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Colloids and Surfaces A: Physicochem. Eng. Aspects 459 (2014) 128–135

Contents lists available at ScienceDirect

Colloids and Surfaces A: Physicochemical andEngineering Aspects

j ourna l h om epa ge: www.elsev ier .com/ locate /co lsur fa

icro and nano bubbles on polystyrene film/water interface

ayong Lia,b,∗, Xuezeng Zhaoa,∗∗

School of Mechanical and Electrical Engineering, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Mechanical Engineering, Heilongjiang University of Science and Technology, Harbin 150022, China

i g h l i g h t s

Big micro surface bubbles wereimaged on PS film with AFM.The influence of surface roughness onsurface bubbles was studied.Size dependence of the contact anglewas investigated in a larger size scale.The effect of line tension on surfacebubbles was analyzed.

g r a p h i c a l a b s t r a c t

r t i c l e i n f o

rticle history:eceived 11 February 2014eceived in revised form 7 June 2014ccepted 11 June 2014vailable online 8 July 2014

eywords:urface nanobubblesontact angleize dependence

a b s t r a c t

Surface bubbles at polystyrene (PS) film/water interface were imaged using the atomic force microscope(AFM), the surface roughness ranged from 0.58 nm to 3.36 nm in scan area of 5 �m2. Big microbubble witha lateral size up to 13 �m and a height up to 400 nm was reported. The possible reasons for nucleationof big microbubbles were investigated and found that surface roughness and surface properties play asignificant role. Further, we focused on the problem “how does the contact angle (measured through air)rely on the bubble size” in a lateral size of 200 nm to 13 �m, which is the largest size scale for surfacebubbles found so far. It was found that the dependence of contact angle on lateral size �(2r) and height�(h) is linear for bubbles on smooth substrates, but nonlinear and even keep constant with the increase ofbubble size for bubbles on rough substrates. While studying the dependence of contact angle on curvature

tomic force microscope (AFM) radius �(Rc), an inversion in direction between the bubbles in different size scale was found. The resultsobtained were in close resemblance with the results of other studies. The line tension of surface bubbleson the seven PS substrates in our experiments was calculated and all of the seven line tension values arenegative (the average line tension in this study was � ≈ −1.07 nN), which should be responsible for theanomalous low contact angle and the size-dependence of the surface bubbles.

. Introduction

In recent decade, one of significant discoveries in interfacialhysics is nanobubbles, which are micro/nano-scopic gaseousomains that form at the interface between solid and liquid. From

∗ Corresponding author at: School of Mechanical and Electrical Engineering,arbin Institute of Technology, Harbin 150001, China. Tel.: +86 13945170437.

∗∗ Corresponding author.E-mail addresses: lidayong 78@163.com (D. Li), Zhaoxz@hit.edu.cn (X. Zhao).

ttp://dx.doi.org/10.1016/j.colsurfa.2014.06.022927-7757/© 2014 Elsevier B.V. All rights reserved.

© 2014 Elsevier B.V. All rights reserved.

the year 2000, nanobubbles have been imaged and studied byatomic force microscope (AFM) [1–16] and other measuring tech-niques such as spectroscopy technique [17] (most recently throughdirect optical visualization [18,19]), rapid cryofixation technique[20] and quartz crystal microbalances technique [21,22]. Studiesshow that surface bubbles appear with the following features:(1) typical spherical cap shaped [7,12,20,23], (2) typical heights

and curvature radii of 10–100 nm and 100–2000 nm [5,12,23]respectively, (3) the contact angle (measured through air) is muchsmaller than that of macroscopic bubbles [7,24–27], (4) abnormallongevity for several days [1,2,17], (5) two or more bubbles close

D. Li, X. Zhao / Colloids and Surfaces A: Physicochem. Eng. Aspects 459 (2014) 128–135 129

Table 1Summary of studies on the dependence of contact angle on the bubble size.

Substrate Gas type RMS roughness Bubble size Tip correction Ref.

HOPG Air 0.2–0.3 nm0.6–2.6 nm

Rc ∼250 nm Yes [7]

HOPG Air 0.7 nm Rc ∼2000 nm Yes [5]HOPG H2; air Rc ∼1800 nm No [35]Gold-ODT

Gold-MHDAAir Rc ∼1200 nm Yes [38]

Si-PFDCS Methane; nitrogen; oxygen 0.4 nm Rc ∼3000 nm Yes [37]Au (1 1 1) Air 0.2 nm r ∼100 nm Yes [36]Si-TMCS Air 2.7 nm 2r ∼800 nm No [31]

S thylchlorosilane; ODT, octadecanethiol; MHDA, 16-mercaptohexadecanoic acid.

td[

cHoabatnaa

cscttdscihcbcvaiLstcrsalibmnss

tbesb

ubstrate abbreviations: PS, polystyrene; PFDCS, 1H,1H,2H,2H-perfluorodecyl-dime

o each other can emerge into a big one [28–31], (6) disappear inegassed water and reappear when the liquid is exposed to air5,6,32,33].

The studies on the properties, influence factors and appli-ations of nanobubbles have been developed deeply [9,10,34].owever, the stability (anomalous longevity) and the contact anglef nanobubbles are still open questions. In the conventional view, as

material property, the contact angle of macroscale bubbles shoulde substrate dependent. But AFM studies [7] show that the contactngle of nanoscale bubbles (measured through air) is much lowerhan that of macroscale bubbles. Thus one would expect that theanoscopic contact angle will be size-dependent, i.e., the contactngle of nanobubbles will increase with the increase of bubble sizend will approach the macroscopic one for large enough bubbles.

So far, many efforts have been made to study the dependence ofontact angle on the size of surface bubbles [5,7,31,35–38]. Table 1hows a brief summary of studies regarding the dependence ofontact angle on the bubble size. First, for the dependence of con-act angle on curvature radius (�(Rc)), Borkent et al. [7] concludedhat contact angle (measured through water, before tip correction)ecreases with an increase of the curvature radius of bubbles. Butuch a dependence changes dramatically after tip correction: theontact angle keeps constant within the experimental error. Sim-larly, other studies have reported that the contact angle on theydrophobic surfaces does not change with radius [5,35,38] whilehanges slightly on the hydrophilic surface [38]. However, Van Lim-eek [37] investigated 7 different types of gas, and found that theontact angle (measured through water) increased with the cur-ature radius of nanobubbles for all gas types they studied, whichre opposite to the results of Borkent. In addition, a recent numer-cal study of Grosfils [39] validated the gas-dependency results ofimbeek. Secondly, for the dependence of contact angle on lateralize (�(2r)), Kameda and Nakabayashi [36] found that the con-act angle increased with the increase in the radius of three-phaseontact line (when lateral size ∼100 nm), which agrees with theesults of Yang et al. [31]. In contrast, for the bubbles in smallerize range (lateral size ∼20 nm), an adverse trend was obtained,nd a probable reason for this was thought to be the effect ofine tension [36]. The previous studies discussed above show thatt is still undefined whether the contact angle of surface bub-les is size-dependent or not. In addition, it should be noted thatost of the previous works focused on the surface bubbles with

anoscale (Table 1). So it is significant to investigate the relation-hip between the contact angle and the bubble size in large sizecale.

The line tension is usually taken into account in the study ofhe relationship between the size and the contact angle of surface

ubbles [31,33,36,37]. The line tension was defined as the excessnergy per unit length of the three-phase contact line [40]. Theources of the excess energy of the contact line were thought toe originated from both the changes in the local interfacial tension

Fig. 1. The sketch of the effect of line tension on the contact angle of surface bubbles.

caused by the unsaturated molecular interactions in the transitionzone and also from the local interfacial deformations in this zonecaused by the surface forces [40]. The effect of line tension willlead to a reduced contact angle of surface bubbles in nanoscale ascompared with the macroscopic contact angle in the transition zone[40], as can be seen in Fig. 1.

The difference between the nanoscopic and macroscopic con-tact angle which is linked to the effect of line tension can also beexplained by the modified Young’s equation [31,41], that is

cos � = cos �Y − �

�lgr(1)

where �Y is Young contact angle, �lg is the liquid–gas surface ten-sion, r is contact line radius which is equal to the reciprocal of thegeodesic curvature and � is the line tension. The range of Youngcontact angle is less than 90◦ measured through air for the bubblesformed on the hydrophobic substrates [7], so cos �Y > 0. If the signof � is negative, together with positive surface tension �lg and con-tact line radius r, then the contact angle � calculated by Eq. (1) willbe a reduced one as compared to the Young contact angle �Y. Thismeans that the negative line tension should be responsible for theanomalously low contact angle. On the basis of the Laplace–Young’sequation, the smaller contact angle means the lower inner pressureof the surface bubbles with the same base radius and thus meansa longer lifetime. At the same time, the negative line tension cancontribute to the three phase contact line pinning by balancing thesurface tension. The pinned contact line which has been provedin experimental [30] and theoretical [42] studies can limit the gas

diffusion through the water and thus stabilize the surface bubbles.The value of line tension of surface bubbles calculated in most ofthe previous studies was negative [31,33,37]. Although Kameda andNakabayashi [36] calculated a positive line tension for bubbles with

130 D. Li, X. Zhao / Colloids and Surfaces A: Physicochem. Eng. Aspects 459 (2014) 128–135

Table 2Root-mean-square (RMS) roughness of seven different substrates.

Substrate 1 2 3 4 5 6 7

RMS (nm) 0.58 0.72 1.14 1.73 2.67 3.01 3.16Scan area (�m2) 5 5 5 5 5 5 5Speed (rpm) 5000 4000 3000 5000 4000 3000 3000Spin coater a a a b b b b

Sso

lpwfctscr

P3o3mtsideeg

2

2

bt4s(v(cBwgabQ5loi

2

Zciic

pin coater a (TA-280, China): the wafer was held on a vacuum chuck by a vacuumuction force when spin coating; Spin coater b (TB-610, China), the wafer was fixedn a holder with spring clamps when spin coating.

ateral size less than 20 nm, which is consistent with Li’s theoreticalrediction [43], i.e., the line tension should be positive for a dropith the radius of contact line approaching to zero. When the sur-

ace bubbles have the lateral size larger than 20 nm, the line tensionalculated in Kameda’s work changes to be negative. Consideringhe lateral size of surface bubbles imaged in most of the previoustudies were always less than 2 �m. Therefore, it is also signifi-ant to investigate whether the line tension of surface bubbles canemain negative for bubbles in large size scale or not.

In this work, we investigated surface bubbles formed onolystyrene (PS) films with a roughness range from 0.58 nm to.36 nm, in water by using AFM. The big microbubbles were imagedn the rougher substrates with surface roughness of 3.11 nm and.36 nm. The possible nucleation reasons and features of the bigicrobubbles were investigated. We have also addressed the ques-

ion “How does the contact angle depend on the surface bubbleize” in a larger bubble size scale (200 nm to 13 �m), includ-ng the dependence of contact angle on lateral size �(2r), theependence of contact angle on height �(h) and the depend-nce of contact angle on curvature radius �(Rc). In addition, theffect of line tension on the imaged surface bubbles was investi-ated.

. Experimental

.1. Substrate/water

The silicon (1 0 0) substrates coated with PS film were preparedy spin coating PS (molecular weight 350000, Sigma–Aldrich) solu-ion with a concentration of 0.50% (weight) at a speed of 3000 rpm,000 rpm and 5000 rpm. To obtain the substrates with differenturface roughness, two spin coaters were used. For one spin coaterTA-280, China), the Si wafer was held on a vacuum chuck by aacuum suction force when spin coating. For the other spin coaterTB-610, China), the wafer was fixed on the holder with springlamps. Seven substrates were produced, as shown in Table 2.efore spin coating, the silicon wafers (dimension 1.0 cm × 1.0 cm)ere cleaned in a sonication bath of strong sulfuric acid and hydro-

en peroxide solution (weight ratio 3:1) for 30 min, followed bycetone for 30 min and purified water for 10 min and subsequentlylew to dry with nitrogen for use. Water was purified using a Milli-

A10 system with resistivity of 18.2 M� cm, and before use, about0 mL of water was allowed to equilibrate in air for hours in a stain-

ess steel container which had a volume of 100 mL, then a dropf water was injected into the liquid cell using a glass syringe formaging.

.2. Atomic force microscopy (AFM)

Tapping-mode AFM (NTEGRA platform, NT-MDT Company,elenograd, Moscow) was used to image the silicon substrate

oated with PS film in both air and purified water. When imag-ng in water, the substrate was immersed in the water, completely,n a fluid cell with a maximum volume of about 1 mL. Rectangularantilevers (CSG30 probe, NT-MDT Company) with a tip curvature

Fig. 2. Height image of PS coated silicon wafer using tapping mode AFM in air.

radii Rt = 17 ± 3 nm measured by SEM imaging, a typical springconstant k = 0.51 ± 0.02 Nm−1 obtained based on the model ofCleveland et al. [44]. The measured resonance frequencies of thecantilever, with a lock-in amplifier (SRS 830), were about 66 kHz inair and about 21 kHz in the experimental water. When the exper-iments were carried out, more than five different scan locationswere chosen, both the height and phase images were recordedsimultaneously with the amplitude set point of 95% and scan-ning rate of 0.5 Hz. The free amplitude A0(nA) was obtained fromamplitude phase distance curves recorded before and after eachcaptured height image [7,16,30]. It was recalculated into nanome-ters by multiplying the deflection sensitivities, and a typical value offree amplitude was A0 = 3.5 ± 0.2 nm. The ambient temperature waskept at 25 ◦C, and for each experiment, all samples were imaged inair before imaging in purified water. The height image of substrate-6 (refer to Table 2) on which the big microbubble was imaged firstlyis shown in Fig. 2. The PS film thickness of substrate-6 was deter-mined by AFM nanoshaving [3], and the average film thickness onscratch profile measurement was 80 ± 2 nm. To avoid contamina-tion, a clean experimental system needs to be kept, the fluid cell,glass pedestal and clip spring should be wiped with a pileless tis-sue and then rinsed with ethanol and water for several times beforeuse. The NT-MDT SPM software (Nova), grain analysis, was used foranalyzing the number, the volume and the projected area of surfacebubbles.

3. Results and discussion

3.1. Formation and properties of surface microbubbles on PS film

In order to image larger size surface bubbles and analyze theirnucleation, we studied surface nanobubbles formed on PS filmswith different surface roughness. Fig. 3 shows the tapping-modeAFM images of surface bubbles at PS film (substrate-6)/water inter-face. In Fig. 3a, a number of surface bubbles were imaged, and mostof them were in micrometer size, even there was a unique bigsurface nanobubble with lateral size exceeding 10 �m. To study

the big microbubble, we readjusted the scan location. Keepingthe amplitude set-point at 95%, the big microbubble was res-canned at time intervals of 10 min and the images are shown inFig. 3c. The cross sectional analysis of the big microbubble in the

D. Li, X. Zhao / Colloids and Surfaces A: Physicochem. Eng. Aspects 459 (2014) 128–135 131

Fig. 3. Microbubbles and nanobubbles were imaged on PS film by AFM. The height image (a) and corresponding phase image (b) show one big microbubble and a number ofrelatively smaller micro or nano bubbles formed on PS film, image (b’) is the magnified section of the rectangle region in image (b). The height image (c) and correspondingphase image (d) of the big microbubble are the magnified section of the rectangle region in image (a), image (e) is the 3D picture of image (c). Height image (f) and phasei . ImagI bles i

seasbTpcmirbcim

mage (g) shows big microbubbles formed on another rougher PS film (substrate-7)mage (i) shows the correlation function of bubble lateral size versus height for bub

uccessive scans is shown in Fig. 3h. It can be noted that the lat-ral size of the big microbubble changes from 10 �m to 13 �mnd height increases from 370 nm to 400 nm in the successivecans. The possible reason should be other invisible smaller bub-les merged into the big microbubble in the course of scanning.his is similar to the results of our recent study [30] and can beroved by the following coalescence phenomenon of bubbles, asan be seen in Fig. 3b’ and d. The bubble b1 and b2 in Fig. 3b’ wereoved and began to merge into the big ones at the site 1 and 2

n Fig. 3d. Fig. 3f shows the surface bubbles formed on anotherough PS film (substrate-7)/water interface. More than 10 surface

ubbles with lateral size exceeding 5 �m were imaged. This indi-ates that the formation of big microbubbles on rougher surfaces not occasional. To further investigate the morphology of the big

icrobubbles, the correlation function of the bubble lateral size

e (h) shows the section analysis of the big microbubble in image (a) and image (c).n image (a) and image (f).

versus the height for the microbubbles imaged in Fig. 3a and f isprovided in Fig. 3i, showing a linear relationship which is consis-tent with the results of surface bubbles in nanoscale in the previousstudy [7].

3.2. The influences of surface roughness on interfacial bubbles

Previous experimental studies showed that roughness can causenanobubble formation in the concave areas which are unfavorablefor the water to penetrate, resulting in a gas cavity and nanobub-bles with lower curvature and thus greater stability [17]. The

surface nanobubbles formed on rough surfaces were often largerand less densely distributed than those on a smooth surface withsimilar hydrophobicity [31]. In order to investigate the influencesof surface roughness on surface bubbles, experiments were carried

1 hysicochem. Eng. Aspects 459 (2014) 128–135

oampiboawabicofhasabti[asfNtb

ia[waasibrn

Oattccianpcossb

3

tsool

Fig. 4. AFM images of surface bubbles on PS films with different surface roughness.Images (a’–e’) are the corresponding phase images of height image (a–e).

32 D. Li, X. Zhao / Colloids and Surfaces A: P

ut on 7 substrates with different surface roughness. Substrate-6nd 7 were imaged before and the required data was obtained asentioned in the discussion above. The height and corresponding

hase images of the rest of 5 different substrates are presentedn Fig. 4, from which the relevant statistical data of surface bub-les was obtained. Table 3 shows the effect of surface roughnessn the morphology of surface bubbles. Lm and Hm are the aver-ge lateral size and average height of surface bubbles, respectively,hile Vm and Am are the average volume and average projected

rea of one surface bubble. Nm, Vt and At are the average num-er, the total volume and the total projected area of nanobubbles

n the area of 1 �m2, respectively. To assure the statistical signifi-ance of surface nanobubbles, the data of all the parameters werebtained on five locations. Table 3 shows that increasing the sur-ace roughness, increases the average lateral size Lm, the averageeight Hm, the average/total volume and the average/total projectrea of surface bubbles. Also, for the surface bubbles on relativelymoother substrates (substrates 1, 2 and 3), an increase in the aver-ge number of bubbles Nm was found. However, for the surfaceubbles on relatively rougher substrates (substrates 4, 5, 6 and 7),he average number Nm showed a dramatic decline with increas-ng surface roughness. Such a result is similar to that of Yang et al.31] and Bhushan [45]. The increase of Nm may be because therere more concave areas on the surface with higher roughness (forubstrates 1, 2 and 3), which can provide more nucleation sitesor surface bubbles formation. The decrease in the average numberm on rougher substrates (substrates 4, 5, 6 and 7) might be due

o the nucleation of microbubbles and the coalescence of surfaceubbles.

Furthermore, polystyrene is negatively charged in water,ncreasing the PS surface roughness can increase the surface areand then leads to a change in surface charge. Bhushan et al.46] studied the effect of charge on surface nanobubbles in pureater by shooting negative charges at smooth PS film with an

nti-static gun, and found an increase in the bubble numbernd a decrease of the bubble diameter. Therefore, the change ofurface charge with the increasing surface roughness will alsonfluence the formation and the morphology of surface nanobub-les. However, the effect of surface charge related to surfaceoughness on surface bubbles is complicated, and further study iseeded.

Now, how to explain the nucleation of the big microbubbles?n the basis of the analysis of our experimental results discussedbove, the high surface roughness can favor the formation ofhe micro bubbles. Moreover, other surface properties, such ashe inhomogeneity, scratches or conical pits of PS film on sili-on substrate can also influence the formation of big bubbles. Theonical pits favor the bubble nucleation by allowing the capillarynduced cavitation, as found by Lubetkin [47] and Wilt [48]. Atchleynd Prosperetti [49] studied the crevice model for heterogeneousucleation of bubbles in water and gave some numerical exam-les to illustrate the complex behavior of nucleation. Therefore, therevices on rough surfaces should be responsible for the nucleationf the big microbubbles. Of course, the coalescence phenomenon ofurface bubbles shown in Fig. 3 indicates that bubble coalescencehould be another important reason for the formation of big surfaceubbles.

.3. Contact angle as a function of size

The imaging of large microbubbles provides us an opportunityo investigate the relationship between contact angle and bubble

ize in a larger size range. To calculate the geometrical parametersf surface bubbles, methods developed and described in previ-us works were applied [7,28]. As shown in Fig. 5, the apparentateral size 2r′, height H were determined firstly, then the apparent

D. Li, X. Zhao / Colloids and Surfaces A: Physicochem. Eng. Aspects 459 (2014) 128–135 133

Table 3Effect of surface roughness on the morphology of surface bubbles.

Substrate 1 Substrate 2 Substrate 3 Substrate 4 Substrate 5 Substrate 6 Substrate 7

RMS (nm) 0.58 0.72 1.14 1.73 2.67 3.01 3.16Nm 1.1 ± 0.1 2.7 ± 0.1 3.0 ± 0.1 0.35 ± 0.05 0.17 ± 0.01 0.13 ± 0.01 0.09 ± 0.001Lm (nm) 157 ± 1 216 ± 1 265 ± 1 581 ± 2 1521 ± 5 1607 ± 6 1780 ± 7Hm (nm) 26.3 ± 0.2 28.6 ± 0.3 36.7 ± 0.5 83.8 ± 0.9 93.5 ± 1.1 118.2 ± 1.5 167.8 ± 2.1Vt × 106 (nm3 �m−2) 1.5 ± 0.1 5.8 ± 0.2 11.7 ± 0.4 14.2 ± 0.2 21.8 ± 1.3 24.2 ± 2 74.4 ± 0.8Vm × 106 (nm3) 1.37 ± 0.01 2.15 ± 0.01 3.89 ± 0. 01 47.3 ± 0.1 128.3 ± 0.1 186.4 ± 0.1 826.5 ± 0.1At (�m2 · �m−2) 0.036 ± 0.003 0.130 ± 0.005 0.255 ± 0.008 0.121 ± 0.002 0.141 ± 0.01 0.153 ± 0.001 0.40 ± 0.005Am (�m · �m) 0.033 ± 0.002 0.048 ± 0.002 0.085 ± 0.002 0.404 ± 0.002 0.81 ± 0.01 1.18 ± 0.01 4.48 ± 0.01

Table 4The values of line tension of surface bubbles on seven different substrates.

Substrate 1 Substrate 2 Substrate 3 Substrate 4 Substrate 5 Substrate 6 Substrate 7

08

c

t�ftfT1tti2aiittao(a2�w[fobr

Range of bubble size (nm) 198–473 233–888 220–12−�/�lg (nm) 50.4 14.5 6.8

� (nN) −3.63 −1.04 −0.49

urvature radius R′c = (r′2 + H2)/2H, curvature radius Rc = R′

c − Rt ,

hree-phase contact line radius r =√

2RcH − H2 and contact angle = 2 arctan (H/r) were calculated. The symbols with seven dif-erent shapes and colors in Fig. 6 refer to different RMS values ofhe seven substrates, on which the resided surface bubbles derivesrom the experimental results above (including Figs. 4a–e and 3c,g).he lateral size of bubbles formed on seven substrates ranges from98 nm to 473 nm, 233 nm to 888 nm, 220 nm to 1208 nm, 257 nmo 2237 nm, 1093 nm to 3617 nm, 1482 nm to 11,180 nm and 1366o 13,182 nm respectively. The corresponding contact angles aren the range of 9.6–31◦, 3.8–27.7◦, 3.4–13.3◦, 3.7–8.4◦, 4.2–8.1◦,.9–8.5◦ and 2.2–7.0◦. In each independent size scale, the contactngle of surface bubbles has a clearly increasing tendency with thencrease of their lateral size (shown in Fig. 6a) and heights (shownn Fig. 6b). This is consistent with the results of � on Rc (beforeip corrected) reported by Borkent et al. [7], which are suggestinghat the contact angle of surface bubbles in nano/micro scale has

tendency toward a macroscopic value as the lateral size/heightf the bubbles increases. In more detail, the first two sets of dataRMS = 0.58 nm, 0.72 nm) of �(2r) in Fig. 5a and �(H) in Fig. 5bre linear, but the other five sets of data (RMS = 1.14 nm, 1.73 nm,.67 nm, 3.01 nm and 3.16 nm) are nonlinear. The dependence of(2r) and �(H) remains constant with the increase of bubble size,hich is in line with the results of Zhang et al. [5], Zhang et al.

35] and Song et al. [38]. However, for the bubbles between dif-

erent size scale in Fig. 6a and b, there shows a marked declinef the contact angle with the increase of roughness. The bub-les formed on substrate-6 and 7 (RMS = 3.01 nm and 3.16 nmespectively) are larger than that formed on other five substrates.

Fig. 5. Sketches of surface bubble on PS/water interface.

257–2237 1093–3617 1482–11180 1366–131822.34 4.41 15.18 10.78−0.17 −0.31 −1.1 −0.78

However, the corresponding contact angle of bubbles formed onsubstrate-6 and 7 is much smaller than that of bubbles formedon any other five substrates. This indicates that although the con-tact angle of bubbles could be size-dependent in each independentsize scale, there is no evidence that the contact angle of nanobub-bles can approach the macroscale one with the increase of bubblesize.

In Fig. 6c, for the bubbles on relatively rougher substrates(RMS = 1.14 nm, 1.73 nm, 2.67 nm, 3.01 nm and 3.16 nm), thedependence of � on Rc shows a similar trend as that in Fig. 6a andb. In contrast, for the bubbles on relatively smoother substrates(RMS = 0.58 nm and 0.72 nm), the contact angle decreases as thecurvature radius increases. This dependence of � on Rc is in match-ing with the results of van Limbeek [37]. Our results regarding thedirection inversion in the dependence of � as function of Rc in dif-ferent size scale are consistent with the results �(2r) reported byKameda [36], which can attribute to the effect of the line tension.On the basis of Eq. (1), the line tension of surface bubbles can beestimated. The relationship between cos � and 1/r in our workscan be obtained through the curves in Fig. 6a, which would leadto seven straight lines with corresponding slopes of −(�/�lg) asshown in Fig. 7. Thus the corresponding line tensions � can becalculated, as shown in Table 4. All of the seven line tension val-ues for the seven sets of bubbles are negative which can tend toexpand the three-phase contact line and is expected to balancethe surface tension that leads to the bubble shrinking, and thusstabilize the nanobubbles formed at these solid–water interfaces[31,36]. The mean value of the line tension that we calculated is� ≈ −1.07 nN, this value is close to the result of van Limbeek [37](� ≈ −0.8 nN), who introduced another line-tension term of theform proposed by Brenner and Lohse [26]. Other reported valuessimilar in magnitude to our result include −0.3 nN [31,33], and∼−0.2 nN [36]. In Table 4, the values of line tension for the surfacenanobubbles between different substrates (bubbles on substrate1–4) decrease with the increasing bubble size, which might indi-cate that the effect of line tension is weakened gradually, however,for the larger microbubbles on substrate 5, 6 and 7, such a trend isbroken. The possible reason to this could be not considering theeffect of surface roughness and heterogeneity which can corru-gate the contact line of larger bubbles. Furthermore, replacing thegeodesic curvature of larger surface bubbles with the reciprocal ofbase radius r is also incorrect. Therefore, besides the error induced

from the calculation of Rc = (r2 + H2)/2H, the influence of surfaceproperties, the larger bubble size, line tension, even the contami-nation may be responsible for the inversion in direction of the �(Rc)dependence.

134 D. Li, X. Zhao / Colloids and Surfaces A: Physicochem. Eng. Aspects 459 (2014) 128–135

Fig. 6. Contact angle as a function of surface bubbles size (tip corrected). Image (a),image (b) and image (c) are the dependence of contact angle on lateral size �(2r),the dependence of contact angle on height �(h) and the dependence of contact angleon curvature radius �(Rc), respectively. The insets in image (a) and image (c) are themagnification of the corresponding rectangle region with dotted line (error barscorrespond to one standard deviation). (For interpretation of the references to colorin text, the reader is referred to the web version of the article.)

Fig. 7. The relationship between cos � and 1/r. The inset is the magnification of theupper left rectangle region with dotted line.

4. Conclusions

We have investigated the surface bubbles formed on PS film withdifferent surface roughness. The big surface microbubbles with lat-eral size exceeding 10 �m were obtained on rougher PS substrates(RMS = 3.01 nm and 3.16 nm) by using a NT-MDT AFM system intapping mode at a set-point ratio of 95%. To investigate the possi-ble reasons of the big microbubble nucleation, experiments werecarried out on 7 PS substrates with different surface roughness. Weconcluded that bubble coalescence, surface roughness and othersurface properties, such as the inhomogeneity and concave pitsare the significant factors affecting the size of surface bubbles. Theincreased surface roughness is usually leading to increased bubblesize.

Further, we have investigated the contact angle of surface bub-bles on PS surface and how does the contact angle of surface bubblesrely on the bubble size in the range of 200 nm to 13 �m. We foundthat the contact angle of bubbles on PS surface is in the range of2.2–31◦, which is much less than the macroscopic contact angle(about 85◦ measured through air) [7]. In addition, the contact anglehas a linearly increasing tendency for small bubbles and nonlinearlyincreasing tendency for large bubbles with the lateral size 2r andthe height H in each independent size range. An obvious declinebetween different size ranges with their lateral size and heightincrease was also observed. With regard to the �(Rc) dependence,an inversion in direction was observed for the bubbles in small sizescale and large size scale. This might be caused by the error in cal-culating the morphology of bubbles, the influence line tension andsurface property. The line tension of bubbles in our experimentswas calculated from seven sets of bubbles and all of the seven linetension values are negative (the average line tension was equal to� ≈ −1.07 nN), which should be responsible for the abnormal lowcontact angle and contribute to the pinned contact line, and thuscontribute to the stability of surface bubbles.

Acknowledgements

The author would like to thank Dr. Khurshid Ahmad, Dr. D.L. Jingand Dr. Y.L. Pan for their helpful discussions.

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