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Colloids and Surfaces A: Physicochem. Eng. Aspects 459 (2014) 128–135
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Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa
Micro and nano bubbles on polystyrene film/water interface Dayong Li a,b,∗ , Xuezeng Zhao a,∗∗ a b
School of Mechanical and Electrical Engineering, Harbin Institute of Technology, Harbin 150001, China School of Mechanical Engineering, Heilongjiang University of Science and Technology, Harbin 150022, China
h i g h l i g h t s
g r a p h i c a l
a b s t r a c t
• Big micro surface bubbles were imaged on PS film with AFM.
• The influence of surface roughness on surface bubbles was studied.
• Size dependence of the contact angle was investigated in a larger size scale.
• The effect of line tension on surface bubbles was analyzed.
a r t i c l e
i n f o
Article history: Received 11 February 2014 Received in revised form 7 June 2014 Accepted 11 June 2014 Available online 8 July 2014 Keywords: Surface nanobubbles Contact angle Size dependence Atomic force microscope (AFM)
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 with a lateral size up to 13 m and a height up to 400 nm was reported. The possible reasons for nucleation of big microbubbles were investigated and found that surface roughness and surface properties play a significant 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 surface bubbles 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 of bubble size for bubbles on rough substrates. While studying the dependence of contact angle on curvature radius (Rc ), an inversion in direction between the bubbles in different size scale was found. The results obtained were in close resemblance with the results of other studies. The line tension of surface bubbles on the seven PS substrates in our experiments was calculated and all of the seven line tension values are negative (the average line tension in this study was ≈ −1.07 nN), which should be responsible for the anomalous low contact angle and the size-dependence of the surface bubbles. © 2014 Elsevier B.V. All rights reserved.
1. Introduction In recent decade, one of significant discoveries in interfacial physics is nanobubbles, which are micro/nano-scopic gaseous domains that form at the interface between solid and liquid. From
∗ Corresponding author at: School of Mechanical and Electrical Engineering, Harbin Institute of Technology, Harbin 150001, China. Tel.: +86 13945170437. ∗∗ Corresponding author. E-mail addresses: lidayong [email protected] (D. Li), [email protected] (X. Zhao). http://dx.doi.org/10.1016/j.colsurfa.2014.06.022 0927-7757/© 2014 Elsevier B.V. All rights reserved.
the year 2000, nanobubbles have been imaged and studied by atomic force microscope (AFM) [1–16] and other measuring techniques such as spectroscopy technique [17] (most recently through direct optical visualization [18,19]), rapid cryofixation technique [20] and quartz crystal microbalances technique [21,22]. Studies show 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 much smaller than that of macroscopic bubbles [7,24–27], (4) abnormal longevity for several days [1,2,17], (5) two or more bubbles close
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Table 1 Summary of studies on the dependence of contact angle on the bubble size. Substrate
Gas type
RMS roughness
Bubble size
Tip correction
Ref.
HOPG
Air
Rc ∼250 nm
Yes
[7]
HOPG HOPG Gold-ODT Gold-MHDA Si-PFDCS Au (1 1 1) Si-TMCS
Air H2 ; air Air
0.2–0.3 nm 0.6–2.6 nm 0.7 nm
Rc ∼2000 nm Rc ∼1800 nm Rc ∼1200 nm
Yes No Yes
[5] [35] [38]
Rc ∼3000 nm r ∼100 nm 2r ∼800 nm
Yes Yes No
[37] [36] [31]
Methane; nitrogen; oxygen Air Air
0.4 nm 0.2 nm 2.7 nm
Substrate abbreviations: PS, polystyrene; PFDCS, 1H,1H,2H,2H-perfluorodecyl-dimethylchlorosilane; ODT, octadecanethiol; MHDA, 16-mercaptohexadecanoic acid.
to each other can emerge into a big one [28–31], (6) disappear in degassed water and reappear when the liquid is exposed to air [5,6,32,33]. The studies on the properties, influence factors and applications of nanobubbles have been developed deeply [9,10,34]. However, the stability (anomalous longevity) and the contact angle of nanobubbles are still open questions. In the conventional view, as a material property, the contact angle of macroscale bubbles should be substrate dependent. But AFM studies [7] show that the contact angle of nanoscale bubbles (measured through air) is much lower than that of macroscale bubbles. Thus one would expect that the nanoscopic contact angle will be size-dependent, i.e., the contact angle of nanobubbles will increase with the increase of bubble size and will approach the macroscopic one for large enough bubbles. So far, many efforts have been made to study the dependence of contact angle on the size of surface bubbles [5,7,31,35–38]. Table 1 shows a brief summary of studies regarding the dependence of contact angle on the bubble size. First, for the dependence of contact angle on curvature radius ((Rc )), Borkent et al. [7] concluded that contact angle (measured through water, before tip correction) decreases with an increase of the curvature radius of bubbles. But such a dependence changes dramatically after tip correction: the contact angle keeps constant within the experimental error. Similarly, other studies have reported that the contact angle on the hydrophobic surfaces does not change with radius [5,35,38] while changes slightly on the hydrophilic surface [38]. However, Van Limbeek [37] investigated 7 different types of gas, and found that the contact angle (measured through water) increased with the curvature radius of nanobubbles for all gas types they studied, which are opposite to the results of Borkent. In addition, a recent numerical study of Grosfils [39] validated the gas-dependency results of Limbeek. Secondly, for the dependence of contact angle on lateral size ((2r)), Kameda and Nakabayashi [36] found that the contact angle increased with the increase in the radius of three-phase contact line (when lateral size ∼100 nm), which agrees with the results of Yang et al. [31]. In contrast, for the bubbles in smaller size range (lateral size ∼20 nm), an adverse trend was obtained, and a probable reason for this was thought to be the effect of line tension [36]. The previous studies discussed above show that it is still undefined whether the contact angle of surface bubbles is size-dependent or not. In addition, it should be noted that most of the previous works focused on the surface bubbles with nanoscale (Table 1). So it is significant to investigate the relationship between the contact angle and the bubble size in large size scale. The line tension is usually taken into account in the study of the relationship between the size and the contact angle of surface bubbles [31,33,36,37]. The line tension was defined as the excess energy per unit length of the three-phase contact line [40]. The sources of the excess energy of the contact line were thought to be 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 transition zone and also from the local interfacial deformations in this zone caused by the surface forces [40]. The effect of line tension will lead to a reduced contact angle of surface bubbles in nanoscale as compared with the macroscopic contact angle in the transition zone [40], as can be seen in Fig. 1. The difference between the nanoscopic and macroscopic contact angle which is linked to the effect of line tension can also be explained by the modified Young’s equation [31,41], that is cos = cos Y −
lg r
(1)
where Y is Young contact angle, lg is the liquid–gas surface tension, r is contact line radius which is equal to the reciprocal of the geodesic curvature and is the line tension. The range of Young contact angle is less than 90◦ measured through air for the bubbles formed on the hydrophobic substrates [7], so cos Y > 0. If the sign of is negative, together with positive surface tension lg and contact line radius r, then the contact angle calculated by Eq. (1) will be a reduced one as compared to the Young contact angle Y . This means that the negative line tension should be responsible for the anomalously low contact angle. On the basis of the Laplace–Young’s equation, the smaller contact angle means the lower inner pressure of the surface bubbles with the same base radius and thus means a longer lifetime. At the same time, the negative line tension can contribute to the three phase contact line pinning by balancing the surface tension. The pinned contact line which has been proved in 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 of the previous studies was negative [31,33,37]. Although Kameda and Nakabayashi [36] calculated a positive line tension for bubbles with
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Table 2 Root-mean-square (RMS) roughness of seven different substrates. Substrate
1
2
3
4
5
6
7
RMS (nm) Scan area (m2 ) Speed (rpm) Spin coater
0.58 5 5000 a
0.72 5 4000 a
1.14 5 3000 a
1.73 5 5000 b
2.67 5 4000 b
3.01 5 3000 b
3.16 5 3000 b
Spin coater a (TA-280, China): the wafer was held on a vacuum chuck by a vacuum suction force when spin coating; Spin coater b (TB-610, China), the wafer was fixed on a holder with spring clamps when spin coating.
lateral size less than 20 nm, which is consistent with Li’s theoretical prediction [43], i.e., the line tension should be positive for a drop with the radius of contact line approaching to zero. When the surface bubbles have the lateral size larger than 20 nm, the line tension calculated in Kameda’s work changes to be negative. Considering the lateral size of surface bubbles imaged in most of the previous studies were always less than 2 m. Therefore, it is also significant to investigate whether the line tension of surface bubbles can remain negative for bubbles in large size scale or not. In this work, we investigated surface bubbles formed on Polystyrene (PS) films with a roughness range from 0.58 nm to 3.36 nm, in water by using AFM. The big microbubbles were imaged on the rougher substrates with surface roughness of 3.11 nm and 3.36 nm. The possible nucleation reasons and features of the big microbubbles were investigated. We have also addressed the question “How does the contact angle depend on the surface bubble size” in a larger bubble size scale (200 nm to 13 m), including the dependence of contact angle on lateral size (2r), the dependence of contact angle on height (h) and the dependence of contact angle on curvature radius (Rc ). In addition, the effect of line tension on the imaged surface bubbles was investigated. 2. Experimental 2.1. Substrate/water The silicon (1 0 0) substrates coated with PS film were prepared by spin coating PS (molecular weight 350000, Sigma–Aldrich) solution with a concentration of 0.50% (weight) at a speed of 3000 rpm, 4000 rpm and 5000 rpm. To obtain the substrates with different surface roughness, two spin coaters were used. For one spin coater (TA-280, China), the Si wafer was held on a vacuum chuck by a vacuum suction force when spin coating. For the other spin coater (TB-610, China), the wafer was fixed on the holder with spring clamps. Seven substrates were produced, as shown in Table 2. Before spin coating, the silicon wafers (dimension 1.0 cm × 1.0 cm) were cleaned in a sonication bath of strong sulfuric acid and hydrogen peroxide solution (weight ratio 3:1) for 30 min, followed by acetone for 30 min and purified water for 10 min and subsequently blew to dry with nitrogen for use. Water was purified using a MilliQ A10 system with resistivity of 18.2 M cm, and before use, about 50 mL of water was allowed to equilibrate in air for hours in a stainless steel container which had a volume of 100 mL, then a drop of water was injected into the liquid cell using a glass syringe for imaging. 2.2. Atomic force microscopy (AFM) Tapping-mode AFM (NTEGRA platform, NT-MDT Company, Zelenograd, Moscow) was used to image the silicon substrate coated with PS film in both air and purified water. When imaging in water, the substrate was immersed in the water, completely, in a fluid cell with a maximum volume of about 1 mL. Rectangular cantilevers (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 spring constant k = 0.51 ± 0.02 Nm−1 obtained based on the model of Cleveland et al. [44]. The measured resonance frequencies of the cantilever, with a lock-in amplifier (SRS 830), were about 66 kHz in air and about 21 kHz in the experimental water. When the experiments were carried out, more than five different scan locations were chosen, both the height and phase images were recorded simultaneously with the amplitude set point of 95% and scanning rate of 0.5 Hz. The free amplitude A0 (nA) was obtained from amplitude phase distance curves recorded before and after each captured height image [7,16,30]. It was recalculated into nanometers by multiplying the deflection sensitivities, and a typical value of free amplitude was A0 = 3.5 ± 0.2 nm. The ambient temperature was kept at 25 ◦ C, and for each experiment, all samples were imaged in air before imaging in purified water. The height image of substrate6 (refer to Table 2) on which the big microbubble was imaged firstly is shown in Fig. 2. The PS film thickness of substrate-6 was determined by AFM nanoshaving [3], and the average film thickness on scratch profile measurement was 80 ± 2 nm. To avoid contamination, a clean experimental system needs to be kept, the fluid cell, glass pedestal and clip spring should be wiped with a pileless tissue and then rinsed with ethanol and water for several times before use. The NT-MDT SPM software (Nova), grain analysis, was used for analyzing the number, the volume and the projected area of surface bubbles. 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 their nucleation, we studied surface nanobubbles formed on PS films with different surface roughness. Fig. 3 shows the tapping-mode AFM images of surface bubbles at PS film (substrate-6)/water interface. In Fig. 3a, a number of surface bubbles were imaged, and most of them were in micrometer size, even there was a unique big surface nanobubble with lateral size exceeding 10 m. To study the big microbubble, we readjusted the scan location. Keeping the amplitude set-point at 95%, the big microbubble was rescanned at time intervals of 10 min and the images are shown in Fig. 3c. The cross sectional analysis of the big microbubble in the
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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 of relatively 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 corresponding phase 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 phase image (g) shows big microbubbles formed on another rougher PS film (substrate-7). Image (h) shows the section analysis of the big microbubble in image (a) and image (c). Image (i) shows the correlation function of bubble lateral size versus height for bubbles in image (a) and image (f).
successive scans is shown in Fig. 3h. It can be noted that the lateral size of the big microbubble changes from 10 m to 13 m and height increases from 370 nm to 400 nm in the successive scans. The possible reason should be other invisible smaller bubbles merged into the big microbubble in the course of scanning. This is similar to the results of our recent study [30] and can be proved by the following coalescence phenomenon of bubbles, as can be seen in Fig. 3b’ and d. The bubble b1 and b2 in Fig. 3b’ were moved and began to merge into the big ones at the site 1 and 2 in Fig. 3d. Fig. 3f shows the surface bubbles formed on another rough PS film (substrate-7)/water interface. More than 10 surface bubbles with lateral size exceeding 5 m were imaged. This indicates that the formation of big microbubbles on rougher surface is not occasional. To further investigate the morphology of the big microbubbles, the correlation function of the bubble lateral size
versus the height for the microbubbles imaged in Fig. 3a and f is provided in Fig. 3i, showing a linear relationship which is consistent with the results of surface bubbles in nanoscale in the previous study [7]. 3.2. The influences of surface roughness on interfacial bubbles Previous experimental studies showed that roughness can cause nanobubble formation in the concave areas which are unfavorable for the water to penetrate, resulting in a gas cavity and nanobubbles with lower curvature and thus greater stability [17]. The surface nanobubbles formed on rough surfaces were often larger and less densely distributed than those on a smooth surface with similar hydrophobicity [31]. In order to investigate the influences of surface roughness on surface bubbles, experiments were carried
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out on 7 substrates with different surface roughness. Substrate-6 and 7 were imaged before and the required data was obtained as mentioned in the discussion above. The height and corresponding phase images of the rest of 5 different substrates are presented in Fig. 4, from which the relevant statistical data of surface bubbles was obtained. Table 3 shows the effect of surface roughness on the morphology of surface bubbles. Lm and Hm are the average lateral size and average height of surface bubbles, respectively, while Vm and Am are the average volume and average projected area of one surface bubble. Nm , Vt and At are the average number, the total volume and the total projected area of nanobubbles in the area of 1 m2 , respectively. To assure the statistical significance of surface nanobubbles, the data of all the parameters were obtained on five locations. Table 3 shows that increasing the surface roughness, increases the average lateral size Lm , the average height Hm , the average/total volume and the average/total project area of surface bubbles. Also, for the surface bubbles on relatively smoother substrates (substrates 1, 2 and 3), an increase in the average number of bubbles Nm was found. However, for the surface bubbles on relatively rougher substrates (substrates 4, 5, 6 and 7), the average number Nm showed a dramatic decline with increasing surface roughness. Such a result is similar to that of Yang et al. [31] and Bhushan [45]. The increase of Nm may be because there are more concave areas on the surface with higher roughness (for substrates 1, 2 and 3), which can provide more nucleation sites for surface bubbles formation. The decrease in the average number Nm on rougher substrates (substrates 4, 5, 6 and 7) might be due to the nucleation of microbubbles and the coalescence of surface bubbles. Furthermore, polystyrene is negatively charged in water, increasing the PS surface roughness can increase the surface area and then leads to a change in surface charge. Bhushan et al. [46] studied the effect of charge on surface nanobubbles in pure water by shooting negative charges at smooth PS film with an anti-static gun, and found an increase in the bubble number and a decrease of the bubble diameter. Therefore, the change of surface charge with the increasing surface roughness will also influence the formation and the morphology of surface nanobubbles. However, the effect of surface charge related to surface roughness on surface bubbles is complicated, and further study is needed. Now, how to explain the nucleation of the big microbubbles? On the basis of the analysis of our experimental results discussed above, the high surface roughness can favor the formation of the micro bubbles. Moreover, other surface properties, such as the inhomogeneity, scratches or conical pits of PS film on silicon substrate can also influence the formation of big bubbles. The conical pits favor the bubble nucleation by allowing the capillary induced cavitation, as found by Lubetkin [47] and Wilt [48]. Atchley and Prosperetti [49] studied the crevice model for heterogeneous nucleation of bubbles in water and gave some numerical examples to illustrate the complex behavior of nucleation. Therefore, the crevices on rough surfaces should be responsible for the nucleation of the big microbubbles. Of course, the coalescence phenomenon of surface bubbles shown in Fig. 3 indicates that bubble coalescence should be another important reason for the formation of big surface bubbles. 3.3. Contact angle as a function of size The imaging of large microbubbles provides us an opportunity to investigate the relationship between contact angle and bubble size in a larger size range. To calculate the geometrical parameters of surface bubbles, methods developed and described in previous works were applied [7,28]. As shown in Fig. 5, the apparent lateral size 2r , height H were determined firstly, then the apparent
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).
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Table 3 Effect of surface roughness on the morphology of surface bubbles.
RMS (nm) Nm Lm (nm) Hm (nm) Vt × 106 (nm3 m−2 ) Vm × 106 (nm3 ) At (m2 · m−2 ) Am (m · m)
Substrate 1
Substrate 2
Substrate 3
Substrate 4
Substrate 5
Substrate 6
Substrate 7
0.58 1.1 ± 157 ± 26.3 ± 1.5 ± 1.37 ± 0.036 ± 0.033 ±
0.72 2.7 ± 216 ± 28.6 ± 5.8 ± 2.15 ± 0.130 ± 0.048 ±
1.14 3.0 ± 265 ± 36.7 ± 11.7 ± 3.89 ± 0.255 ± 0.085 ±
1.73 0.35 ± 581 ± 83.8 ± 14.2 ± 47.3 ± 0.121 ± 0.404 ±
2.67 0.17 ± 1521 ± 93.5 ± 21.8 ± 128.3 ± 0.141 ± 0.81 ±
3.01 0.13 ± 1607 ± 118.2 ± 24.2 ± 186.4 ± 0.153 ± 1.18 ±
3.16 0.09 ± 1780 ± 167.8 ± 74.4 ± 826.5 ± 0.40 ± 4.48 ±
0.1 1 0.2 0.1 0.01 0.003 0.002
0.1 1 0.3 0.2 0.01 0.005 0.002
0.1 1 0.5 0.4 0. 01 0.008 0.002
0.05 2 0.9 0.2 0.1 0.002 0.002
0.01 5 1.1 1.3 0.1 0.01 0.01
0.01 6 1.5 2 0.1 0.001 0.01
0.001 7 2.1 0.8 0.1 0.005 0.01
Table 4 The values of line tension of surface bubbles on seven different substrates.
Range of bubble size (nm) −/lg (nm) (nN)
Substrate 1
Substrate 2
Substrate 3
Substrate 4
Substrate 5
Substrate 6
Substrate 7
198–473 50.4 −3.63
233–888 14.5 −1.04
220–1208 6.8 −0.49
257–2237 2.34 −0.17
1093–3617 4.41 −0.31
1482–11180 15.18 −1.1
1366–13182 10.78 −0.78
curvature radius Rc = (r 2 + H 2 )/2H, curvature radius Rc = Rc − Rt ,
three-phase contact line radius r = 2Rc H − H 2 and contact angle = 2 arctan (H/r) were calculated. The symbols with seven different shapes and colors in Fig. 6 refer to different RMS values of the seven substrates, on which the resided surface bubbles derives from the experimental results above (including Figs. 4a–e and 3c,g). The lateral size of bubbles formed on seven substrates ranges from 198 nm to 473 nm, 233 nm to 888 nm, 220 nm to 1208 nm, 257 nm to 2237 nm, 1093 nm to 3617 nm, 1482 nm to 11,180 nm and 1366 to 13,182 nm respectively. The corresponding contact angles are in the range of 9.6–31◦ , 3.8–27.7◦ , 3.4–13.3◦ , 3.7–8.4◦ , 4.2–8.1◦ , 2.9–8.5◦ and 2.2–7.0◦ . In each independent size scale, the contact angle of surface bubbles has a clearly increasing tendency with the increase of their lateral size (shown in Fig. 6a) and heights (shown in Fig. 6b). This is consistent with the results of on Rc (before tip corrected) reported by Borkent et al. [7], which are suggesting that the contact angle of surface bubbles in nano/micro scale has a tendency toward a macroscopic value as the lateral size/height of the bubbles increases. In more detail, the first two sets of data (RMS = 0.58 nm, 0.72 nm) of (2r) in Fig. 5a and (H) in Fig. 5b are linear, but the other five sets of data (RMS = 1.14 nm, 1.73 nm, 2.67 nm, 3.01 nm and 3.16 nm) are nonlinear. The dependence of (2r) and (H) remains constant with the increase of bubble size, which 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 different size scale in Fig. 6a and b, there shows a marked decline of the contact angle with the increase of roughness. The bubbles formed on substrate-6 and 7 (RMS = 3.01 nm and 3.16 nm respectively) are larger than that formed on other five substrates.
Fig. 5. Sketches of surface bubble on PS/water interface.
However, the corresponding contact angle of bubbles formed on substrate-6 and 7 is much smaller than that of bubbles formed on any other five substrates. This indicates that although the contact angle of bubbles could be size-dependent in each independent size scale, there is no evidence that the contact angle of nanobubbles can approach the macroscale one with the increase of bubble size. 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), the dependence of on Rc shows a similar trend as that in Fig. 6a and b. In contrast, for the bubbles on relatively smoother substrates (RMS = 0.58 nm and 0.72 nm), the contact angle decreases as the curvature radius increases. This dependence of on Rc is in matching with the results of van Limbeek [37]. Our results regarding the direction inversion in the dependence of as function of Rc in different size scale are consistent with the results (2r) reported by Kameda [36], which can attribute to the effect of the line tension. On the basis of Eq. (1), the line tension of surface bubbles can be estimated. The relationship between cos and 1/r in our works can be obtained through the curves in Fig. 6a, which would lead to seven straight lines with corresponding slopes of −(/lg ) as shown in Fig. 7. Thus the corresponding line tensions can be calculated, as shown in Table 4. All of the seven line tension values for the seven sets of bubbles are negative which can tend to expand the three-phase contact line and is expected to balance the surface tension that leads to the bubble shrinking, and thus stabilize 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 the form proposed by Brenner and Lohse [26]. Other reported values similar 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 surface nanobubbles between different substrates (bubbles on substrate 1–4) decrease with the increasing bubble size, which might indicate that the effect of line tension is weakened gradually, however, for the larger microbubbles on substrate 5, 6 and 7, such a trend is broken. The possible reason to this could be not considering the effect of surface roughness and heterogeneity which can corrugate the contact line of larger bubbles. Furthermore, replacing the geodesic curvature of larger surface bubbles with the reciprocal of base radius r is also incorrect. Therefore, besides the error induced from the calculation of Rc = (r 2 + H 2 )/2H, the influence of surface properties, the larger bubble size, line tension, even the contamination may be responsible for the inversion in direction of the (Rc ) dependence.
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Fig. 7. The relationship between cos and 1/r. The inset is the magnification of the upper left rectangle region with dotted line.
4. Conclusions We have investigated the surface bubbles formed on PS film with different surface roughness. The big surface microbubbles with lateral 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 in tapping mode at a set-point ratio of 95%. To investigate the possible reasons of the big microbubble nucleation, experiments were carried out on 7 PS substrates with different surface roughness. We concluded that bubble coalescence, surface roughness and other surface properties, such as the inhomogeneity and concave pits are the significant factors affecting the size of surface bubbles. The increased surface roughness is usually leading to increased bubble size. Further, we have investigated the contact angle of surface bubbles on PS surface and how does the contact angle of surface bubbles rely on the bubble size in the range of 200 nm to 13 m. We found that the contact angle of bubbles on PS surface is in the range of 2.2–31◦ , which is much less than the macroscopic contact angle (about 85◦ measured through air) [7]. In addition, the contact angle has a linearly increasing tendency for small bubbles and nonlinearly increasing tendency for large bubbles with the lateral size 2r and the height H in each independent size range. An obvious decline between different size ranges with their lateral size and height increase was also observed. With regard to the (Rc ) dependence, an inversion in direction was observed for the bubbles in small size scale and large size scale. This might be caused by the error in calculating the morphology of bubbles, the influence line tension and surface property. The line tension of bubbles in our experiments was calculated from seven sets of bubbles and all of the seven line tension values are negative (the average line tension was equal to ≈ −1.07 nN), which should be responsible for the abnormal low contact angle and contribute to the pinned contact line, and thus contribute to the stability of surface bubbles. Acknowledgements 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 angle on curvature radius (Rc ), respectively. The insets in image (a) and image (c) are the magnification of the corresponding rectangle region with dotted line (error bars correspond to one standard deviation). (For interpretation of the references to color in text, the reader is referred to the web version of the article.)
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Contents lists available at ScienceDirect
Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa
Micro and nano bubbles on polystyrene film/water interface Dayong Li a,b,∗ , Xuezeng Zhao a,∗∗ a b
School of Mechanical and Electrical Engineering, Harbin Institute of Technology, Harbin 150001, China School of Mechanical Engineering, Heilongjiang University of Science and Technology, Harbin 150022, China
h i g h l i g h t s
g r a p h i c a l
a b s t r a c t
• Big micro surface bubbles were imaged on PS film with AFM.
• The influence of surface roughness on surface bubbles was studied.
• Size dependence of the contact angle was investigated in a larger size scale.
• The effect of line tension on surface bubbles was analyzed.
a r t i c l e
i n f o
Article history: Received 11 February 2014 Received in revised form 7 June 2014 Accepted 11 June 2014 Available online 8 July 2014 Keywords: Surface nanobubbles Contact angle Size dependence Atomic force microscope (AFM)
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 with a lateral size up to 13 m and a height up to 400 nm was reported. The possible reasons for nucleation of big microbubbles were investigated and found that surface roughness and surface properties play a significant 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 surface bubbles 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 of bubble size for bubbles on rough substrates. While studying the dependence of contact angle on curvature radius (Rc ), an inversion in direction between the bubbles in different size scale was found. The results obtained were in close resemblance with the results of other studies. The line tension of surface bubbles on the seven PS substrates in our experiments was calculated and all of the seven line tension values are negative (the average line tension in this study was ≈ −1.07 nN), which should be responsible for the anomalous low contact angle and the size-dependence of the surface bubbles. © 2014 Elsevier B.V. All rights reserved.
1. Introduction In recent decade, one of significant discoveries in interfacial physics is nanobubbles, which are micro/nano-scopic gaseous domains that form at the interface between solid and liquid. From
∗ Corresponding author at: School of Mechanical and Electrical Engineering, Harbin Institute of Technology, Harbin 150001, China. Tel.: +86 13945170437. ∗∗ Corresponding author. E-mail addresses: lidayong [email protected] (D. Li), [email protected] (X. Zhao). http://dx.doi.org/10.1016/j.colsurfa.2014.06.022 0927-7757/© 2014 Elsevier B.V. All rights reserved.
the year 2000, nanobubbles have been imaged and studied by atomic force microscope (AFM) [1–16] and other measuring techniques such as spectroscopy technique [17] (most recently through direct optical visualization [18,19]), rapid cryofixation technique [20] and quartz crystal microbalances technique [21,22]. Studies show 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 much smaller than that of macroscopic bubbles [7,24–27], (4) abnormal longevity for several days [1,2,17], (5) two or more bubbles close
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Table 1 Summary of studies on the dependence of contact angle on the bubble size. Substrate
Gas type
RMS roughness
Bubble size
Tip correction
Ref.
HOPG
Air
Rc ∼250 nm
Yes
[7]
HOPG HOPG Gold-ODT Gold-MHDA Si-PFDCS Au (1 1 1) Si-TMCS
Air H2 ; air Air
0.2–0.3 nm 0.6–2.6 nm 0.7 nm
Rc ∼2000 nm Rc ∼1800 nm Rc ∼1200 nm
Yes No Yes
[5] [35] [38]
Rc ∼3000 nm r ∼100 nm 2r ∼800 nm
Yes Yes No
[37] [36] [31]
Methane; nitrogen; oxygen Air Air
0.4 nm 0.2 nm 2.7 nm
Substrate abbreviations: PS, polystyrene; PFDCS, 1H,1H,2H,2H-perfluorodecyl-dimethylchlorosilane; ODT, octadecanethiol; MHDA, 16-mercaptohexadecanoic acid.
to each other can emerge into a big one [28–31], (6) disappear in degassed water and reappear when the liquid is exposed to air [5,6,32,33]. The studies on the properties, influence factors and applications of nanobubbles have been developed deeply [9,10,34]. However, the stability (anomalous longevity) and the contact angle of nanobubbles are still open questions. In the conventional view, as a material property, the contact angle of macroscale bubbles should be substrate dependent. But AFM studies [7] show that the contact angle of nanoscale bubbles (measured through air) is much lower than that of macroscale bubbles. Thus one would expect that the nanoscopic contact angle will be size-dependent, i.e., the contact angle of nanobubbles will increase with the increase of bubble size and will approach the macroscopic one for large enough bubbles. So far, many efforts have been made to study the dependence of contact angle on the size of surface bubbles [5,7,31,35–38]. Table 1 shows a brief summary of studies regarding the dependence of contact angle on the bubble size. First, for the dependence of contact angle on curvature radius ((Rc )), Borkent et al. [7] concluded that contact angle (measured through water, before tip correction) decreases with an increase of the curvature radius of bubbles. But such a dependence changes dramatically after tip correction: the contact angle keeps constant within the experimental error. Similarly, other studies have reported that the contact angle on the hydrophobic surfaces does not change with radius [5,35,38] while changes slightly on the hydrophilic surface [38]. However, Van Limbeek [37] investigated 7 different types of gas, and found that the contact angle (measured through water) increased with the curvature radius of nanobubbles for all gas types they studied, which are opposite to the results of Borkent. In addition, a recent numerical study of Grosfils [39] validated the gas-dependency results of Limbeek. Secondly, for the dependence of contact angle on lateral size ((2r)), Kameda and Nakabayashi [36] found that the contact angle increased with the increase in the radius of three-phase contact line (when lateral size ∼100 nm), which agrees with the results of Yang et al. [31]. In contrast, for the bubbles in smaller size range (lateral size ∼20 nm), an adverse trend was obtained, and a probable reason for this was thought to be the effect of line tension [36]. The previous studies discussed above show that it is still undefined whether the contact angle of surface bubbles is size-dependent or not. In addition, it should be noted that most of the previous works focused on the surface bubbles with nanoscale (Table 1). So it is significant to investigate the relationship between the contact angle and the bubble size in large size scale. The line tension is usually taken into account in the study of the relationship between the size and the contact angle of surface bubbles [31,33,36,37]. The line tension was defined as the excess energy per unit length of the three-phase contact line [40]. The sources of the excess energy of the contact line were thought to be 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 transition zone and also from the local interfacial deformations in this zone caused by the surface forces [40]. The effect of line tension will lead to a reduced contact angle of surface bubbles in nanoscale as compared with the macroscopic contact angle in the transition zone [40], as can be seen in Fig. 1. The difference between the nanoscopic and macroscopic contact angle which is linked to the effect of line tension can also be explained by the modified Young’s equation [31,41], that is cos = cos Y −
lg r
(1)
where Y is Young contact angle, lg is the liquid–gas surface tension, r is contact line radius which is equal to the reciprocal of the geodesic curvature and is the line tension. The range of Young contact angle is less than 90◦ measured through air for the bubbles formed on the hydrophobic substrates [7], so cos Y > 0. If the sign of is negative, together with positive surface tension lg and contact line radius r, then the contact angle calculated by Eq. (1) will be a reduced one as compared to the Young contact angle Y . This means that the negative line tension should be responsible for the anomalously low contact angle. On the basis of the Laplace–Young’s equation, the smaller contact angle means the lower inner pressure of the surface bubbles with the same base radius and thus means a longer lifetime. At the same time, the negative line tension can contribute to the three phase contact line pinning by balancing the surface tension. The pinned contact line which has been proved in 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 of the previous studies was negative [31,33,37]. Although Kameda and Nakabayashi [36] calculated a positive line tension for bubbles with
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Table 2 Root-mean-square (RMS) roughness of seven different substrates. Substrate
1
2
3
4
5
6
7
RMS (nm) Scan area (m2 ) Speed (rpm) Spin coater
0.58 5 5000 a
0.72 5 4000 a
1.14 5 3000 a
1.73 5 5000 b
2.67 5 4000 b
3.01 5 3000 b
3.16 5 3000 b
Spin coater a (TA-280, China): the wafer was held on a vacuum chuck by a vacuum suction force when spin coating; Spin coater b (TB-610, China), the wafer was fixed on a holder with spring clamps when spin coating.
lateral size less than 20 nm, which is consistent with Li’s theoretical prediction [43], i.e., the line tension should be positive for a drop with the radius of contact line approaching to zero. When the surface bubbles have the lateral size larger than 20 nm, the line tension calculated in Kameda’s work changes to be negative. Considering the lateral size of surface bubbles imaged in most of the previous studies were always less than 2 m. Therefore, it is also significant to investigate whether the line tension of surface bubbles can remain negative for bubbles in large size scale or not. In this work, we investigated surface bubbles formed on Polystyrene (PS) films with a roughness range from 0.58 nm to 3.36 nm, in water by using AFM. The big microbubbles were imaged on the rougher substrates with surface roughness of 3.11 nm and 3.36 nm. The possible nucleation reasons and features of the big microbubbles were investigated. We have also addressed the question “How does the contact angle depend on the surface bubble size” in a larger bubble size scale (200 nm to 13 m), including the dependence of contact angle on lateral size (2r), the dependence of contact angle on height (h) and the dependence of contact angle on curvature radius (Rc ). In addition, the effect of line tension on the imaged surface bubbles was investigated. 2. Experimental 2.1. Substrate/water The silicon (1 0 0) substrates coated with PS film were prepared by spin coating PS (molecular weight 350000, Sigma–Aldrich) solution with a concentration of 0.50% (weight) at a speed of 3000 rpm, 4000 rpm and 5000 rpm. To obtain the substrates with different surface roughness, two spin coaters were used. For one spin coater (TA-280, China), the Si wafer was held on a vacuum chuck by a vacuum suction force when spin coating. For the other spin coater (TB-610, China), the wafer was fixed on the holder with spring clamps. Seven substrates were produced, as shown in Table 2. Before spin coating, the silicon wafers (dimension 1.0 cm × 1.0 cm) were cleaned in a sonication bath of strong sulfuric acid and hydrogen peroxide solution (weight ratio 3:1) for 30 min, followed by acetone for 30 min and purified water for 10 min and subsequently blew to dry with nitrogen for use. Water was purified using a MilliQ A10 system with resistivity of 18.2 M cm, and before use, about 50 mL of water was allowed to equilibrate in air for hours in a stainless steel container which had a volume of 100 mL, then a drop of water was injected into the liquid cell using a glass syringe for imaging. 2.2. Atomic force microscopy (AFM) Tapping-mode AFM (NTEGRA platform, NT-MDT Company, Zelenograd, Moscow) was used to image the silicon substrate coated with PS film in both air and purified water. When imaging in water, the substrate was immersed in the water, completely, in a fluid cell with a maximum volume of about 1 mL. Rectangular cantilevers (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 spring constant k = 0.51 ± 0.02 Nm−1 obtained based on the model of Cleveland et al. [44]. The measured resonance frequencies of the cantilever, with a lock-in amplifier (SRS 830), were about 66 kHz in air and about 21 kHz in the experimental water. When the experiments were carried out, more than five different scan locations were chosen, both the height and phase images were recorded simultaneously with the amplitude set point of 95% and scanning rate of 0.5 Hz. The free amplitude A0 (nA) was obtained from amplitude phase distance curves recorded before and after each captured height image [7,16,30]. It was recalculated into nanometers by multiplying the deflection sensitivities, and a typical value of free amplitude was A0 = 3.5 ± 0.2 nm. The ambient temperature was kept at 25 ◦ C, and for each experiment, all samples were imaged in air before imaging in purified water. The height image of substrate6 (refer to Table 2) on which the big microbubble was imaged firstly is shown in Fig. 2. The PS film thickness of substrate-6 was determined by AFM nanoshaving [3], and the average film thickness on scratch profile measurement was 80 ± 2 nm. To avoid contamination, a clean experimental system needs to be kept, the fluid cell, glass pedestal and clip spring should be wiped with a pileless tissue and then rinsed with ethanol and water for several times before use. The NT-MDT SPM software (Nova), grain analysis, was used for analyzing the number, the volume and the projected area of surface bubbles. 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 their nucleation, we studied surface nanobubbles formed on PS films with different surface roughness. Fig. 3 shows the tapping-mode AFM images of surface bubbles at PS film (substrate-6)/water interface. In Fig. 3a, a number of surface bubbles were imaged, and most of them were in micrometer size, even there was a unique big surface nanobubble with lateral size exceeding 10 m. To study the big microbubble, we readjusted the scan location. Keeping the amplitude set-point at 95%, the big microbubble was rescanned at time intervals of 10 min and the images are shown in Fig. 3c. The cross sectional analysis of the big microbubble in the
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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 of relatively 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 corresponding phase 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 phase image (g) shows big microbubbles formed on another rougher PS film (substrate-7). Image (h) shows the section analysis of the big microbubble in image (a) and image (c). Image (i) shows the correlation function of bubble lateral size versus height for bubbles in image (a) and image (f).
successive scans is shown in Fig. 3h. It can be noted that the lateral size of the big microbubble changes from 10 m to 13 m and height increases from 370 nm to 400 nm in the successive scans. The possible reason should be other invisible smaller bubbles merged into the big microbubble in the course of scanning. This is similar to the results of our recent study [30] and can be proved by the following coalescence phenomenon of bubbles, as can be seen in Fig. 3b’ and d. The bubble b1 and b2 in Fig. 3b’ were moved and began to merge into the big ones at the site 1 and 2 in Fig. 3d. Fig. 3f shows the surface bubbles formed on another rough PS film (substrate-7)/water interface. More than 10 surface bubbles with lateral size exceeding 5 m were imaged. This indicates that the formation of big microbubbles on rougher surface is not occasional. To further investigate the morphology of the big microbubbles, the correlation function of the bubble lateral size
versus the height for the microbubbles imaged in Fig. 3a and f is provided in Fig. 3i, showing a linear relationship which is consistent with the results of surface bubbles in nanoscale in the previous study [7]. 3.2. The influences of surface roughness on interfacial bubbles Previous experimental studies showed that roughness can cause nanobubble formation in the concave areas which are unfavorable for the water to penetrate, resulting in a gas cavity and nanobubbles with lower curvature and thus greater stability [17]. The surface nanobubbles formed on rough surfaces were often larger and less densely distributed than those on a smooth surface with similar hydrophobicity [31]. In order to investigate the influences of surface roughness on surface bubbles, experiments were carried
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out on 7 substrates with different surface roughness. Substrate-6 and 7 were imaged before and the required data was obtained as mentioned in the discussion above. The height and corresponding phase images of the rest of 5 different substrates are presented in Fig. 4, from which the relevant statistical data of surface bubbles was obtained. Table 3 shows the effect of surface roughness on the morphology of surface bubbles. Lm and Hm are the average lateral size and average height of surface bubbles, respectively, while Vm and Am are the average volume and average projected area of one surface bubble. Nm , Vt and At are the average number, the total volume and the total projected area of nanobubbles in the area of 1 m2 , respectively. To assure the statistical significance of surface nanobubbles, the data of all the parameters were obtained on five locations. Table 3 shows that increasing the surface roughness, increases the average lateral size Lm , the average height Hm , the average/total volume and the average/total project area of surface bubbles. Also, for the surface bubbles on relatively smoother substrates (substrates 1, 2 and 3), an increase in the average number of bubbles Nm was found. However, for the surface bubbles on relatively rougher substrates (substrates 4, 5, 6 and 7), the average number Nm showed a dramatic decline with increasing surface roughness. Such a result is similar to that of Yang et al. [31] and Bhushan [45]. The increase of Nm may be because there are more concave areas on the surface with higher roughness (for substrates 1, 2 and 3), which can provide more nucleation sites for surface bubbles formation. The decrease in the average number Nm on rougher substrates (substrates 4, 5, 6 and 7) might be due to the nucleation of microbubbles and the coalescence of surface bubbles. Furthermore, polystyrene is negatively charged in water, increasing the PS surface roughness can increase the surface area and then leads to a change in surface charge. Bhushan et al. [46] studied the effect of charge on surface nanobubbles in pure water by shooting negative charges at smooth PS film with an anti-static gun, and found an increase in the bubble number and a decrease of the bubble diameter. Therefore, the change of surface charge with the increasing surface roughness will also influence the formation and the morphology of surface nanobubbles. However, the effect of surface charge related to surface roughness on surface bubbles is complicated, and further study is needed. Now, how to explain the nucleation of the big microbubbles? On the basis of the analysis of our experimental results discussed above, the high surface roughness can favor the formation of the micro bubbles. Moreover, other surface properties, such as the inhomogeneity, scratches or conical pits of PS film on silicon substrate can also influence the formation of big bubbles. The conical pits favor the bubble nucleation by allowing the capillary induced cavitation, as found by Lubetkin [47] and Wilt [48]. Atchley and Prosperetti [49] studied the crevice model for heterogeneous nucleation of bubbles in water and gave some numerical examples to illustrate the complex behavior of nucleation. Therefore, the crevices on rough surfaces should be responsible for the nucleation of the big microbubbles. Of course, the coalescence phenomenon of surface bubbles shown in Fig. 3 indicates that bubble coalescence should be another important reason for the formation of big surface bubbles. 3.3. Contact angle as a function of size The imaging of large microbubbles provides us an opportunity to investigate the relationship between contact angle and bubble size in a larger size range. To calculate the geometrical parameters of surface bubbles, methods developed and described in previous works were applied [7,28]. As shown in Fig. 5, the apparent lateral size 2r , height H were determined firstly, then the apparent
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).
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Table 3 Effect of surface roughness on the morphology of surface bubbles.
RMS (nm) Nm Lm (nm) Hm (nm) Vt × 106 (nm3 m−2 ) Vm × 106 (nm3 ) At (m2 · m−2 ) Am (m · m)
Substrate 1
Substrate 2
Substrate 3
Substrate 4
Substrate 5
Substrate 6
Substrate 7
0.58 1.1 ± 157 ± 26.3 ± 1.5 ± 1.37 ± 0.036 ± 0.033 ±
0.72 2.7 ± 216 ± 28.6 ± 5.8 ± 2.15 ± 0.130 ± 0.048 ±
1.14 3.0 ± 265 ± 36.7 ± 11.7 ± 3.89 ± 0.255 ± 0.085 ±
1.73 0.35 ± 581 ± 83.8 ± 14.2 ± 47.3 ± 0.121 ± 0.404 ±
2.67 0.17 ± 1521 ± 93.5 ± 21.8 ± 128.3 ± 0.141 ± 0.81 ±
3.01 0.13 ± 1607 ± 118.2 ± 24.2 ± 186.4 ± 0.153 ± 1.18 ±
3.16 0.09 ± 1780 ± 167.8 ± 74.4 ± 826.5 ± 0.40 ± 4.48 ±
0.1 1 0.2 0.1 0.01 0.003 0.002
0.1 1 0.3 0.2 0.01 0.005 0.002
0.1 1 0.5 0.4 0. 01 0.008 0.002
0.05 2 0.9 0.2 0.1 0.002 0.002
0.01 5 1.1 1.3 0.1 0.01 0.01
0.01 6 1.5 2 0.1 0.001 0.01
0.001 7 2.1 0.8 0.1 0.005 0.01
Table 4 The values of line tension of surface bubbles on seven different substrates.
Range of bubble size (nm) −/lg (nm) (nN)
Substrate 1
Substrate 2
Substrate 3
Substrate 4
Substrate 5
Substrate 6
Substrate 7
198–473 50.4 −3.63
233–888 14.5 −1.04
220–1208 6.8 −0.49
257–2237 2.34 −0.17
1093–3617 4.41 −0.31
1482–11180 15.18 −1.1
1366–13182 10.78 −0.78
curvature radius Rc = (r 2 + H 2 )/2H, curvature radius Rc = Rc − Rt ,
three-phase contact line radius r = 2Rc H − H 2 and contact angle = 2 arctan (H/r) were calculated. The symbols with seven different shapes and colors in Fig. 6 refer to different RMS values of the seven substrates, on which the resided surface bubbles derives from the experimental results above (including Figs. 4a–e and 3c,g). The lateral size of bubbles formed on seven substrates ranges from 198 nm to 473 nm, 233 nm to 888 nm, 220 nm to 1208 nm, 257 nm to 2237 nm, 1093 nm to 3617 nm, 1482 nm to 11,180 nm and 1366 to 13,182 nm respectively. The corresponding contact angles are in the range of 9.6–31◦ , 3.8–27.7◦ , 3.4–13.3◦ , 3.7–8.4◦ , 4.2–8.1◦ , 2.9–8.5◦ and 2.2–7.0◦ . In each independent size scale, the contact angle of surface bubbles has a clearly increasing tendency with the increase of their lateral size (shown in Fig. 6a) and heights (shown in Fig. 6b). This is consistent with the results of on Rc (before tip corrected) reported by Borkent et al. [7], which are suggesting that the contact angle of surface bubbles in nano/micro scale has a tendency toward a macroscopic value as the lateral size/height of the bubbles increases. In more detail, the first two sets of data (RMS = 0.58 nm, 0.72 nm) of (2r) in Fig. 5a and (H) in Fig. 5b are linear, but the other five sets of data (RMS = 1.14 nm, 1.73 nm, 2.67 nm, 3.01 nm and 3.16 nm) are nonlinear. The dependence of (2r) and (H) remains constant with the increase of bubble size, which 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 different size scale in Fig. 6a and b, there shows a marked decline of the contact angle with the increase of roughness. The bubbles formed on substrate-6 and 7 (RMS = 3.01 nm and 3.16 nm respectively) are larger than that formed on other five substrates.
Fig. 5. Sketches of surface bubble on PS/water interface.
However, the corresponding contact angle of bubbles formed on substrate-6 and 7 is much smaller than that of bubbles formed on any other five substrates. This indicates that although the contact angle of bubbles could be size-dependent in each independent size scale, there is no evidence that the contact angle of nanobubbles can approach the macroscale one with the increase of bubble size. 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), the dependence of on Rc shows a similar trend as that in Fig. 6a and b. In contrast, for the bubbles on relatively smoother substrates (RMS = 0.58 nm and 0.72 nm), the contact angle decreases as the curvature radius increases. This dependence of on Rc is in matching with the results of van Limbeek [37]. Our results regarding the direction inversion in the dependence of as function of Rc in different size scale are consistent with the results (2r) reported by Kameda [36], which can attribute to the effect of the line tension. On the basis of Eq. (1), the line tension of surface bubbles can be estimated. The relationship between cos and 1/r in our works can be obtained through the curves in Fig. 6a, which would lead to seven straight lines with corresponding slopes of −(/lg ) as shown in Fig. 7. Thus the corresponding line tensions can be calculated, as shown in Table 4. All of the seven line tension values for the seven sets of bubbles are negative which can tend to expand the three-phase contact line and is expected to balance the surface tension that leads to the bubble shrinking, and thus stabilize 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 the form proposed by Brenner and Lohse [26]. Other reported values similar 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 surface nanobubbles between different substrates (bubbles on substrate 1–4) decrease with the increasing bubble size, which might indicate that the effect of line tension is weakened gradually, however, for the larger microbubbles on substrate 5, 6 and 7, such a trend is broken. The possible reason to this could be not considering the effect of surface roughness and heterogeneity which can corrugate the contact line of larger bubbles. Furthermore, replacing the geodesic curvature of larger surface bubbles with the reciprocal of base radius r is also incorrect. Therefore, besides the error induced from the calculation of Rc = (r 2 + H 2 )/2H, the influence of surface properties, the larger bubble size, line tension, even the contamination may be responsible for the inversion in direction of the (Rc ) dependence.
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Fig. 7. The relationship between cos and 1/r. The inset is the magnification of the upper left rectangle region with dotted line.
4. Conclusions We have investigated the surface bubbles formed on PS film with different surface roughness. The big surface microbubbles with lateral 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 in tapping mode at a set-point ratio of 95%. To investigate the possible reasons of the big microbubble nucleation, experiments were carried out on 7 PS substrates with different surface roughness. We concluded that bubble coalescence, surface roughness and other surface properties, such as the inhomogeneity and concave pits are the significant factors affecting the size of surface bubbles. The increased surface roughness is usually leading to increased bubble size. Further, we have investigated the contact angle of surface bubbles on PS surface and how does the contact angle of surface bubbles rely on the bubble size in the range of 200 nm to 13 m. We found that the contact angle of bubbles on PS surface is in the range of 2.2–31◦ , which is much less than the macroscopic contact angle (about 85◦ measured through air) [7]. In addition, the contact angle has a linearly increasing tendency for small bubbles and nonlinearly increasing tendency for large bubbles with the lateral size 2r and the height H in each independent size range. An obvious decline between different size ranges with their lateral size and height increase was also observed. With regard to the (Rc ) dependence, an inversion in direction was observed for the bubbles in small size scale and large size scale. This might be caused by the error in calculating the morphology of bubbles, the influence line tension and surface property. The line tension of bubbles in our experiments was calculated from seven sets of bubbles and all of the seven line tension values are negative (the average line tension was equal to ≈ −1.07 nN), which should be responsible for the abnormal low contact angle and contribute to the pinned contact line, and thus contribute to the stability of surface bubbles. Acknowledgements 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 angle on curvature radius (Rc ), respectively. The insets in image (a) and image (c) are the magnification of the corresponding rectangle region with dotted line (error bars correspond to one standard deviation). (For interpretation of the references to color in text, the reader is referred to the web version of the article.)
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