Coalescence and Stability Analysis of Surface Nanobubbles on the

May 12, 2014 - Our analysis shows that a reasonable explanation should be an influx of gas into the bubble caused by the depinning of the contact line...
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Coalescence and Stability Analysis of Surface Nanobubbles on the Polystyrene/Water Interface Dayong Li,*,†,‡ Dalei Jing,† Yunlu Pan,† Weijie Wang,† and Xuezeng Zhao† †

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

‡

S Supporting Information *

ABSTRACT: In this article, we have studied the surface nanobubbles on polystyrene (PS)/water interfaces using tapping mode atomic force microscopy (TM-AFM). Detailed bubble coalescence phenomenon of differently sized surface nanobubbles (with lateral size up to about ∼10 μm) was obtained. The quantity of gas molecules, before and after coalescence, was calculated. It was found that after coalescence the quantity of gas molecules was increased by approximately 112.5%. The possible reasons for this phenomenon were analyzed and discussed. Our analysis shows that a reasonable explanation should be an influx of gas into the bubble caused by the depinning of the contact line and the decrease in the inner pressure during bubble coalescence. The factors affecting the coalescence speed of surface bubbles were also discussed. It was found that the coalescence speed of larger bubbles is usually slower than that of the smaller ones. We also noticed that it is uncertain whether a larger or smaller bubble will move first to merge into others. This is due to the combined effects of the contact line and the surface properties. Furthermore, the temporal evolution of surface bubbles was studied. The three-phase contact line of bubbles kept the pinning within the incubation time. This was consistent with the contact line pinning theory, based on which the theoretical lifetime of the surface bubbles in our experiments was calculated to be tb ≈ 6.9 h. This value is close to the experimental results. Meanwhile, the faster gas diffusion from the oversized bubbles after 12 h of incubation was observed and analyzed. Our results indicate that a viable stability mechanism for surface nanobubbles would be favored simultaneously by the contact line pinning, gas influx near the contact line from an interfacial gas enrichment (IGE), a thin “contaminant film” around the gas/liquid interface, and even the electrostatic effect. most promising mechanisms are contamination,15 contact line pinning,25,26 and dynamic equilibrium.27 The contamination hypothesis15 says that the nanobubbles are covered with a film of insoluble contaminants at the air/water interface, which effectively blocks the diffusion of gas. Contrary to this, Zhang et al.28 demonstrated that surfactants have no effect on the lifetime of surface nanobubbles. However, a study by Berkelaar et al.29 showed a salt film covering a bubble surface. Such a film might block gas dissolution and partially stabilize the nanobubbles. Recently, experimental1 and theoretical25,26,30 studies indicated that the pinned contact line of a nanobubble can lead to a slow dissolution rate. This conclusion is based on the assumptions that nanobubbles are pinned and that abnormally long bubble lifetimes depend on limited gas diffusion through water. Now, an important question is what will happen to gas diffusion when the contact line is depinned. This is still unclear and needs to be verified by further study. Dynamic equilibrium theory27 suggests that the gas diffusion from the top of bubbles is compensated for by a continuous

1. INTRODUCTION Surface nanobubbles are nanoscopic or microscopic gaseous domains that are formed at the solid/liquid interface. The term “nano” in nanobubble often refers only to its height and not to the diameter of the nanobubble, which is usually larger than a micrometer.1 Studies related to nanobubbles have the potential for applications in many fields, such as boundary slip in fluids,2,3 froth flotation,4 protein adsorption,5 and immersion lithography.6 Various experimental techniques such as rapid cryofixation,7 neutron reflectometry,8 the quartz crystal microbalance technique,9 direct optical visualization10,11 and the AFM12−21 measurement method have been widely used to study surface nanobubbles. As compared to other techniques, AFM has been excessively used and has become the standard technique for measuring surface nanobubbles due to its ability to investigate the morphology of nanoscale objects in liquids. So far, many important features of nanobubbles have been studied using TM-AFM. Recently, another technique called peak force tapping mode AFM (P FT-AFM) has also been introduced.22−24 However, a comprehensive understanding of the anomalous longevity (stability) of nanobubbles is still an open question. For the proposed surface nanobubble stability theories, the © 2014 American Chemical Society

Received: October 9, 2013 Revised: May 11, 2014 Published: May 12, 2014 6079

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dry for use with nitrogen. After being spin coated, the wafer pieces were put in a culture dish and left in an oven for 5 h at 50 °C. In our experiments, pure water was used as the liquid which was purified using a Milli-QA10 system (18.2 MΩ cm). Before imaging, about 50 mL of water in a stainless steel container was allowed to equilibrate at atmospheric pressure for several hours to ensure gas saturation. A glass syringe was used to inject water (about 0.8 mL) into the liquid cell (with a sample installed). 2.2. Atomic Force Microscopy (AFM). TM-AFM (NTEGRA platform, NT-MDT Company, Zelenograd, Moscow) was used to image the PS-coated silicon both in air and purified water. Rectangular cantilevers (CSG30, NT-MDT Company) with spring constants of k = 0.13−2 N m−1 (actual spring constant k = 0.68 ± 0.02 N m−1 determined by the resonance frequency method42) were used. The measured resonance frequencies of the cantilever in air and water, with a lock-in amplifier (SRS 830), were about 65 and 21 kHz, respectively. The typical radius of curvature of the tip was Rt = 15 ± 2 nm as measured by SEM imaging. For different experiments, the height images were recorded at different set-point ratios (95−87%), and the chosen set-point values were changed according to the following description. The free amplitude A0 (nA) was calculated from amplitude−distance curves recorded before and after each captured height image.43,44 It was recalculated in nanometers by multiplying the corresponding value of the deflection sensitivity, and the typical value of the free amplitude was about 3.7 ± 0.2 nm. With these necessary data, the applied force (Fa) is given by Fa = kA0(1 − sp), where sp = A1/A0 is the set-point ratio and A1 is the reduced amplitude. The alternate scanning frequencies we used were 1 and 0.5 Hz. While imaging in the liquid condition, we used an open fluid cell with a maximum volume of 1 mL. Also, a clean operation system needs to be maintained, including the fluid cell, clip spring, and glass pedestal. All of these need to be wiped with a pileless tissue and then rinsed with ethanol and pure water before use. All of the necessary precautions were taken during our experiments, and all of the experiments were performed at a room temperature of 25 °C.

influx of gas near the contact line, and thus the bubbles are stabilized. Seddon et al.31 refined the dynamic equilibrium model and proposed that Knudsen gas can provide nanobubble stability. The Knudsen model and AFM experimental study31 reported a vertical water jet at the top of a bubble with velocities of approximately 3.3 and 2.7 m/s, respectively. Petsev et al.32 developed an alternate formulation of this mechanism and concluded that nanobubbles should form only in a narrow temperature range and that their sizes should decrease monotonically with temperature. Also, the molecular dynamics (MD) simulation33,34 and experimental results8,35,36 regarding the existence of interfacial gas enrichment (IGE) seemingly support the dynamic equilibrium model. However, the particle tracing experiments11,37 did not measure the recirculation flow around surface nanobubbles, and the energy source required for dynamic gas flow is also still unclear. For the last two nanobubble stability theories mentioned above, a key factor is the three-phase contact line which is related to the morphology of surface nanobubbles. As AFM is an invasive technique, the tip−bubble interaction affects the morphology of the surface bubbles during scanning.13,24 Sometimes, the tip−bubble interaction causes the movement of surface nanobubbles or even renders bubble coalescence. Such a phenomenon has been reported in previous works,8,12,38,39 but the bubble coalescence process in the previous works is not clear because not enough and not clear enough information was provided for the bubbles which have merged together to form a larger bubble. Also, it should be noted that bubble coalescence will lead to the depinning of the three-phase contact lines. In that way, can the depinning of the three-phase contact line in the course of bubble coalescence influence the gas diffusion and provide valuable information regarding the abnormally long bubble lifetimes? To answer this question, a detailed and clear investigation of the bubble coalescence process is a requisite. In this article, surface nanobubbles on the PS/water interface were investigated by using TM-AFM. The bubble movement and detailed bubble coalescence process was imaged and analyzed. Furthermore, the quantity of gas molecules trapped in the surface nanobubbles before and after coalescence was calculated, and a correlation between the coalescence and the stability of surface nanobubbles was established. Moreover, oversized surface nanobubbles with a lateral size of about 10 μm were imaged and analyzed. The temporal evolution experiment was conducted and is the basis on which the contact line pinning theory was discussed.

3. RESULTS AND DISCUSSIONS 3.1. Imaging and Analysis of the Detailed Process of Surface Bubble Coalescence. Although the coalescence

2. EXPERIMENTAL SECTION 2.1. Sample/Water. Two samples of PS coated on 1 cm × 1 cm silicon(100) substrates with different surface roughnesses were prepared with a spin-coated PS (molecular weight 350 000, SigmaAldrich) solution with different concentrations of about 0.30 and 0.50% (by weight) at a speed of 2000 rpm. Using the TM-AFM in air, we found the root-mean-square (RMS) values over a scanning area of 5 μm × 5 μm for substrates 1 and 2 to be 1.52 and 3.37 nm, respectively. The PS film thickness of these substrates was determined by AFM nanoshaving,40,41 and corresponding values for the scratch profile measurement were 33 ± 2 and 80 ± 2 nm, respectively. The contact angle was measured with the sessile drop method. The values were about 94 ± 2° on substrate 1 and 96 ± 2° on substrate 2. Before being spin coated, the silicon(100) wafers were boiled in a sonication bath with a 3:1 mixture of concentrated sulfuric acid and hydrogen peroxide for 30 min and then acetone for 30 min and then were rinsed with ethanol and pure water (each for 2 min) before they were blown

Figure 1. Detailed process of surface bubble coalescence. Continuous scan at intervals of about 10 min and with the same set point of 95% and scan frequency of 1 Hz (image scale, 5 μm × 5 μm; height scale, 100 nm).

phenomenon of surface bubbles has been reported in previous works, so far, the detailed coalescence process has not been imaged by AFM. We have made an attempt to provide detailed information on the coalescence process using AFM. The experiments were carefully performed in order to get more reliable results. To minimize the effect of the cantilever tip on the bubble morphology, we first scanned the surface continuously at an amplitude set point of 95% and a scan frequency of 1 Hz, and then successive images were obtained at about 10 min intervals. Figure 1 illustrates the clear coalescence 6080

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A comparable result was obtained by Wang et al.,46 showing that the movability of nanobubbles deteriorated on a rough surface with island-like structures as compared to the smooth surfaces without surface structures while sometimes the larger bubbles might be found moving first and merging into other ones. This is because of the relative effect of the contact line, i.e., the ratio of the contact line length 2πRb to the projected area πRb2 of the bubbles, which is smaller for larger bubbles than that for smaller bubbles. Therefore, the surface bubble coalescence has no defined rules, and it is uncertain which bubble (big or small) will be moved first in order to merge into the other one. A good example can be shown in Figure 1, where the bubble that moved first was neither the smaller one (bubble 4 or 5) nor the largest one; rather, it was medium-sized surface bubble 2. This can also be attributed to the pinning of the contact line and surface properties. To carry out an accurate quantitative analysis of the quantity of gas molecules trapped in surface nanobubbles before and after coalescence, the geometrical parameters, consisting of the lateral size L and height H were measured first from five measurements at sections in different directions (the center cross-sectional analysis of the bubbles 1, 2 and 3′′′′ can be seen in Figure 3b), followed by the calculation of base radius Rb = L/ 2 and radius of curvature Rc = (Rb)2 + H2/2H for each surface bubble. While calculating the geometrical parameters of surface bubbles, a tip correction was adopted as mentioned in ref 44. The ideal gas law (Pi × Vi = nRT) was used to evaluate the quantity of gas molecules in the surface bubbles, where Pi is the inside pressure, Vi is the volume of the bubbles, n is the quantity of gas molecules, R(∼8.314 J/mol K) is the universal gas constant, and T (∼298.15 K) is the gas temperature. We consider the bubbles to be spherical in shape. Figure 2 shows the 3D images and the section analysis of bubbles before and after coalescence, which indicates the spherical shape of bubbles. The section analysis of bubble 1 (shown in Figure S1 in Supporting Information) in five different directions also proves the spherical shape of bubbles. For spherical-cap-shaped surface bubbles, Vi and Pi were calculated based on eqs 1 and 2

Figure 2. (a) Three-dimensional image of the bubble coalescence in Figure 1a,b,f. (b) Section analysis of the bubbles before and after coalescence with a center cross line.

process of two surface nanobubbles. Figure 1a shows the topography of surface nanobubbles obtained from TM-AFM on substrate 1 (RMS = 1.52 nm) immersed in pure water. The diameter and height of these spherical cap-shaped nanobubbles are generally on the order of ∼1 μm and ∼100 nm, respectively. Bubbles 1 and 2 in Figure 1a are two independent surface nanobubbles; however, in Figure 1b, small bubble 2 was moved and began to merge into bubble 1 and generated a new, larger bubble 3. In the scans shown in Figure 1c−h, irregularly shaped bubble 3 gradually changed to a round shape. The 3D images shown in Figure 2a clearly illustrate the coalescence process of the spherical cap-shaped bubbles. Moreover, the coalescence of two smaller bubbles 4 and 5 was also captured, but they merged into bubble 3 faster than the coalescence of bubble 1 and 2 occurred, which is consistent with the findings in previous studies.12,38,39 What makes such a difference in the speed of bubble coalescence? The pinning of the three-phase contact line and the surface properties should be key factors. A recent simulation study45 has also shown that the pinning force of surface bubbles is affected by the surface properties and local structures of substrates. If a bubble is moved and merged into another one, then the pinning must first be overcome. The surface properties will influence the larger bubbles relatively more than the smaller ones due to their longer contact lines, i.e., the inhomogeneity of the surface can corrugate the contact line of larger surface bubbles and hence increases the immobility of bubbles and slows down the coalescence process.

Vi = π × H ×

3(R b)2 + H2 6

Pi = Po + ΔP = Po +

2γ 2γ = Po + sin θ Rc Rb

(1)

(2)

where Po is the outside pressure, ΔP is the pressure difference between Pi and Po, γ = 0.072 N m−1 is the surface tension of the

Figure 3. (a) AFM image of micropancakes on a PS film. (b) The cross-sectional profile of the micropancake−nanobubble composite in image (a) and the inset is the 3D image of the corresponding micropancake. (c) Force curve between the tip and micropancake in image (a). 6081

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Table 1. Parameters of Bubble Morphology and the Quantity of Gas Molecules Trapped into Surface Bubbles before and after Coalescence bubble 1 2 3′′′′ 3′′′′′ 3′′′′′′ 4 5

base radius Rbi (nm)

height Hi (nm) 72.4 28.6 96.4 96.7 96.5 8.5 7.9

± ± ± ± ± ± ±

2.3 1.7 2.9 3.0 3.0 0.83 0.78

574 279 821 823 822 132 129

± ± ± ± ± ± ±

13.9 13.1 25.6 26.1 25.7 9.3 8.8

curvature radius Rci (nm) 2316 1377 3545 3550 3549 1021 1155

± ± ± ± ± ± ±

87.5 62.3 132 135 133 45.2 47.1

pressure Pi (atm) 1.58 2.02 1.40 1.40 1.40 2.24 2.31

± ± ± ± ± ± ±

surface area Ai(× 106 nm2)

0.03 0.05 0.02 0.02 0.02 0.05 0.05

16

18

39

51

range of bubble size (nm) τ (nN)

100−500

100−500

100−800

100−600

−0.8

−0.3

−0.3

−0.2

± ± ± ± ± ± ±

0.05 0.01 0.08 0.08 0.08 0.005 0.005

37.7 3.5 102.8 103.3 102.9 0.23 0.21

± ± ± ± ± ± ±

1.7 0.5 7.1 7.2 7.1 0.01 0.01

gas molecules (Pi × Vi)/RT(× 10−18 mol) 2.40 0.29 5.80 5.83 5.81 0.021 0.020

± ± ± ± ± ± ±

0.12 0.04 0.39 0.40 0.39 0.001 0.001

quantity of gas molecules in bubble 3′′′′ is 5.8 × 10−18 mol, which is 115.6% larger than the sum of the gas molecule quantities in bubbles 1 and 2, i.e., 2.69 × 10−18 mol. It is important to note that even if the gas molecule quantity of bubbles 4 and 5, which merged into bubble 3, is considered, then the gas molecule quantity inside the bubble after coalescence is still about 112.5% higher than that before coalescence. While analyzing the stability of surface nanobubbles, the electrostatic effects are often neglected.27,30 The gas/water interfaces of bubbles are thought to be negatively charged,13,21,27,30,47 and the electrostatic effects are thought to be causing a reduction of the inner pressure of surface bubbles.21,30,47 Studies48 show that the PS surface is also slightly negatively charged in water, so by analyzing its effect on the bubbles, we assume that the charges at the liquid/solid interface (including the PS surface and other bubbles) outside the surface bubbles have the same effects on both the large and small bubbles and can be neglected, as the surface bubbles are too small compared to the whole substrate. If the gas/solid

Table 2. Relation of Calculated Line Tension and Bubble Size in Previous Studies ref

1.05 0.25 2.15 2.16 2.15 0.05 0.05

volume Vi(× 106 nm3)

water/gas interface, and θ is the contact angle measured through air. Table 1 shows the parameters of bubble morphology and the results of the gas trapped inside the surface bubbles before and after coalescence. (Here the effects of the electrostatic force, line tension, and the possibly changed surface tension caused by the presence of an impurity are not considered, and all three factors will be discussed in detail in the following sections.) We can find that the quantities of gas molecules in bubbles 3′′′′, 3′′′′′, and 3′′′′′′ are almost constant. This means that the process of bubble coalescence is complete and has reached equilibrium. Thus, the thermodynamic equilibrium in eq 2 can be used to evaluate the gas quantity for the bubble formed after coalescence. After coalescence, the

Figure 4. Influence of set-point ratios on the morphology of surface bubbles and the morphology change of these bubbles during the incubation time. (b) Magnification of the rectangular region in (a), where two oversized surface bubbles B1 and B2 were in the beginning stage of coalescence. (The image shows two oversized bubbles before coalescence, as can be seen in Figure S3 in the Supporting Information.) (a, b) Images captured at the same amplitude set point of 95% and scan frequency of 1 Hz. (c−e) Scans at a time interval of 10 min after the image in (b) was obtained, with set-point ratios of 90, 87, and 95% from (c−e), respectively, at a scan frequency of 0.5 Hz. (c−e) The change in the set point has no effect on further coalescence of the oversized bubbles. (f−h) Morphology of surface bubbles after 12 h of incubation at a time interval of 10 min with the same amplitude set point of 95%. All experiments were completed in “air-equilibrated” water at an ambient temperature of 25 °C. 6082

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Figure 5. Section analysis of (a) oversized surface bubble b2 and (b) small bubble b1 obtained from Figure 4a−h (■, ●, ★, ⧫, ○, Δ, □, respectively).

▲,

Table 3. Details from the Profiles of the Oversized Surface Bubble b2 during Incubation and the Profiles under Different Amplitude Set-Point Ratios time (h)

set point

0.25 0.42 0.59 0.76 0.94 12 12.17 12.33

0.95 0.95 0.90 0.87 0.95 0.95 0.95 0.95

height (nm) 290 305 170 150 255 31 12 10

± ± ± ± ± ± ± ±

2.2 3.5 1.7 1.5 2.0 0.8 0.6 0.5

base radius (nm) 4275 4656 4655 4653 4652 4662 4665 4663

± ± ± ± ± ± ± ±

radius of curvature (nm)

20 26 22 23 21 19 20 22

31 655 35 599 63 817 72 227 42 561 350 643 906 765 1 086 833

± ± ± ± ± ± ± ±

288 390 591 700 271 2864 7597 10 164

gas molecules (Pi × Vi)/RT (× 10−9 nmol) 351.6 419.8 233.8 206.1 350.2 42.7 16.5 13.8

± ± ± ± ± ± ± ±

2.3 17.1 6.8 5.6 2.2 0.9 0.2 0.1

softer than the smaller ones. This softness of the larger bubbles, due to the lower internal pressure, can cause a larger underestimation in the measurement of their height and volume as compared to that of smaller bubbles under the same experimental condition. Therefore, in view of the Laplace− Young equation and the scanning results, there would be an apparent decrease in the number of molecules in the newly formed larger bubble, while the decrease in the number of gas molecules is contradictory to the experimental results. Even the supposition that some smaller invisible nanobubbles might have merged into bubble 3 cannot support such a huge increase in the gas quantity. Note that contaminants have effects on the surface nanobubbles15 and special attention is paid to the introduction of impurities into the experimental system. Therefore, we assume that the concentration of some inevitable soluble impurity species in the liquid is very low, thus on the basis of the Henry isotherm model49 of Γ = KhC, where Kh is the equilibrium adsorption constant, Γ is the number of contaminant molecules per unit area adsorbed at the gas/ liquid interface of bubbles, which depends linearly on the concentration C of these soluble impurities. The surface area A = 2πRcH of newly formed bubble 3′′′′ is about 2.15 × 106 nm2 in our experiments, as shown in Table 1, which is much larger than the sum (1.4 × 106 nm2) of surface areas for the bubbles 1, 2, 4, and 5. As the surface area of bubbles increases, more impurity molecules are adsorbed from the liquid to the gas/ liquid interface. Therefore, the value of C decreases with a constant liquid volume, followed by a decrease in the value of Γ. The impurity molecules at the interface can prevent the water molecules from forming hydrogen bonds with neighboring water molecules, which leads to a reduced surface tension.50 Therefore, the newly formed bubble with a reduced number of impurity molecules per unit surface area has a larger surface tension than do bubbles before coalescence. In this case, the

Figure 6. Schematic diagrams of tip−bubble interaction (the same tip) (a) for small surface bubbles and (b) for oversized surface bubbles (scale changed).

interface is negatively charged,21 then the repulsive force between the gas/liquid and gas/solid interfaces will also lower the internal pressure of the bubbles. Unlike smaller bubbles, the larger bubbles have greater heights and thus have their gas/ liquid interfaces further from the substrate. Therefore, on the basis of the Coulomb law, there should be larger electrostatic effects on smaller bubbles as compared to those on larger bubbles. Similarly, larger electrostatic effects on the smaller bubbles should also be caused by the charges on the gas/liquid interfaces as their diameters are small. Therefore, the reduction of internal pressure caused by the electrostatic effect for smaller bubbles should be higher than that for larger bubbles. It is therefore possible that the calculated quantity (as shown in Table 1) of gas molecules using the equation Pi × Vi = nRT, for the bubble after coalescence, is an underestimation of the real values. To explain the gas increase after coalescence, we might first think about the uncertainties in the measurement of bubble volume because surface bubbles are highly deformable and the bubble height can be underestimated during imaging.13,20,43 According to the Laplace−Young equation, the larger nanobubbles would have a lower inner pressure and hence would be 6083

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the coexistence of IGE with bubbles. In particular, measurable IGE (called micropancakes) has been imaged at the perfluorodecyltrichlorosilane (PFDTS)/water interface.55 It was also imaged in coexistence with surface bubbles at the highly oriented pyrolytic graphite (HOPG)/water interface56,57 and PS surfaces.40 In our experiments, we also captured micro/ nanopancakes coexisting with nanobubbles on PS surfaces; as shown in Figure 3a, it is possible that there is more than one nanobubbles sitting on top of the micropancakes. Figure 3b shows the section analysis of nanobubbles sitting on a pancake, where the height of the micropancake is about 6 nm, which can also be judged from the force curves between the AFM tip and micropancake. In Figure 3c, the retraction curve perspicuously shows that the AFM tip is separate from the hard substrate at about 7 nm, which is followed by a soft tip−pancake interaction and then a “pull off” at about 13 nm. In the course of bubble coalescence, the relaxing of the threephase contact line, the tip−IGE interaction, and the reduction of inner pressure may lead to an influx of gas at the contact line. It should be noted that based on the analysis above, although the electrostatic effects and the changed surface tension caused by the introduction of contaminants are not responsible for the gas increase after bubble coalescence, both factors can reduce the inner pressure of bubbles and thus help the gas influx into the newly formed bubble from IGE. The gas influx from IGE is similar to the dynamic equilibrium mechanism of Brenner and Lohse,27 which states that there is an influx of gas into the bubble from the three-phase line to compensate for the gas dissolved in the water because of the large Laplace pressure. Therefore, the coexistence of nanobubbles with interfacial gas enrichment (IGE)36 should be responsible for the approximately 112.5% increase in the quantity of gas, before and after coalescence. In turn, the gas increase after coalescence can provide another important experimental proof for the coexistence of nanobubbles with IGE. Also, it can help in understanding the abnormally long life of surface bubbles. Bhushan et al.38 reported a decrease of 14.5% in the number of gas molecules after coalescence, which is opposite to our results. There are three main possible reasons for this: (1) There might be a higher underestimation of the height of the larger surface nanobubbles (after coalescence) than that of smaller bubbles (before coalescence) during imaging by TMAFM. (2) Improper tracing of the coalescence phenomenon in which the AFM images do not give enough information about the bubbles before and after coalescence, i.e., there was no clear identification of the surface bubbles which merged to form a larger bubble. Hence, this might have resulted in a miscalculation. (3) The bubble size is much smaller (325.6− 550.3 nm) than our results (558−1148 nm). Because a smaller bubble has a higher inner pressure, there is more outflux of gas expected in their case, thus causing a decrease in the quantity of gas in the course of coalescence. However, our results indicate that the depinning of the contact line due to bubble coalescence does not increase the gas diffusion; rather, it leads to an approximately 112.5% increase in the quantity of gas molecules. The coalescence images of other neighboring bubbles and the relevant calculations which support our conclusions can be shown in the Supporting Information. Please refer to Figure S2 and Table S1. Furthermore, the increase in the number of gas molecules inside bubbles before and after coalescence (shown in Table 1) clearly shows the gaseous nature of these bubbles. Thus, these results overrule the possibility of the presence of liquid droplet contaminants.

Young−Laplace equation (ΔP = 2γ/Rc) will give a larger difference in the values of ΔP for bubbles before and after coalescence. This indicates that there would be a larger difference in the quantity of the gas molecules before and after coalescence. Therefore, based on the discussion above, the 112.5% gas increase is also underestimated as compared to the real value (considering the effects of contaminants). Therefore, the question of where the extra gas quantity comes from is still unanswered. In recent works, the contact angle was thought to be sizedependent,13,16,17,39,44,51 and a possible reason was the influence of the line tension.16,39,51 Does the line tension influence the inner pressure because of the depinning of the contact line in the course of bubble coalescence, thus leading to an increase in the gas molecule quantity after bubble coalescence? To analyze this, the modified Young’s equation39 is introduced τ cos θ = cos θY − γR b (3) where θY is the Young contact angle and τ is the line tension. On the basis of eqs 2 and 3, the relation between ΔP and τ can be given as 2⎤ ⎡ ⎛ 2γ ⎞2 ⎛ 4γ 2 ⎢ τ ⎞⎥ (Δp) = ⎜ sin θY ⎟ = 1 − ⎜cos θY − ⎟ γR b ⎠ ⎥⎦ R b 2 ⎢⎣ ⎝ Rb ⎠ ⎝ 2

(4)

By calculating the first derivative of eq 4 with respect to τ, we can obtain d(Δp)2 8γ ⎛ τ ⎞ = cos θY − ⎟ 3⎜ γR b ⎠ dτ Rb ⎝

(5)

Consider that the calculated value of the line tension of surface bubbles in other studies was usually negative, as can be shown in Table 2. Also, the theoretical study52 demonstrates that the line tension of a spherical drop is always negative. We therefore assume that the line tension of surface bubbles is negative, i.e., τ < 0. The range of the Young contact angle (through air) is 0° < θY < 90°,44 so cos θY > 0. Together with a positive surface tension γ, eq 5 is positive. This means that eq 4 is a monotonically increasing function with respect to τ, i.e., ΔP increases with the increase in τ. If τ increases with the increase in bubble size as well, then the higher ΔP of larger bubbles caused by the line tension should be responsible for the increase in the gas molecule quantity after coalescence. However, previous studies (Table 2) show that there is no obvious increase in line tension with the increase in bubble size. The effects of surface properties on the larger bubbles make the calculation of the true line tension more complicated,21 and comprehensive studies are needed. Therefore, the relation of line tension to bubble size is not clear, and thus there is not enough evidence which may support that the line tension can lead to the gas increase in the bubble after coalescence. So in these cases, where does the extra 112.5% gas quantity come from? A reasonable explanation is that there is an interfacial gas enrichment (IGE) coexisting with nanobubbles. A number of theoretical33,34,53 and experimental studies8,35 have indicated that the density of water is reduced due to the accumulation of dissolved gases in a depleted layer near the hydrophobic surface. The recent force curve analysis and molecular simulation results of Nguyen et al.36,54 also support 6084

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3.2. Coalescence of Oversized Nanobubbles and Tip− Bubble Interaction. Figure 4a shows the scanned images of a rougher PS substrate, i.e., substrate 2 with RMS = 3.37 nm. It shows several oversized surface bubbles with a lateral size of up to 9.3 μm; the most prominent feature is that two oversized surface bubbles B1 and B2 are in the beginning stage of coalescence. A number of small microscale surface bubbles can also be seen. Figure 4b shows the result of a magnified rectangular region in Figure 4a (with the same amplitude set point of 95% and scan frequency of 1 Hz). Figure 4c,d show a further study of the coalescence of the two oversized surface bubbles. Successive scans were taken at a lower scan frequency of 0.5 Hz and different set-point ratios rsp = 90 and 87%, respectively, which means that an increased force was applied during scanning. However, the coalescence behavior of the oversized surface nanobubbles did not go further. This indicates that the coalescence process of oversized bubbles is more complicated, which can be influenced by other factors besides scan load and scan speed.38 In addition, implicit evidence of bubble coalescence for smaller surface nanobubbles can be shown in Figure 5a. From the section analysis of one oversized surface bubble b2 at a 95% set point, the fit curve of the first scan (■) is smaller than that of the second scan (●). This might be due to the fast merging of some nearby smaller nanobubbles into the oversized bubble during the scanning process for Figure 4b. Also, such a conjecture can be confirmed from the change in the quantity of gas molecules as shown in Table 3. The quantity for the second scan is much larger (419.8 × 10−18 mol) than that for the first scan (351.6 × 10−18 mol). The complex coalescence process of oversized surface nanobubbles and the fast emergence of the smaller invisible nanobubbles indicate again that the bubble coalescence is uncertain. The dependence of bubble coalescence on the contact line depinning, inhomogeneity of the surface, surface roughness, and surface scratches make it more unpredictable and uncertain. The deformability of the surface nanobubbles shown in Figure 5 is similar to the TM-AFM observation13,20,43 of surface nanobubbles at different set-point ratios and the PF (peak force)−AFM observations22 of the surface nanobubbles as the peak force is increased. When the set-point ratio was varied from 95 to 87%, the corresponding profiles of the oversized bubbles showed a large variation. Figure 5a shows that the bubble height of the oversized surface bubble (b2 in Figure 4b) was reduced to about a half. However, the height of relatively smaller surface nanobubble (b1 in Figure 4b) did not show a significant change with the decreasing set-point ratios, as shown in Figure 5b. This indicates that the larger bubbles are more sensitive to the applied AFM tip force. To examine the repeatability, a third scan at a 95% set point was performed after the scan at a set point of 87%. The result is close to the initial two scans taken for the smaller surface bubble b1, at a set point of 95%, but differs from those taken for oversized surface bubble b2 at the same set point. Therefore, the larger surface nanobubbles have a softer property, and the tip−bubble interaction has a larger influence on the larger surface nanobubbles than do the smaller ones. This is consistent with a recent experimental result reported by Hu et al.24 in which the stiffness of nanobubles was size-dependent and large nanobubbles had a lower stiffness. 3.3. Morphology Analysis of Surface Nanobubbles during Incubation. For a further investigation, an in situ temporal evolution experiment was carried out. To reduce the

evaporation of water in the liquid cell and keep the gas concentration approximately constant, during the incubation time we covered the AFM system with a sealed mask. (A diagram of the AFM system covered with a sealed mask can be seen in Figure S4 in the Supporting Information.) It is particularly noteworthy that there is enough space in the mask to ensure an ambient air interface for the AFM tip and water and thus ensure air-equilibrated water. Figure 4f shows the height images scanned at an amplitude set-point ratio of 95% after 12 h of incubation in air-equilibrated water. The height of small bubbles (an example is bubble b1 in Figure 4b) did not change considerably, which can be seen from the section analysis of b1 in Figure 5b. However, the heights of the oversized bubbles showed a drastic decrease in Figure 4f and nearly disappeared in the following scans as shown in Figure 4g,h. The same results also can be seen from the fit curves of one oversized bubble b2 (in Figure 4b), shown in Figure 5a, which again clearly shows the gaseous nature of these bubbles. Table 3 shows the detailed size information on oversized bubble b2 within the incubation time. An outstanding feature that can be seen in Table 3 is that the bubble height was reduced dramatically with time while the lateral size remained almost constant. Interestingly, the pinned contact lines of the oversized bubbles, in the incubation time, can be seen clearly in Figure 4e−h, which provides visible supporting proof of the pinning and dissolution theory of Weijs et al.30 If the nanobubbles were pinned, then the lifetime of surface bubbles tb can be characterized as the time scale of gas diffusion through the water layer, i.e., tb = l2/D, where D is the diffusion constant of the gas in water and l is the thickness of the liquid layer. The height of water in the liquid cell is about 5 mm as used in our experiments, and with a typical value of D = 10−9 m2/s,30 we can obtain the theoretical lifetime of the surface bubbles tb ≈ 6.9 h. Compared to previous estimates of microseconds,19,27 this value is close to the lifetimes of bubbles obtained in experiments. However, it is still less than the lifetime of several days58 and even less than the shortest lifetime (12 h) of the oversized bubbles observed in our incubation experiments. Therefore, besides the effect of contact line pinning, the superstability of surface bubbles should be affected by other factors simultaneously. Why did the oversized bubbles shrink so much faster than small surface bubbles within the incubation time? The larger bubble has a lower inner pressure and hence should have a slower gas diffusion and longer lifetime. Also, this is opposite to the Ostwald ripening,1 which indicates that the larger surface nanobubbles should be expected to grow with time at the expense of the smaller bubbles. A good explanation of this could be that the tip−bubble interaction breaks the protective film, as mentioned in the impurity hypothesis of Ducker,15 and causes fast diffusion from the nanobubbles to the water. If there is indeed a film at the gas/water interface of surface nanobubbles, then how could the oversized surface bubbles be punctured by the AFM probe tip? On the basis of the capillary force model of Holmberg et al.,59 the tip−bubble interaction can be indicated, and the total interaction force along the vertical direction between the cantilever tip and bubble is Ft = 2πrt γ cos α cos(α + β). As shown in Figure 6a, α is the angle between the vertical direction of the tip and the tangent to the contact line where the tip and the bubble interact, β is the contact angle with a typical value of 4°,59 rt is the radius of curvature of the probe tip, and γ refers to the surface tension of the liquid/gas interface. As the probe tip snaps in, α decreases 6085

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from Ft to cantilever tip angle φ, and the tip−bubble interaction force Ft increases with the decrease in α. Since the contaminant adsorption at the water/gas interface will decrease the surface tension, here we assume a value of γ = 0.05 N m−1, which is a decrease of more than 30% of the value of pure water and implies relatively heavy contamination. When α reaches the minimum value, a maximum value of Ft ≈ 4.2 nN will be obtained for a tip with rt = 15 nm and a specified side angle (half) of φ = 18 ± 2°. Actually, this value should be underestimated if the electrostatic effects are considered. Because there are negative charges on the gas/liquid interface and if the gas−solid surface is negatively charged,21 then the tip will endure the repulsive force from the electrostatic effects during the tip−bubble interaction and thereby the maximum value of the tip−bubble interaction force Ft should be larger than 4.2 nN. Keeping in view the discussion regarding the effect of contaminants on bubbles before and after coalescence, for the soluble contaminant species the quantity of adsorbed contaminants per unit area of the newly formed bubble gets smaller than that of bubbles before coalescence. This means that after coalescence the contaminant layer gets thinner, making gas escape easier. Also, a thinner contaminant layer can be easily punctured. As discussed above, the fewer impurity molecules per unit area, the higher the surface tension and thus the larger the tip−bubble interaction force Ft. Therefore, to analyze the tip−bubble interaction qualitatively, the bubbles after coalescence would be covered with a thinner contaminant film and the oversized bubbles would endure a larger acting force because of their larger height and the relatively larger surface tension. Therefore, the oversized surface bubbles are likely to be punctured by the AFM probe tip. A schematic diagram of tip−bubble interaction (not to scale) for the oversized bubbles is shown in Figure 6b, and that for the smaller bubbles is shown in Figure 6a. From the section analysis of relatively small bubble b1 (in Figure 4b), with a lateral size of about 3 μm (shown in Figure 5b), if its film was punctured then the air leakage will be faster than that of oversized bubble b2 because of the higher inner pressure. Unlike this, the gas diffusion of bubble b1 was obviously slower than that of b2 as shown in Figures 4 and 5 and Table 3. Furthermore, with the gas diffusion, the oversized bubbles become softer and softer. So keeping in mind the results obtained, another reason for the instant decay of the oversized bubbles might be the larger influence of the tip−bubble interaction on the morphology of the bubbles. In the work of Yang et al.,22 they concluded that the protective film theory was not consistent with their force measurements. According to their work, while imaging the nanobubbles with a high loading force, if there is a film to prevent gas from leaking out of the surface bubbles, then the tip should break the film and lead to instant gas dissolution from the surface bubbles. A similar conclusion was also found in the study of Hu et al.24 However, the lateral size of the surface nanobubbles measured in their study was ∼2 μm, and the force acting on the nanobubbles in their measurements was ∼2000 pN, which is less than half of the maximum value, i.e., 4.2 nN, as mentioned above. Also, it should be noted that in their study the nanobubbles disappeared completely due to the property of reversible deformation (the bubbles reappeared at a peak force of 200 pN22) at peak forces of 125022 and 2000 pN.24 This means that the tip has already reached the substrate and the tip−bubble interaction has changed to be the tip−substrate

interaction. In this case, the real tip−bubble interaction force should be less than 1250 22 and 2000 pN24 in their measurements. Thus, the protected film of surface bubbles can remain intact during the tip−substrate interaction.

4. CONCLUSIONS In this study, surface nanobubbles were imaged using TM-AFM on PS/water interfaces. The lateral size was in the range of 100 nm to about 10 μm, and the height was in the range of 10 nm to about 300 nm. The coalescence of different-sized surface nanobubbles was studied, and a detailed bubble coalescence process was imaged. The presented findings and previous AFM observations reveal that the occurrence of bubble coalescence is complex. In addition to the well-known parameters of scan load and scan speed, the pinning of the contact line and surface properties are also important parameters which affect the coalescence of surface nanobubbles. The larger bubbles usually have a slower coalescence process than the smaller ones due to their longer contact lines which are affected more by the surface properties. On the basis of the AFM imaging of the detailed nanobubble coalescence process, a quantitative calculation of gas molecules trapped in bubbles before and after coalescence was carried out. After coalescence, an increase of approximately 112.5% in the quantity of gas molecules was found, which provides more experimental proof for the coexistence of nanobubbles with interfacial gas enrichment (IGE). Furthermore, a temporal evolution experiment for the surface bubbles in air-equilibrated water was performed. Within the incubation time, the three-phase contact line of bubbles remained pinned. This was in accordance with the pinning and dissolution theory,30 based on which the lifetime of the surface bubbles in our experiments was calculated to be tb ≈ 6.9 h. This value is similar to the lifetime observed in experiments, but there is still a difference with respect to the experimental research conducted for several days. In addition, the fast gas diffusion of the oversized surface nanobubbles was discussed. A possible explanation of this is that a hypothetical film at the gas/water interface of bubbles existed and that the film was punctured under the large acting force, thus causing the fast diffusion of gas into water. In short, our results indicate that a viable stability mechanism for surface nanobubbles would be favored simultaneously by the contact line pinning, the gas supplement from an IGE, a thin film around the gas/liquid interface (the schematic diagrams of this stability mechanism are shown in Figure 7), and even an electrostatic effect. The pinning of the contact line,

Figure 7. Schematic diagrams of the stability of surface bubbles. The abnormally long life of surface bubbles would be favored simultaneously by the pinned contact line, the gas influx from the contact line, and a protective film around the gas/water interface. 6086

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the protected film, and the electrostatic effect can lead to a slow gas dissolution rate, and the influx of gas from IGE can compensate for the outflux of gas, thus prolonging the lifetime of bubbles. Of course, the stability mechanism of nanobubbles is very intricate, and we hope our experimental results will be helpful in understanding the properties and the stability of surface nanobubbles.

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ASSOCIATED CONTENT

S Supporting Information *

Section analysis of bubble 2 (in Figure 1a) in five different direction. Coalescence of other neighboring pairs of bubbles and the relevant calculation of gas molecules trapped in bubbles before and after coalescence. Two oversized bubbles B1 and B2 before coalescence in Figure 3a. Diagram of the AFM system covered with a sealed mask. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Khurshid Ahmad for helpful discussions. REFERENCES

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