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Colloids and Surfaces A: Physicochemical and Engineering Aspects 156 (1999) 271 – 279 The relation between Young’s equilibrium contact angle and the hysteresis on rough paraffin wax surfaces H. Kamusewitz a, *, W. Possart b , D. Paul a a GKSS Research Center Geesthacht GmbH, Institute of Chemistry, Kantstrasse 55, D-14513 Teltow, Germany b Uni6ersity of the Saarland, Structure Research, Polymers, Interphases, POB 151 150, D-66041 Saarbru ¨cken, Germany Received 30 September 1998; accepted 5 January 1999 Abstract The influence of the suface roughness of paraffin wax surfaces on the static and dynamic contact angle hysteresis is investigated by means of the Wilhelmy method and water, ethylene glycol as well as ethanol as test liquids at 20°C in order to estimate the true Young’s equilibrium contact angles. These angles can be derived from the quasistatic contact angle hysteresis data as produced by roughness variatiom using the presented empirical model. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Dynamic contact angles; Equilibrium contact angle; Contact angle hysteresis; Paraffin wax www.elsevier.nl/locate/colsurfa 1. Introduction The famous Young’s equation presumes equi- librium wetting of an ideal solid which means that it is chemically homogeneous, rigid and flat as well as that the solid is not perturbed by adsorp- tion or by a chemical interaction with the wetting liquid [1]. However, a contact angle hysteresis Du is observed in almost all investigations on real solids instead of Young’s angle u e . The advancing angle u a is measured or calculated as upper value of the hysteresis and the receding angle u r is obtained as the lower limit. The hysteresis is given as Du =u a -u r . One of the important causes of this phenomenon is the roughness produced by corrugations of the solid surface. Further impor- tant reasons are the chemical heterogeneity and the molecular reorientation effects occurring in different surroundings. The influence of the sur- face roughness on the contact angle hysteresis can be isolated from the other factors by using a homogeneous solid where the molecular mobility does not result in changes of the surface state. A growing body of publications addresses the theoretical basis of the hysteresis on chemically homogeneous solids [2–6]. One of the most cited models is Wenzel’s ratio (defined as the ratio of the true surface area of the solid to the area apparent from the geometric dimensions of the solid sample). The papers [2–6] predict that two * Corresponding author. 0927-7757/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII:S0927-7757(99)00079-5

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Colloids and Surfaces

A: Physicochemical and Engineering Aspects 156 (1999) 271–279

The relation between Young’s equilibrium contact angle andthe hysteresis on rough paraffin wax surfaces

H. Kamusewitz a,*, W. Possart b, D. Paul a

a GKSS Research Center Geesthacht GmbH, Institute of Chemistry, Kantstrasse 55, D-14513 Teltow, Germanyb Uni6ersity of the Saarland, Structure Research, Polymers, Interphases, POB 151 150, D-66041 Saarbrucken, Germany

Received 30 September 1998; accepted 5 January 1999

Abstract

The influence of the suface roughness of paraffin wax surfaces on the static and dynamic contact angle hysteresisis investigated by means of the Wilhelmy method and water, ethylene glycol as well as ethanol as test liquids at 20°Cin order to estimate the true Young’s equilibrium contact angles. These angles can be derived from the quasistaticcontact angle hysteresis data as produced by roughness variatiom using the presented empirical model. © 1999Elsevier Science B.V. All rights reserved.

Keywords: Dynamic contact angles; Equilibrium contact angle; Contact angle hysteresis; Paraffin wax

www.elsevier.nl/locate/colsurfa

1. Introduction

The famous Young’s equation presumes equi-librium wetting of an ideal solid which means thatit is chemically homogeneous, rigid and flat aswell as that the solid is not perturbed by adsorp-tion or by a chemical interaction with the wettingliquid [1]. However, a contact angle hysteresis Du

is observed in almost all investigations on realsolids instead of Young’s angle ue. The advancingangle ua is measured or calculated as upper valueof the hysteresis and the receding angle ur isobtained as the lower limit. The hysteresis is givenas Du=ua−ur. One of the important causes of

this phenomenon is the roughness produced bycorrugations of the solid surface. Further impor-tant reasons are the chemical heterogeneity andthe molecular reorientation effects occurring indifferent surroundings. The influence of the sur-face roughness on the contact angle hysteresis canbe isolated from the other factors by using ahomogeneous solid where the molecular mobilitydoes not result in changes of the surface state.

A growing body of publications addresses thetheoretical basis of the hysteresis on chemicallyhomogeneous solids [2–6]. One of the most citedmodels is Wenzel’s ratio (defined as the ratio ofthe true surface area of the solid to the areaapparent from the geometric dimensions of thesolid sample). The papers [2–6] predict that two* Corresponding author.

0927-7757/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.

PII: S0927 -7757 (99 )00079 -5

H. Kamusewitz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 156 (1999) 271–279272

different effects occur in wetting experiments on arough and chemically homogeneous solid. Thefirst is called the barrier effect, i.e. that the hys-teresis increases with growing roughness which isrelated to higher asperities. Moreover, ua in-creases by the same amount as ur decreases withgrowing roughness due to the barrier effect. Thatmeans that a pure barrier effect would give thearithmetic mean

ue=0.5(ua+ur) (1)

as the relationship between ue and the two accessi-ble contact angles. The second effect is the capil-lary attraction or capillary depression of groovesin the surface [4,5,7]. As a result, the relationshipbetween the hysteresis and Young’s angle changesat ue=90°. For ueB90°, each liquid will wet therough surface of a given solid better than thecorresponding smooth surface. For ue\90° onthe other hand, the wettability of such liquids onthe rough solid is worse than on the ideallysmooth solid surface. According to the literaturee.g. [4,5,7], the capillarity also invalidates the ap-plicability of Eq. (1). For ue\90°, the capillaritycauses an increase of both ua and ur with growingroughness as compared with values expected forthe pure barrier effect. For ueB90°, the inversesituation appears: ua and ur are smaller than therespective values for the barrier effect. In otherwords, the arithmetic mean 0.5(ua+ur) is nolonger a constant but it increases (for ue\90°) ordecreases (for ueB90°) with increasing surfaceroughness if capillarity is acting. Only for ue=90°, the capillarity has no effect and the arith-metic mean becomes independent of theroughness. Various experimental studies e.g. [7,8]depict these influences qualitatively in relation toWenzel’s ratio which, however can not be de-tected exactly.

For various test liquids, the advancing andreceding angles are presented as a function ofroughness in order to estimate the true Young’sequilibrium contact angles for the paraffin/liquid/vapour combinations. These quantities are re-quired for describing the relationship betweenYoung’s equilibrium contact angle ue and thediscussed hysteresis Du.

2. Review of published data

Paraffin wax is widely investigated as a modelsubstance in the literature but the contact angledata scatter considerably even with water as thetest liquid. Fox and Zisman [9] report ua=108°for a paraffin wax with a melting range of 68–72°C. Bosanquet and Hartley [10] get ua=106°(at 14°C) and Strom [11] found ua in the range of103.0–108.5°. Later, Zisman [12] stated that purewater on paraffin provides an advancing contactangle between 105 and 110° with a ‘smooth’ sur-face while surface roughening results in anglesgreater than 110°. Values up to 140° have beenobserved. Wenzel [2] found 109BuaB112° oncrystalline and amorphous kinds of paraffin wax.Neumann [13] calculated ua=114° on freshly pre-pared paraffin wax surfaces with two differentmethods. An ageing effect was observed for thesesurfaces during exposure to air. After 1 and 16 h,the ua-data increased to 118.7 and 123.0°, respec-tively. Static advancing and receding angles ob-served with water normally give a hysteresis Du ofless than 15° on relatively smooth paraffin waxprepared by different techniques. For example,Dettre and Johnson [7] achieved Du=7° by press-ing the softened wax on a glass microscope slide.With the same technique, Bartell and Shepard [15]observed Du=11°. Ray and Bartell [17] obtainedno hysteresis on smooth surfaces of purifiedparaffin wax. Wolfram [18] used a polished filmobtained from a molten paraffin wax (meltingrange 56–58°C) and measured Du=13.5°.Buzagh and Wolfram [19] found Du=8° on aparaffin wax film cast from a solution. Ablett [20]prepared special paraffin wax surfaces where thehysteresis was negligibly small.

Bartell and Shepard [14–16] detected ua- andur-data for a set of liquids on paraffin wax withvarying model surfaces consisting of pyramids.The analysis of these data shows that both con-tact angles depend in a different way on theroughness of these model surfaces. For example,the water advancing contact angles on paraffinincrease strongly with increasing roughness by 50°(from 110 to 160°) while the corresponding reced-ing angles decrease moderately only by 5° (from99 to 94°). For ethylene glycol, the advancing

H. Kamusewitz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 156 (1999) 271–279 273

angles increase by 39° (from 81 to 120°) withincreasing roughness while the corresponding re-ceding angles decrease by 57° (from 74 to 17°).

In [21] we proposed a quantitative empiricalapproach that describes such dependencies onroughness

ua(Du)=ue−Aa·Du (2)

ur(Du)=ue−Ar·Du (3)

For each test liquid, these linear equations yieldthe slopes Aa and Ar as well as the correspondingue-value which is found as the intersection of bothstraight lines with the ordinate in a plot of ua andur over Du. The application of Eqs. (2) and (3) onthe data presented by Bartell and Shepard [14–16]shows clearly that not only ue but also Aa and Ar

depend on the system used for the investigation.For example, the system paraffin/water providesAa=0.86, Ar= −0.14 and ue=102.6° whereasparaffin/ethylene glycol results in Aa=0.38, Ar=−0.62 and ue=81.3°.

In [14–16], the inclusion of air bubbles beneaththe test liquid between sufficiently large asperitieson the model surface is discussed as a possiblecomplication of the contact angle determination.Dettre and Johnson [7] denote such systems ascomposite surfaces similar to those observed byCassie and Baxter [22] on paraffin coated wiregrids. The work of Dettre and Johnson [7] pro-vides some hint on the roughness scale that maycause a composite surface. They produced rough-ness elements in the micrometer range on paraffinwax and found for the samples with mediumroughness a collapse of the hysteresis and contactangles up to 160° for the largest roughness both inwetting and dewetting experiments with water [7].Obviously, water completely avoids the valleys ofthe profile above a critical roughness.

This work concerns with the characterization ofnon-composite paraffin wax surfaces. Therefore, apossibility is required to identify a composite sur-face in the experiment although the smallest va-pour bubbles may be not visible. As the Wilhelmyexperiment registers also the buoyancy of theimmersed part of the sample, entrapped air willproduce additional buoyancy which is indicated inthe tensiogram by a change of the curve slopes.

Hence, a comparison of Wilhelmy experiments on‘smooth’ and rough solid surfaces can be used toidentify air trapping.

3. Experimental

The measurements were performed with theWilhelmy balance for both the characterization ofthe liquids and the solids using the digital ten-siometer KC 14, the original glass beaker, and thesoftware provided by Kruss, Hamburg. The theo-retical background of the Wilhelmy experimentand the calculation of the contact angles is de-scribed in detail in [23,24].

The interfacial tensions of the test liquids inpresence of their own saturated vapour phasewere obtained with a freshly annealed platinumplate at 20°C as a function of time just before thecontact angles were determined. This way, ageingeffects of the liquid are registered. Pure deionizedwater (gw,v=72,7 mN/m90.3 mN/m), diethyleneglycol (supplied by Merck, degree of purification:‘reinst’, geg,v=48.2 mN/m90.5 mN/m) andethanol (supplier: Merck, degree of purification:‘reinst’, ge,v=22.6 mN/m90.5 mN/m) served asthe test liquids. In the subsequent wetting anddewetting experiments, deviations from the initialvalue of within three measuring cycles are ac-cepted as long as they are below 1 mN/m.

The paraffin surfaces were prepared on thesurface of polypropylene tubes with an outer di-ameter of 2.38 mm. Such tubes were dippedquickly into molten paraffin wax for three timesafter short waiting periods. The three wax materi-als possess different molecular weights and solid-ify at temperatures of Tsp=42–44°C (Merck),57–60°C (Merck) and 68–74°C (Fluka), respec-tively. The paraffin fills the polypropylene tubescompletely and coats their surface with a layer ofconstant thickness (about 0.15 mm as measuredby an optomechanical system). By this means,reproducible paraffin wax layers with a verysmooth surface are obtained. These samples pro-vided the smallest hysteresis values in the wettingexperiments. Then, such samples were roughenedby contacting the rotating tube gently with differ-ent brushes, soft textiles or tissues in order to get

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surfaces with varying random roughness. As abra-sion was avoided the macroscopic thickness of theparaffin layers did not change remarkably. Thesmooth and the roughened samples were charac-terized within 1 h after the last step ofpreparation.

The dynamic contact angle hysteresis was deter-mined at 20°C for each paraffin surface and threewetting/dewetting cycles using a speed of 2 mm/min. The maximum immersion depth was 12 mmbut only the data between 1 and 12 mm wereincluded in the calculation of the contact angles.Therefore the data points of both the wetting andthe dewetting parts of the cycles were fitted bystraight lines and extrapolated to zero immersiondepth. Fig. 1 provides a typical tensiogram asmeasured for the system paraffin wax/water/va-pour with medium surface roughness. It will dis-cussed in more detail in Section 4.

As the equilibrium contact angle ue is neededfor the Young equation it has to be checkedwhether there is a difference between the dynamicand the static data for the contact angles and thehysteresis. Therefore, the motion of the samplewas stopped several times during dipping andwithdrawal of samples with varying roughnessand different liquids. Then, the change of force as

a function of time was recorded. The static anglewas calculated after the equilibration. As a result,the static contact angle hysteresis was obtainedfor the equilibrium of wetting and dewetting atthe given surface with the chosen liquid.

4. Results and discussion

Fig. 1 shows the original data of a typicaltensiogram for the system water/paraffin wax withmedium surface roughness at 20°C including threecycles with 12 mm maximum immersion depth.The two straight lines are obtained by linearregression with more than 120 data points perdirection. The slope Am reflects the change ofbuoyancy with immersion depth. Therefore, Am isexpected to be constant for a given sample. This isthe case in Fig. 1 where Am= −0.005 with corre-lation coefficients of r= −0.995 and r=−0.989 for wetting and dewetting, respectively.Lower Am during wetting and dewetting indicatethat the surface relief entraps air bubbles. Thisway, composite surfaces can be identified andsuch data are excluded from the following discus-sion. From Fig. 1, the calculation provides dy-namic contact angles of ua=116.392° and

Fig. 1. Tensiogram for three wetting/dewetting cycles for the system paraffin wax/water with medium roughness of the paraffinsurface.

H. Kamusewitz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 156 (1999) 271–279 275

Fig. 2. Advancing and receding contact angles versus thehysteresis for the system paraffin wax/water at 20°C. Plots arefitted by linear regressions. Tsp=43.0°C.

Note that the liquid, the solid, the surface profile,the temperature and the immersion speed mayinfluence the range of such equality between dy-namic and static contact angles.

The Fig. 2 presents the plots of the dynamicwater contact angles as a function of the dynamichysteresis for one of the three paraffin waxes withvaried surface roughness. The paraffin wax withthe lowest solidification point was most suitablefor preparing a broad range of surface roughness.Therefore, the smallest (3.6°) and the largest hys-teresis values (61°) were observed with this mate-rial and the preparation technique describedabove. The roughness preparation is reproduciblebut not as feasible with the two paraffin waxes ofhigher solidification points.

According to Eqs. (2) and (3) the data points inFig. 2 are fitted by straight lines and ue is calcu-lated. Table 1 summarizes the results for all threewaxes and compares them with the ue-valuederived from the data by Bartell and Shepard [14]using the same mathematical procedure.

Our contact angle data (Table 1, columns 2–4)provide an equal Young’s thermodynamic equi-librium contact angle of ue=103.090.4° for thethree paraffin waxes, well within the scatter ofmeasurement. The literature data [14] also yieldthe same ue-value within experimental error. Thisresult confirms the presumption that the paraffinsform surfaces which are stable under wettingconditions.

Further, Table 1 reveals considerable variationsfor both slopes Aa and Ar. At least in part, thismust be attributed to some variation in thestochastic surface profiles during preparation even

ur=92.193° and hence a dynamic contact anglehysteresis of Du=24.295°.

The static contact angle data and the statichysteresis were obtained after a waiting period atthe end of the wetting and the dewetting modes,respectively. For example, on the roughest sam-ples the advancing water contact angle decreasesby 1° and the receding angle increases up to 4°after 15 min. However, no difference is observedbetween dynamic and static angles for surfaceswith lower roughness and dynamic hysteresis val-ues of less than about 10°. Hence, the followingconsiderations are generally based on these dy-namic measurements using the speed 2 mm/min.

Table 1Young’s equilibrium contact angles ue, the slopes (Aa, Ar) and the linear regression coefficients r for the wetting and dewetting ofthree different paraffin waxes as well as for literature data [14] for a paraffin (last column)

Paraffin/Water Bartell et al. [14]Tsp=42–44°C Tsp=57–60°C Tsp=68–74°Csamples

Wetting Dewetting Wetting WettingDewetting DewettingWettingDewetting

16 21 21 12 12 18 1816103.4 102.7ue 103.0103.4 103.0 102.8 102.6 102.6−0.3343 0.5853 −0.4161 0.6172A −0.37440.6665 0.8606 −0.1393

−0.56820.9735−0.91580.9158−0.88240.9779 0.9318r −0.9149

H. Kamusewitz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 156 (1999) 271–279276

Fig. 3. Comparison of literature data [15] (+ , × ) and mea-sured data (�, �) for the advancing and receding contactangles as a function of the hysteresis for the system paraffinwax/ethylene glycol at 20°C. The plot includes the data fordifferent waxes.

and Ar= −0.6218 (r= −0.9891). As for water,the sets of experimental data from different sam-ples yield the same ue-value. This can be consid-ered as a strong support for the suitability of theour method for determining ue on homogeneousrough solids. Moreover, Bartell and Shepard [14–16] used the static sessile drop method while weutilized the Wilhelmy method in the dynamicregime. Since the ue-values are the same for bothtechniques we conclude that the dynamics of theliquid menisci are not important in our case. Thissupports to some extent the opinion of Morrowand Nguyen [25] that dynamic wetting experi-ments on both rough and smooth low-energysurfaces essentially do not depend on the velocityof the liquid front in the low speed range. Now,the capillarity produces AaB0.5 and ArB−0.5since ue=82.1° B90°. Again, the arithmeticmean does not give ue.

With ethanol, a liquid was found which meetsapproximately the special case ua=ue of Eq. (2)on the paraffin wax surfaces with varying rough-ness (see Fig. 4). The linear regressions yieldue=3392° and the slopes Aa=0.011 (r=0.9651) as well as Ar= −0.987 (r=0.9858). Wenote that the capillarity for ethanol on rough

for our samples and obviously for the samplesused in [14]. The inclusion of air bubbles can beexcluded for our data while it may have occurredin the experiments in [14]. The comparison of thecorrelation coefficients for the wetting and thedewetting curves shows that the fits for the wet-ting data are better than for the dewetting results.This is the consequence of the different scatter ofthe advancing and the receding angle mentionedabove.

According to Section 1, a ue=90° will lead toAa=0.5 and Ar= −0.5 in this case of no capil-larity since ue=0.5(ua+ur) is possible only forthese slopes. The data in Table 1 confirm forue=103\90° that Aa\0.5 and Ar\−0.5.These findings reveal that ue cannot be calculatedsimply as the arithmetic mean of the ua- andur-data as it is proposed in the literaturesometimes.

Fig. 3 depicts the contact angle data obtainedwith ethylene glycol on the three paraffin waxes aswell as the data from [15]. As expected from thefindings with water there are no significant differ-ences in the wetting behaviour of the materials.The linear regressions according to Eqs. (2) and(3) provide ue=82.1°, Aa=0.3781 (r=0.9713)

Fig. 4. Advancing and receding contact angles as a function ofthe hysteresis for the system paraffin wax/ethanol at 20°C. Thelines are obtained by linear regressions. The plot includes thethree waxes with different Tsp.

H. Kamusewitz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 156 (1999) 271–279 277

Fig. 5. Girifalco–Good diagram for the calculated Young’sangle (1) and the advancing (2) and receding angles (3) mea-sured at a hysteresis of 20°.

as well as the coincidence of our contact angledata for ethylene glycol with the static valuespublished by Bartell and Shepard [15] for thesame system (see. Fig. 3) support the expectationthat the derived ue-data are at least approximatelyequal to the corresponding Young’s equilibriumcontact angles.

Further, the well-known Girifalco–Good con-cept [26] can be used to test in an independentand more direct way whether the deduced ue-dataare genuine thermodynamic equilibrium contactangles. In the concept, the contact angles aredepicted in a (cos ue; g l,v

−0.5)-plot for various testliquids on a solid (see Fig. 5). A straight line hasto be found in case that equilibrium contact an-gles are used and the interaction parameter Fsl isthe same for all liquids. Now, this line has tocross the ordinate at −1. In Fig. 5, curve 1belongs to the ue-data which we deduced for thethree liquids under investigation. The fittedstraight line does not meet the ordinate exactly at−1. This could be a result of a variation in Fsl

which depends on the polarity of the liquids. Thedashed curve 2 in Fig. 5 is found for a set ofadvancing angles that corresponds to a hysteresisof 20° whereas the curve 3 belongs to the recedingangles, respectively. Obviously, the deduced ue-

paraffin wax surfaces influences both angles veryintensively. The increase of the advancing anglewith roughness as expected due to the barriereffect is now completely compensated by the cap-illarity of the rough surface. It seems possible touse this liquid as a probe which provides Young’sangle directly from the wetting mode withoutdepending on the roughness of the paraffin waxsurface.

Of course, additional evidence is required toshow that the described method and the dynamiccontact angle determinations really provideYoung’s equilibrium angle by the linear fits ac-cording to Eqs. (2) and (3). The utilized speed of2 mm/min is responsible for a stationary non-equilibrium stage during the whole measurement.As noted above, this results in time dependentangles on the roughest paraffin wax surfaces. Thelargest observed change was up to 4° (found withwater during the dewetting mode). On the otherhand, even lower speeds consume more measuringtime (with 2 mm/min, three cycles take about 35min). In that case, the above discussed ageingeffect observed by Neumann [13] could change theproperties of the system remarkably. The appliedspeed seems to be a suitable compromise there-fore. The observation of very small hysteresisvalues on relatively smooth samples (around 4°)

Fig. 6. Visualization of the influence of the surface capillarityon the wetting properties of rough paraffin wax. At the point(0.5; 90°), the capillarity effect is inactive.

H. Kamusewitz et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 156 (1999) 271–279278

data meet the expectations of the Girifalco–Good theory better than the advancing angles.

Finally, we see that the slopes Aa decreasewith ue for the considered liquids in the se-quence water, ethylene glycol and ethanol onparaffin wax of different roughness (compareFigs. 2–4). In Fig. 6, the values for Aa are plot-ted versus ue and the point (Aa=0.5; ue=90°)is added where the capillarity effect is absent.More or less accidentally, these four points fitwell to a straight line. Furthermore, the curvepresumes that systems should exist where AaB0, e.g. that the advancing angle decrease withthe increase of the surface roughness. It is atask for future experimental work to find such asystem.

5. Conclusions

For paraffin wax and some liquids as exam-ple, it is demonstrated that the Young equi-librium contact angles can be derived to a goodapproximation from the quasistatic contact an-gle hysteresis data as produced by roughnessvariation (4BDuB61°) and from the modelEqs. (2) and (3). The ue-values for differentparaffin waxes by means of water are equalwithin the accuracy of the contact angle deter-mination by the Wilhelmy method.

The capillary depression of the solid surface isresponsible for the increase of advancing andreceding water contact angles relative to whatone would expect as result of the barrier effect.With ethylene glycol the capillary attraction pro-duces advancing and receding angles which aretoo low compared to barrier effect. In the sys-tem paraffin/ethanol, the advancing angle evendoes not depend on the roughness in the investi-gated range due to the action of capillarity.

Acknowledgements

The authors gratefully acknowledge MsYvonne Fritzsche for sample preparation andcontact angle determinations.

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