Article Cite This: Langmuir 2019, 35, 8482−8489
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Stability of Surface Nanobubbles without Contact Line Pinning Zhenjiang Guo,† Xian Wang,† and Xianren Zhang* State Key Laboratory of Organic−Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China
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S Supporting Information *
ABSTRACT: Although the stability of most surface nanobubbles observed can be well interpreted by contact line pinning and supersaturation theory, there is increasing evidence that at least for certain situations, contact line pinning is not required for nanobubble stability. This raises a significant question of what is the stability mechanism for those sessile nanobubbles. Through theoretical analysis and molecular dynamics simulations, in this work, we report two mechanisms for stabilizing surface nanobubbles on flat and homogeneous substrates. One is attributed to constant adsorption of trace impurities on the nanobubble gas−liquid interface, through which nanobubble growing or shrinking causes the increase and decrease of interfacial tension, acting as a restoring force to bring the nanobubble to its equilibrium size. The other is attributed to the deformation of a soft substrate induced by the formed nanobubble, which in turn stabilizes the nanobubble via impeding the contact line motion, similar to self-pinning of microdroplets on soft substrates. Both mechanisms can interpret, depending on the specified conditions, how surface nanobubbles can remain stable in the absence of contact line pinning.
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INTRODUCTION The mechanism for the unexpected stability of nanobubbles is central to their potential applications,1,2 including water recovery,3,4 flotation,5,6 detection in analytical chemistry,7,8 and promoting growth of plants and animals. 9 The experimentally confirmed existence of surface nanobubbles that appear on solid substrates immersed in solvent has invoked numerous studies on their extraordinary stability. Although several models have been proposed,10−20 the stability of most of the observed surface nanobubbles can be interpreted well by contact line pinning14−16 and supersaturation theory,12,13 which suggest that under a gas supersaturation environment, surface nanobubbles become stable if their contact lines are pinned by the geometric or chemical inhomogeneity of substrates. The needed contact line pinning for stable nanobubbles has been repeatedly verified both experimentally14 and theoretically,12 resulting in the most extraordinary properties of surface nanobubbles. However, there is increasing evidence that at least for certain situations, contact line pinning is not required for nanobubble stability.21−26 An et al.24 found that nanobubbles on PFOTS surfaces were very mobile under the mechanical disturbance exerted by an AFM cantilever, showing that the bubbles were not strongly pinned by the substrates. In particular, Bull et al.22 © 2019 American Chemical Society
observed that unlike on rigid solid surfaces, surface nanobubbles could be formed randomly on homogeneous substrates covered by copolymer brushes, suggesting that the contact line pinning caused by physical roughness or chemical inhomogeneity of surfaces is not necessary for nanobubble stability. Thus, those findings raise a significant question: is contact line pinning always required for nanobubble stability? If not, what is the stability mechanism for those sessile bubbles when contact line pinning does not seem to be present? Here we try to answer these questions. On the basis of theoretical analysis and computer simulations, we report two possible mechanisms for nanobubble stability when substrates initially seem to be flat and homogeneous: (i) constant adsorption of trace impurities (typically small organic molecules) on the gas−liquid interface of a surface nanobubble generates a morphology-dependent surface tension, which serves as a restoring force (surface tension) as a function of bubble size that brings the nanobubbles back toward equilibrium (gas−liquid interface restoration), and (ii) geometric deformation of the soft substrate induced by the formed Received: March 15, 2019 Revised: May 10, 2019 Published: May 29, 2019 8482
DOI: 10.1021/acs.langmuir.9b00772 Langmuir 2019, 35, 8482−8489
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Figure 1. Two stability mechanisms proposed for nanobubbles sitting on initially homogeneous substrates. (left) Restoration of gas−liquid interface of a nanobubble because of the constant adsorption of small organic molecules on the nanobubble surface, and (right) self-pinning of the contact line of a nanobubble because of the deformation of the soft substrate induced by bubble formation.
liquid interface of stable surface nanobubbles remains unchanged when undergoing thermodynamic fluctuations because of not only preferable adsorption of organic contaminants but also their sufficiently low concentration in solution. On the basis of a simple mixing rule, the interfacial tension of a surface nanobubble (for the gas−liquid interface), γbubble, on a rigid substrate immersed in water could be expressed as
nanobubble in turn impedes the free slip of the nanobubble contact line (self-pinning of contact line). Both of them show an interesting phenomenon: contact line slip is apparently impeded, although the pinning sites are absent initially. Hence, under favorable external conditions, nanobubbles would prevent themselves from growing or shrinking, via interface restoration and/or self-pinning of the contact line, even though the substrate seems not to provide pinning sites (i.e., inhomogeneous sites). Here we call the two mechanisms for stable surface nanobubbles, respectively, the interface restoration model and the self-pinning model.
l o Sso Sso zyz o ji o o Sso ≤ S bubble γbubble = ·γso + jjj1 − z·γ o o j S bubble S bubble zz{ water m k o o o o o Sso > S bubble γ = γso o n bubble
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TWO MECHANISMS FOR STABLE SURFACE NANOBUBBLES Nanobubble Surface Restoration via Responsive Surface Tension Change Induced by Covered Impurities. We first considered the effects of trace organic impurities on the stability of surface nanobubbles sitting on flat and hard substrates via theoretical analysis. In nanobubble solutions, other unexpected compounds including various impurities may exist as a variety of species from different origins. It was even reported that using disposable medical plastic syringes and cannulas to deliver liquids may induce the contamination of solution,27,28 leading to the generation of both nanobubbles and nanodroplets within a single experiment. The concentration of impurities is normally extremely low; however, they seem to play an essential role in nanobubble stability. Carefully prepared experiments indicate that trace organic contaminants seem to be necessary for stable bulk nanobubbles.29 This clearly implies the importance of the trace impurities (typically small organic molecules) in the stability of surface nanobubbles, which has not been included in the pinning and supersaturation model. For trace organic contaminations staying in solutions, they prefer to adsorb on nanobubble gas−liquid interfaces because of their hydrophobic or partly hydrophobic (amphiphilic) nature. Because the amount of small organic molecules is sufficiently low, as in the practical situations of most nanobubble nucleation experiments, the number of organic molecules adsorbed onto the surfaces of nanobubbles can be reasonably considered as invariable. Here we considered the situations for which the stability of surface nanobubbles is controlled by the adsorbed impurity. In other words, we assume that the number of organic molecules on the gas−
(1)
where Sbubble and Sso represent the total gas−liquid interfacial area of the surface nanobubble and that covered by small organic molecules. γso represents the surface tension for a pure liquid of the small organic molecules, and γwater is the surface tension for water. Note that Sso is proportional the number of small organic molecules covering the bubble, and Sso > Sbubble means that the surface of bubble is fully covered by small organic molecules. We assume that the surface nanobubble is spherical, with a curvature radius RC, lateral radius RL, and contact angle from the bubble side θ (see Figure 1a). Thus, the nanobubble volume Vbubble, area of the gas−liquid interface Sbubble, and lateral area covered by the nanobubble are respectively determined by Vbubble =
1 πR C3(1 − cos θ )2 (2 + cos θ ) 3
(2a)
S bubble = 2πR C 2(1 − cos θ )
(2b)
SL = πRL 2 = πR C 2 sin 2 θ
(2c)
In the grand canonical ensemble, the grand energy barrier for forming a nanobubble on the substrate ΔΩ is ΔΩ = −(Pin − Pout)Vbubble + γbubbleS bubble + (γgs − γls)SL (3)
with Pin and Pout being the pressures inside and outside the nanobubble. γgs and γls are respectively the gas−substrate and liquid−substrate interfacial tensions, both depending on the properties of the selected substrate. In the grand canonical 8483
DOI: 10.1021/acs.langmuir.9b00772 Langmuir 2019, 35, 8482−8489
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Figure 2. (a) Needed work for forming nanobubbles of different sizes at constant adsorption of small organic molecules of Sso = 4000 nm2. (b,c) Corresponding change of (b) the nanobubble height and lateral size as well as (c) the contact angle and curvature radius as a function of nanobubble volume.
demonstrates that this is because increasing bubble volume causes an increase of surface tension (eq 1), which provides the restoring force to prevent the further growth of the surface nanobubble. In fact, the initial increase of the bubble volume induces simultaneously the increase of the nanobubble height (Figure 2b) and the decrease of the curvature radius (Figure 2c), both canceling out the increase of the lateral radius and causing the contact line to be nearly motionless (Figure 2b). Therefore, the movement of the contact line seems to be restrained as the nanobubble volume grows. Similarly, when the nanobubble initially shrinks, the resulting decrease of surface tension (eq 1) would counterbalance the shrinking, resulting in a stable nanobubble. As shown in Figure 2b,c, when the bubble size decreases, the curvature radius increases while nanobubble height decreases, causing the nearly unchanged lateral radius. Within the framework of the pinning and supersaturation model for nanobubble stability, the contact line pinning effect comes from the existence of substrate heterogeneity (physical roughness or chemical defects). However, here we show that for a nanobubble subject to volume fluctuation, even though the substrate is completely homogeneous, the resulting change of the nanobubble surface tension (under the condition of constant adsorption of small organic molecules) may provide a restoring force that prevents the nanobubble from infinitely growing or shrinking. The contamination-adsorption-induced surface tension change thus minimizes the change of the lateral size of nanobubbles, giving rise of an apparent pinning of the nanobubble contact line although there are no pinning sites. Different from the pinning effect caused by substrate heterogeneity, this specific pinning-like behavior does not constrain the slide of nanobubbles, making the movement of surface nanobubbles along the solid surface unrestricted. For the interface restoration model, how the stable surface nanobubbles change with gas supersaturation and with interfacial adsorption of small organic molecules is shown in Figure 3. With the increase of the gas supersaturation, the volume, height, and contact angle θ of the resulting stable nanobubbles increase and the curvature radius decreases accordingly (Figure 3a), similar to the nanobubbles with a pinned contact line by the substrate reported before.13,16,30 This is because at constant adsorption of small organic molecules, the surface tension increases with the level of gas supersaturation (Figure 3a). The effect of surface adsorption of small organic molecules is similar to that of gas supersaturation (see Figure 3b). With the
ensemble, the chemical potential for gas inside the bubble should be equal to the chemical potential for gas dissolved in the bulk liquid. This equality is guaranteed by applying Henry’s law. Henry’s law gives the relation between the pressure inside the nanobubble and the concentration of the dissolved gas Pin = HC = H(1 + ξ)Cs
(4)
where H is Henry’s constant, C and Cs are the actual concentration and saturation concentration of dissolved gas, and gas supersaturation is given by ξ = C/Cs − 1. In addition, the force equilibrium at nanobubble contact line demands cos θ = (γls − γgs)/γbubble, as in the impurity-free solution, the Young’s contact angle from the bubble side satisfies cos θY = (γls − γgs)/γwater, which thus leads to cos θ = cos θYγwater /γbubble
(5)
Substituting eqs 1, 2a−2c, 4, and 5 into eq 3 gives a relation between ΔΩ and bubble volume V, which can be determined numerically to find out the stability of the formed nanobubbles according to the extreme of ΔΩ. In our numerical calculations, we considered nanobubbles on a homogeneous and hydrophobic substrate, for which the pinning effect is absent, with a Young’s contact angle of θY = 73.6° (Young’s contact angle from the bubble side). In determining ΔΩ as a function of bubble volume, we set the temperature T = 298.15 K, Pout = 1.0 bar, and γls − γgs = 0.02 N/m. For small organic molecules, the pure liquid has a surface tension of γso = 0.022 N/m, and unless otherwise specified, the fixed number of small organic molecules results in a covered area of Sso = 4000 nm2. At saturated dissolution of gas, Henry’s law requires HCs ≈ 1.0 bar, whereas for stable nanobubbles, the gas supersaturation required is determined by Pin = HC = H(1 + ξ)Cs. The numerically determined grand energy barrier for forming a bubble ΔΩ is shown in Figure 2a as a function of bubble volume. The figure shows that at a given gas supersaturation, there exists a local minimum of free energy as nanobubble volume changes. This clearly indicates that at the extremum, the formed surface nanobubble is thermodynamically stable in an open system, even though there is no substrate heterogeneity to produce contact line pinning. When the formed nanobubble grows or shrinks, the corresponding shape change is shown in Figure 2b,c. Closed to the state corresponding to the stable surface nanobubble, we found unexpectedly that the curvature radius decreases as bubble volume increases (Figure 2c). Detailed inspection 8484
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Figure 3. Gas supersaturation and adsorbed impurity affect the properties of obtained stable surface nanobubbles. (a) At a given adsorption of impurity (Sso = 4000 nm2), the stable nanobubble changes its volume, geometric size (including curvature radius, height, and lateral radius), contact angle, and gas/liquid surface tension as the level of gas supersaturation ξ increases. (b) Corresponding changes when the amount of adsorbed impurity increases, at the given gas supersaturation of ξ = 30.
contaminated gaseous bubbles from clean (but pinned) ones. Different from distinguishing the gaseous nanobubbles and nanodroplet (contaminants) with established techniques,31−34 this is a tricky task and needs further experimental study. Self-Pinning of Nanobubbles Induced by Deforming Soft Substrates. In previous studies, surface nanobubbles were most frequently generated from rigid solid substrates, and the nanobubbles could often be reproduced on the same positions because of the immovable heterogeneous pinned sites.2 However, surface nanobubbles have been observed to appear randomly on homogeneous substrates that are covered by copolymer brushes,22 suggesting that the contact line pinning effect by physical roughness or chemical inhomogeneity of substrates is not necessarily required for the stability of the surface nanobubble. An unanswered question therefore arises, namely, what is the underlying mechanism for the nanobubbles to be stable? To answer this question, we need to consider deformable substrates, above which the formation of surface nanobubbles might deform the substrates, similar to
increase of the number of the small organic molecules, the change of stable nanobubbles exhibits trends similar to that of increasing the level of gas supersaturation (Figure 3a). It is observed, as expected, that except the curvature radius, other characteristic parameters including the volume, height, lateral radius, contact angle, and interface tension increase with the overall areas covered by small organic molecules (Figure 3b). With increasing the amount of adsorbed impurity, the volume of the stable nanobubble increases rapidly. However, the simultaneous increase of the lateral radius and height of the bubble minimizes the change of the contact angle (Figure 3b). We need to point out that to simplify the question, we assumed here that organic contaminants are evenly adsorbed on the nanobubble surface. However, in experimental situations, the adsorbed contaminants (especially for macromolecules and nanoparticles) may be distributed heterogeneously on nanobubble surfaces, which might lead to a nonspherical surface shape and affect nanobubble stability. This study also raises a question of how to differentiate 8485
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Figure 4. (a) Typical representation of the simulation setup. The white particles represent liquid molecules, the blue particles represent gas molecules, the red particles represent polymers, the cyan particles represent solid particles forming the top substrate, and the gray particles represent the bottom substrate. The boxed area shows the source region that controls the gas concentration in the reservoir. (b) Summarized nanobubble stability as a function of polymer length Nc and hydrophobicity εps. (c,d) Time evolution of nanobubble as a function of time for (c) stable nanobubbles and (d) unstable nanobubbles. The shape evolution of nanobubbles is also shown in a typical snapshot (see the inset). The polymer length and hydrophobicity were set respectively to (c, top) Nc = 16 and εps = 0.55, (c, bottom) Nc = 8 and εps = 0.6, (d, top) Nc = 16 and εps = 0.7, and (d, bottom) Nc = 8 and εps = 0.45.
the deformation of soft substrates induced by droplets.35−38 Here we built a simple model to demonstrate via molecular dynamics (MD) simulations how nanobubble stability is in turn affected by the resulting substrate deformation. Here, coarse grained MD simulations in isothermal and isostress (NP ZZ T) ensembles were performed using LAMMPS39 to find out the stability mechanism for surface nanobubbles on specific soft substrates that were decorated by the packing of linear homopolymers. We constructed a minimal model system composed of single Lennard−Jones (LJ) atoms to represent respectively solvent molecules, gas molecules, and solid atoms forming two substrates (see Figure 4a). A quasi-two-dimensional simulation box having a size of 101 × 5 × H in units σ (the LJ diameter) was used, for which the height of the simulation box H fluctuated at a given pressure that was maintained by exerting an external force along the z-direction on the top substrate. To model soft substrates, the bottom substrate was regularly decorated by 153 linear homopolymers, each containing 8−24 LJ atoms (monomers) of a single type that were connected by the FENE potential. To mimic the sufficiently large environment with the given concentration of dissolved gas surrounding a nanobubble, a source region representing the infinite reservoir was included in the simulation box (see the boxed region in Figure
4a). The identity exchange between solvent and gas molecules in this region was periodically carried out after a given time interval of regular MD simulations to keep the gas concentration in the reservoir fixed. In this work, we systematically varied the interaction between polymer monomer and solvent molecule, εps, to control the polymer hydrophobicity, which was shown to be essential for nanobubble stability.22 See the Supporting Information for the detailed simulation methods and models. First, we simulated the evolution of surface nanobubbles on the substrates covered by homopolymers. By adjusting the length and hydrophobicity of the linear polymers, we performed multiple sets of MD simulations, several of which demonstrate the existence of stable nanobubbles (Figure 4b). Through detailed inspection of our simulation results (see Figure 4b), we observed three different situations for the initially formed nanobubbles: (i) the nanobubble continues to grow infinitely; (ii) the nanobubble fluctuates and finally reaches stability; (iii) the nanobubble gradually disappears as gas molecules inside the nanobubble continuously dissolve. This stabilizing behavior is highly unexpected, because the steadily moving contact line is not pinned. But this observation is indeed consistent with experimental results,22 confirming 8486
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Figure 5. Deformation of soft substrates induced by the formation of a nanobubble. (a) shows the height distribution for the polymers immersed in liquid and for those beneath the formed nanobubble. In this figure, Nc = 24 and εps = 0.5. (b) shows the cosine value for the angle between the orientation of the polymers belonging to different regions and the substrate (x-axis), respectively, for polymer chains inside the nanobubble, nearby the contact line, and immersed in liquid. In this figure, three types of stable nanobubbles were considered (see Figure 4b): group 1 represents the case of Nc = 8 and εps = 0.6; group 2 shows the case of Nc = 16 and εps = 0.55; group 3 shows Nc = 24 and εps = 0.5.
Figure 6. Two sets of simulation runs to demonstrate the nanobubble-induced surface heterogeneity in turn to stabilize the nanobubble (Nc = 8 and εps = 0.6). (a) shows typical simulation results, in which the polymers were fixed after bubble formation (at 50 ns), thus leading to self-pinning of the contact line. (b) shows the simulation results in which the polymers were fixed before the bubble formation (0 ns), and thus, the substrate deformation induced by the formed nanobubble is absent.
that the nanobubble can be stable on soft substrates, even though the underlying contact line pinning is absent. To illustrate the different fates of the initially formed nanobubbles, Figure 4c,d shows several typical variations of the height of the simulation box with time during MD simulations. In Figure 4c, we give two independent simulations that finally lead to a stable nanobubble, in which the height of the simulated box initially increased with time until it reached the equilibrium height that corresponds to stable nanobubbles. In addition, we also give snapshots at 10, 30, and 50 ns, which visually reflect the nanobubble evolution on soft substrates. Figure 4b not only shows that nanobubbles are possibly stable on soft substrates even though pinning sites are absent but also indicates that the stability depends on polymer length and hydrophobicity. Stable nanobubbles are observed only when chain-like molecules are weakly hydrophobic, as shown in the middle region of Figure 4b. When the chains are much more hydrophobic, the nanobubble would grow to form a gas layer between the liquid and solid phases (Figure 4d). This is
because the most hydrophobic surface would cause significant enrichment of gas molecules that destabilizes the nanobubble through continuously enlarging the readily moving contact line. When the polymer chains are much more hydrophilic, on the other hand, the hydrophilic nature of polymer molecules causes the spreading of solvent along nanobubble contact line, giving rise in the continuous dissolution of encapsulated gas molecules until the bubble completely disappears (Figure 4d). The figure also indicates that as the chain length increases, nanobubble stabilization requires the chain to be more hydrophobic. In summary, the nanobubble is stable only under the situations with suitable polymer length and polymer hydrophobicity, which seems to be consistent with the experimental observations.22 We then turn to the underlying molecular mechanism that stabilizes the surface nanobubbles on soft substrates. We examined the distribution of the height of polymer chains along the lateral direction and found that it is not uniformly distributed. The average height for polymers inside the 8487
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restrict contact line motion, stable surface nanobubbles are observed (see Figure 4b). The key insight of the current model is that substrate deformation induced by the formed nanobubbles would in turn restrict the contact line motion, providing a generic mechanism for the stability of nanobubbles on soft media. However, the specific substrate deformation observed here can be tuned by varying the model used to represent soft substrates. For example, to simplify the model, we used homopolymers rather than block copolymers to represent soft substrates.22 Replacing homopolymers with copolymers would certainly strengthen or reduce the substrate deformation, depending on the copolymer structure, and thus modify the stability of sessile nanobubbles. We also note that in our model, the substrate deformation near the contact line is mainly due to the hydrophobic interaction between solvent and homopolymers, which makes the adjacent polymers pointing toward the nanobubble minimize the unfavorable interaction (see Figure 1b). We anticipate that, however, if a solvent model having a high surface tension is used rather than the Lennard−Jones fluid used here that is featured with a rather small surface tension, a surface ridge may form near the nanobubble contact line, because the high surface tension would pull up the soft substrate as is observed for microdroplets on soft substrates.35−38
nanobubble and those outside are shown in Figure 5a as a function of simulation time. The figure clearly demonstrates that the average height of the homopolymers inside the nanobubble is higher than that for polymers outside. That is to say, after forming a surface nanobubble, the different environments inside and outside of the nanobubble affect homopolymer configurations, producing physical inhomogeneity on the soft substrate, which may in turn provide a pinning effect on the nanobubble contact line to improve its stability. Further, in the immediate vicinity of the contact line of the surface nanobubbles a sharp nanosized surface deformation was observed, as shown in Figure 5b. The averaged cosine value of the angle between the homopolymers and the substrate is shown in Figure 5b, and it clearly demonstrates that the direction of homopolymers near the contact line region (averaged only over the polymers outside the nanobubble but within 5σ from the contact line) is different from that in the bubble interior and that for the exterior environment far from the contact line. Therefore, a significant substrate deformation takes place near the contact line, which in turn drastically influences the nanobubble stability. These observations prove that the physical nonuniformity generated by the formed surface nanobubble in turn provides a pinning effect on the free slip of the contact line and thus stabilizes the nanobubble. For simplicity, in this work, this molecular mechanism for surface nanobubble stability is called the selfpinning model. In order to further confirm the so-called self-pinning model, we performed a series of extra simulations as a comparative study. Under the conditions of generating stable nanobubbles as shown in Figure 4b, first, a 50 ns MD run was performed to produce stable nanobubbles as done in Figure 4b, followed by another 50 ns MD run, in which, differently, the configurations of polymers were kept fixed. As expected, we found that the nanobubble remained stable (see Figure 6a). This is because the surface heterogeneity as shown in Figure 5 has already been generated by the formed nanobubble during the first MD run, which stabilizes the nanobubble in the subsequent simulation run, although the configuration fluctuation of the homopolymers was totally removed. However, if we fixed the polymer chains at the beginning (0 ns), before which the surface heterogeneity has not been generated, the subsequent MD run shows that the formed nanobubble is unstable, and it disappears rather quickly (see Figure 6b). In this case, the fixed chain configuration inhibits the formation of substrate inhomogeneity that is required for stable nanobubbles. Through this set of comparative study, we confirm that the stability of the nanobubble is due to the existence of the physical nonuniformity of soft substrates, which is created by the formation of nanobubbles. The self-pinning model is further confirmed by investigating the effect of homopolymer grafting density. Three homopolymer densities were considered by setting the distance between neighboring homopolymers (with a chain length of 8) to 1σ, 2σ, and 3σ, respectively. For the interhomopolymer distance equal to 1σ, the overcrowded homopolymers inhibit the substrate deformation, whereas for the distance of 3σ, the dangling ends of sparsely distributed homopolymers seem to be totally flexible. Both of them are unable to stabilize nanobubbles. Only when the interhomopolymer distance equals 2σ, for which the substrate is deformable and able to
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CONCLUSIONS In summary, we uncover generic mechanisms of how surface nanobubbles reamin stable in the absence of contact line pinning. Through theoretical analysis and molecular simulations, we report two mechanisms for stabilizing surface nanobubbles on flat and homogeneous substrates. One is the so-called interface restoration model, resulting from the constant adsorption of trace impurities on the gas−liquid interface of a nanobubble, which generates a restoring force to stabilize the surface nanobubble. The other is the self-pinning model, in which deformation of a soft substrate induced by the formed nanobubble in turn stabilizes the nanobubble through impeding contact line motion. Finally, we want to point out that the two stability mechanisms proposed here do not contradict with the pinning mechanism, and instead they work under different conditions. Different from the pinning mechanism, the interface restoration model requires the existence of trace contamination with interfacial activity, whereas the self-pinning model only applies when surface nanobubbles sit on deformable substrates. We show that new components are needed to be added for our understanding of nanobubble stability when contact line pinning is absent and suggest that the prevalence of surface nanobubbles may have been underestimated.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.9b00772.
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Detailed simulation methods and models (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. (X.Z.) 8488
DOI: 10.1021/acs.langmuir.9b00772 Langmuir 2019, 35, 8482−8489
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Xianren Zhang: 0000-0002-8026-9012 Author Contributions †
Z.G. and X.W. contributed equally to this work.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grant No. 91434204). REFERENCES
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DOI: 10.1021/acs.langmuir.9b00772 Langmuir 2019, 35, 8482−8489
