedes, there is a tendency roughened polymer surfaces (polyethylene and poly tetra-! for the liquid to stay at polar sites of the heterogeneous ftuoroethylene) are analyzed with the sessile-drop and cap-~ surface, due to stronger interactions between polar phases tive-bubble contact angle techniques. Agreement for advanc-, (liquid and solid) than between polar liquid and nonpolar ing contact angles, as well as for receding contact angles,j surface sites. For the case of the receding liquid front, the as determined with two different techniques, sessile-dropI area fraction of polar sites of solid surface per unit of drop and captive-bubble, was obtained for a close-to-ideal system,

(bubble) perimeter in the vicinity of the three-phase contact i.e., a freshly prepared self-assembled monolayer of dodeca-line exceeds the average area fraction of polar sites calcu- nethiol on a smooth, pure gold film. Increasing roughnesslated over the entire solid surface. As a consequence, the and heterogeneity of the solid surfaces caused differencesreceding contact angle is smaller than the contact angle value between the measured receding contact angles when deter-expected theoretically from an analysis of thermodynamics mined with different methods, sessile-drop or captive-bub-

, for the system. A reverse situation is for the advancing con- ble. Similar discrepancies between the two experimental1 tact angle and the contact angle value is. larger than an aver- techniques, but to a lesser extent, were observed for advanc-I age contact angle value expected theoretIcally for a heteroge- ing contact angles.I neous surface. There is, in general, ,tendency for the ad- The contact angle as measured for the air bubble/liquid/

vancing liquid front to locate at nonpolar sites of the solid system, where the air bubble was deposited onto theheterogeneous surface. solid surface with the dynamic captive-bubble technique (re-

i Line tension contribution. The contact angle for a liquid lease of gas bubble into the bulk liquid and transport to the1 drop at a heterogeneous surface, where contortion of the solid surface due to buoyancy) corresponded to the recedingI three-phase contact line appears, can be predicted from the contact angle as measured with the static captive-bubble~ theoretical relationship proposed in Refs. (1O, 34, 66). This technique for most of the systems examined. On the other~ relationship for methylated quartz surface is hand, when rough and heterogeneous solid surfaces werei

~

1

,.!~-

.-""".,

CONTACT ANGLE MEASUREMENTS 49 I~

used, intermediate contact angles (contact angles between REFERENCESadvancing and receding) were also observed. These experi-mental data emphasize a disadvantage of the dynamic tech- 1. Neumann, A. W., and Good, R. J., Surf Colloid Sci. 11,31 (1979).nique, for which it can be concluded that the contact angle 2. Mack, G. L., J. Phys. Chern. 40, 159 (1936). -cannot be uniquely defined when nonideal systems are exam- 3. Vesselovsky, W. S., and PeltZov, W. N., J. Phys. Chern. USSR 8,5ined with this technique. However, it must be remembered (1936).that a unique advantage of this technique is the ability to 4. Leja, J., ~,d Poling, G. .W., "~e~dings of the International Mineral

.Congress, p. 325. Institute of Mmmg and Metallurgy, London, 1960.examIne the contact angle/bubble (drop) size relationship 5. Johnson, R. E., Jr., J. Phys. Chern. 63, 1655 (1959).over a wide range of bubble (drop) volumes, from several 6. Collins, R. E., and ~ke, C. E., Trans. Faraday Soc. 55, 1602 (1959).micrometers to several millimeters in diameter (16, 17). 7. Kitchener, J. A., "Proceedings of the Third International Congress on

The effect of drop (bubble) size on advancing and reced- Surface Activity," Vol. 2, p. 426. Univ. of Mainz Press, Mainz, Ger-. 1 d ed s: 1 many, 1960.mg. contact ang es was emo~strat lor severa systems. 8. Goodrich, F. C., Surf Colloid Sci. 1, 1 (1969).ThIs phenomenon becomes an Important feature of the three- 9. Lucassen-Reynders, E. H., and Lucassen, J., in "The Scientific Basisphase systems when a solid surface exhibits nonideality; i.e., of Flotation" (K. J. Ives, Ed.), p. 79. Nijhoff, Lancaster, 1984.the solid surface is either rough or heterogeneous, or both. 10. Drelich, J., and Miller, J. D., Part. Sci. Technol. 10, 1 (1992).Metastable states, which are responsible for the contact angle 11. Gershfeld, N. L., and Good, R. J., J. Theor. Bioi. 17,246 (1967).hysteres 's al f ~ t th t t I /d (b bbl ) 12. Gaydos, J., and Neumann, A. W., J. Colloid Interface Sci. 120, 76

.I .' ma~ so a lec e co~ ac ang e rop u. e (1987).sIze relatIO~S~Ip. To support thIS statement a th~oretIcal 13. Li, D., and Neumany. A. W., Colloids Surf 43,307 (1990).model descnbmg the contact angle/drop (bubble) sIze rei a- 14. Janczuk, B., and Bialopiotrowicz, T., Polish J. Chern. 65,487 (1991).tionship is required. It should be remembered, in a formula- 15. Good, R. J., and Koo, M. N., J. Colloid Interface Sci. 71,283 (1979).tion of such theoretical relationship, that the solid surface 16. Drelich, J., Miller, J. D., and Hupka, J., J. Colloid Interface Sci. 155,h . d h . I .., h h 379(1993).eterogeneltyan roug ness cause megu antIes m t e s ape 17. Drelich, J., and Miller, J. D., J. Colloid Interface Sci. 164,252 (1994).

of the three-phase contact line, and these may affect a varia- 18. Harkins, W. D., J. Chern. Phys. 5, 135 (1937).tion of the internal free energy of the liquid drop (gas bub- 19. De Feijter, J. A., and Vrij, A., J. Electroanal. Chern. 37,9 (1972).ble) at such solid surfaces. 20. Rowlinson, J. S., and Widom, B., in "Molecular Theory of Capillar-

The experimental data presented show that surface ity," p. 240. Oxford Sci. Pub., New York, 1984.h d h t . af~ d th 1 /dr 21. Mingins, J., and Scheludko, A., J. Chern. Soc. Faraday Trans. 175, 1

roug ness an e erogenelty lecte e contact ang e op (1979).(bubble) size relationship. more for the receding contact 22. Schultze, H. J., "Physico-Chemical Processes in Flotation," p. 163,angle than for the advancing contact angle when systems 253. Elsevier, Oxford, 1984.with 1-7 mm drop (bubble) base diameters were examined. 23. Zorin, Z., Platikanov, D., and Kolarov, T., Colloids Surf 22, 147Also, experimental results clearly show that a slight variation (1987).. th d . t 1 I s: .11' 24. Kralchevsky, P. A., Nikolov, A. D., and Ivanov, I. B., J. Colloidmea vancmg contac ang e va ue over a lew lD1 Imeters Interface Sci. 112, 132 (1986).change in drop (bubble) base diameter does not quarantee 25. Ponter, A. B., and Boyes, A. P., Can. J. Chern. 50,2419 (1972).a high-quality surface state. Measurements of the receding 26. Boyes, A. P., and Ponter, A. B., J. Chern. Eng. Jpn. 7,314 (1974).contact angles should always be included with the advancing 27. Ponter, A. B., and Yekta-Fard, M., Colloid Polyrn. Sci. 263, 673contact angle measurements. This practice is strongly recom- (1985). .'

d d b s: .. f 1 /d 28. Yekta-Fard, M., and Ponter, A. B., J. Colloid Interface SCI. 126, 134men e elore any InterpretatIon 0 contact ang e rop (1988).(bubble) size relationship is undertaken; particularly in such 29. Yekta-Fard, M., and Ponter, A. B., J. Adhes. Sci. Technol. 6, 253cases where thermodynamic parameters like line tension are ( 1992).calculated from contact angle data. 30. Semiczuk-Szulc, S., Zesz. Nauk. Inst. Maszyn Przepl. 13, 1 (1977).

It is demonstrated in this contribution that the contact 31. Karnusewitz, H., and Possart, W.,lnt. J. Adhes. Adhes. 5,211 (1985).1 h ... fi 1 . th d (b bbl ) 32. Israel, S. C., Yang, w. C., Chae, C. H., and Wong, C., Polyrn. Prepr.

ang e ysteresls may vary sigm cant y WI rop u e 30,328 (1989).volume. In this regard, there is a need for examination of 33. Drelich, J., and Miller, J. D., Colloids Surf 69,35 (1992).the advancing and receding contact angles with varying drop 34. Drelich, J., Ph.D. thesis, University of Utah, Salt Lake City, 1993.(bubble) size whenever the sessile-drop and captive-bubble 35. Good, R. J., Surf Colloid Sci. 11, 1 (1979).techniques are used. Such an examination may be a way to 36. Lester,G. R., J. Colloid Sci. 16,315 (1961).

... d. th 1. f l 'd 37. Shanahan, M. E. R., J. Phys. DAppl. Phys. 20,945 (1987).obtaIn more InformatIon regar mg e qua Ity 0 a so I 38. Shanahan, M. E. R., Adhesion 14,71 (1989).surface. 39. Drelich, J., Miller, J.D., Kumar, A., and WlIitesides, G. M., Colloids

Surf A: Physicochern. Eng. Aspects 93,1 (1994).40. Troughton, E. B., Bain, C. D., WlIitesides, G. M., Nuzzo, R. G., Allara,

ACKNOWLEDGMENTS D. L., and Porter, M. D., Langrnuir 4,365 (1988).41. WlIitesides, G. M., and Laibinis, P. E., Langrnuir 6,87 (1990).42. Bain, C. D., Troughton, E. B., Tao, Y. T., Evall, J. E., WlIitesides,

This work was suppori,ed by Department of Energy Grant DE-FC2l- G. M., and Nuzzo, R. G., J. Arn. Chern. Soc. 111,321 (1989).89MC26268, and by National Science Foundation Grant CTS-92l542l. 43. Johnson, R. E., Jr., and Dettre, R. H., Surf Colloid Sci. 2,85 (1969).

.\: ..

..50 DRELICH, MILLER, AND GOOD

44. Guerra, 1. M., Srinivasarao, M., and Stein, R. S., Science 262, 1395 58. Dann, 1. R., J. Colloid Interface Sci. 32,302 (1970).(1993). 59. Fowkes, F. M., McCarthy, D. C., and Mostafa, M. A., J. Colloid

45. Good, R. J., J. Am. Chern. Soc. 74,5041 (1952). Interface Sci. 78,200 (1980).46. Johnson, E. I., Jr., and Dettre, R. H., Adv. Chern. Ser. 43, 112 ( 1964). 60. Shonohom, H., Nature 210, 896 ( 1966).47. Neumann, A. W., Adv. Colloid Interface Sci. 4, 105 (1974).48 Ei k 1 D Good R 1 dN A W 1 Cll .d ' ~ 61. Iohnson,R.E.,Ir.,andDettre,R.H.,J.Phys.Chem.68,1744(1964).

.c,.., ,.., an eumann, ..,. 0 01 Inte'Juce

Sci. 53,235 (1975). 62. Neumann, A. W., and Good, R.I., J. Colloid Interface Sci. 38, 34149. Huh, C., and Mason, S. G., J. Colloid Interface Sci. 60, II (1977). (1972).50. Wenzel, R. N., Ind. Eng. Chern. 28,988 (1936). 63. Schwartz, L. W., and Garoff, S., Langmuir 1, 219 (1985).51. Wenzel, R. N., J. Phys. Colloid Chern. 53, 1466 (1949). 64. Schwartz, L. W., and Garoff, S., J. Colloid Interface Sci. 106,42252. Bartell, F. E., and Shepard, 1. W., J. Phys. Chern. 57,211 (1953). (1985).53. Cassie, A. B. D., and Baxter, S., Trans. Faraday Soc. 40, 546 (1944). 65. Marmur, A., J. Colloid Interface Sci. 168,40 (1994).54. Baxter, S., and Cassie, A. B. D., J. Text. Inst. 36, T67 (1945). 66. Drelich, J., and Miller, J. D., Langmuir 9,619 (1993).55. He, Y. B., and Laskowski,J., Coal Prep. 10,19(1992). 67 C . A B D D .r:o --'- S 3 11(1948)56. Fox, H. W., and Zisman, W. A., J. Colloid Surf. 5,514 (1950). ..assle, , ISCUSS. raruuuy oc. , ...57. EI-Shimi, A., and Goddard, E. D., J. Colloid Interface Sci. 48, 242 68. Lt, D., Lrn, F. Y. H., and Neumann, A. W.., J. Colloid Interface SCI.

(1974). 142,224 (1991).

I

,

--