Formation, dissolution and properties of surface nanobubbles

Zhizhao Che1 and Panagiotis E. Theodorakis2

1State Key Laboratory of Engines, Tianjin University, Tianjin, 300072, China.2Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland.

Abstract

Surface nanobubbles are stable gaseous phases in liquids that form on solid substrates. While theirexistence has been confirmed, there are many open questions related to their formation and dissolutionprocesses along with their structures and properties, which are difficult to investigate experimentally.To address these issues, we carried out molecular dynamics simulations based on atomistic force fields forsystems comprised of water, air (N2 and O2), and a Highly Oriented Pyrolytic Graphite (HOPG) substrate.Our results provide insights into the formation/dissolution mechanisms of nanobubbles and estimates fortheir density, contact angle, and surface tension. We found that the formation of nanobubbles is drivenby an initial nucleation process of air molecules and the subsequent coalescence of the formed air clusters.The clusters form favorably on the substrate, which provides an enhanced stability to the clusters. Incontrast, nanobubbles formed in the bulk either move randomly to the substrate and spread or move tothe waterair surface and pop immediately. Moreover, nanobubbles consist of a condensed gaseous phasewith a surface tension smaller than that of an equivalent system under atmospheric conditions, and contactangles larger than those in the equivalent nanodroplet case. We anticipate that this study will provideuseful insights into the physics of nanobubbles and will stimulate further research in the field by usingall-atom simulations.

1 Introduction

Surface nanobubbles are gaseous phases that canform spontaneously at solidliquid interfaces [1, 2](Figure 1). They were observed in experiments totypically have diameters of 50100 nm and heights of1020 nm. Moreover, they are unexpectedly stable,namely they can exist for days without dissolvingas, for example, in the case of a Highly OrientedPyrolytic Graphite (HOPG) substrate immersed inwater [1]. This is only one of the features thathave motivated research on nanobubbles in variousfields, including the relatively new field of plasmonicbubbles in the context of energy conversion [3, 4]. Inaddition, nanobubbles find important applications innanomaterial engineering [5], transport in nanoflu-idics (e.g., autonomous motion of nanoparticles)[6], catalysis and electrolysis [7], cleaning [8], andflotation [9]. In the case of flotation, for example,nanobubbles attached to nanoparticles of certainsizes rise together due to buoyancy, in this wayfacilitating the separation of nanoparticles or evenfine oil nanodroplets.

The existence of nanobubbles was speculatedabout twenty years ago [10], while the first atomic-force microscopy (AFM) image of nanobubbles wastaken in the year 2000 [11, 12]. Initially [13],researchers believed that the presence of nanobub-bles on the image was an artifact, but the use of

chezhizhao@tju.edu.cn

additional methods confirmed their existence [1416]. However, the experimental characterizationof these nano-objects still remains a difficult taskdespite significant efforts over the last decade. Forexample, the most popular method for studyingnanobubbles, AFM [11, 12, 17], can only provide longtime averages, preventing the study of nanobubbleformation and dissolution [1]. In another example,surface plasmon resonance spectroscopy is sensitiveto the chemical properties of interfaces [18]. As aresult, it is difficult to isolate the properties of thenanobubbles from those of the interface. In addition,the control of the nanobubble size in experimentshas to be involved, which is crucial for analyzingtheir size-dependent properties [11, 19]. These areonly a few of the reasons that many universalproperties of nanobubbles still remain unexplored[1]. For example, nanobubbles are known to bestable for days, which contrasts with the expectationof their rapid dissolution within the diffusive timescale (microseconds) due to the high Laplace pressureinside nanobubbles [20]. Some studies suggest thatcontamination on the substrate may play a role inthis stability [21], whereas other studies explain thisphenomenon through the balance between gas influxand outflux [22, 23], pinning [2426], and gas oversat-uration [27, 28]. Recently, molecular dynamics (MD)simulations of a coarse-grained model suggested thatnanobubbles dissolve within less than a microsecond,claiming that the experimental nanobubbles are sta-

1

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609.

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ysic

s.fl

u-dy

n] 1

6 O

ct 2

016

Water

Nanobubble

Figure 1: Schematic illustration of a nanobubble(in white) surrounded by water (in blue) on a solidsubstrate (bottom).

bilized by a nonequilibrium mechanism [29].Hence, many fundamental questions are still open;

even the proof that nanobubbles actually consist ofa gaseous phase is under debate [1]. Clearly, weneed systematic approaches to study the formation,dissolution and properties of nanobubbles targetingrealistic systems. Understanding these phenomenarequires the access to an atomistic/molecular-scaledescription of the phenomena, the absolute controlof system parameters (e.g., thermodynamic condi-tions), and the ability to follow in detail the timeevolution of the formation and dissolution processesof nanobubbles. To address these issues, we employedMD simulations based on atomistic force fields. Inparticular, we studied the spontaneous formationand dissolution mechanisms of air nanobubbles (N2and O2 molecules) on an HOPG substrate immersedin water. This paper describes simulation resultsfor this realistic situation and provides insights intomorphological properties of nanobubbles, such astheir size, density, contact angle, and interfacialtension.

2 Materials and methods

2.1 System configuration

The system consisted of an HOPG substrate at thebottom of a rectangular simulation box, air (N2and O2) and water (H2O) molecules, and a solidlayer of silicon atoms on a square lattice at the topof the simulation box to regulate the pressure inthe system and to prevent the air molecules fromescaping from the simulation box (see Figure 2).The top silicon layer and the bottom substrate werenormal to the z direction and defined the size ofthe system in this direction, while periodic boundaryconditions were applied in the x and y directions.The distance between the top surface and the watermolecules was large enough to guarantee that thesetwo components did not interact directly during thesimulations. Moreover, the distance between thetop surface and the liquidvapor interface was largeenough to capture the air molecules escaping fromthe liquid phase.

The amount of water used in experiments is be-yond the reach of molecular-level simulations, which

Upper bound layer

HOPG

H2O+O2+N2

x

x

yz

Figure 2: Perspective view of an initial configurationof the system used in a simulation to investigate thesubsequent formation of surface nanobubbles on anHOPG substrate in water. The magnified regionhighlights the gas molecules (cyan color for N2 andgreen color for O2) dispersed randomly within theaqueous medium (in red). The HOPG substrate (inblue) at the bottom of the simulation box consists ofthree layers of carbon atoms arranged on a hexagonallattice. The red straight lines indicate the boundariesof the simulation box with periodic boundary condi-tions applied in the x and y directions. The top of thesimulation box is bound by a silicon wall (in black).

makes the simulation of the whole system almostimpossible due to the high demand in CPU time.A test of different water volumes was performedand a largest possible system was selected to con-sider most features of the relevant processes withreasonable requirement in CPU time. Therefore,the escape rate of the air molecules was inevitablymuch higher than in experiments. However, it isbelieved that this does not affect significantly theunderstanding of the formation and the propertiesof nanobubbles [29]. The HOPG substrate is oneof the most well-studied cases in the context ofnanobubbles in experiments [3032], hence our choicein this study. Here, the HOPG substrate is an idealform of synthetic graphite (without contamination ordefects) consisting of several layers of carbon atomsin a hexagonal arrangement (see Figure 2).

2.2 MD simulation method

The study was performed by using MD simulationsof atomistic force fields [3335]. Simulations werecarried out in the NVT ensemble by using the Nose-Hoover thermostat as implemented in the LAMMPSpackage [36]. Therefore, the number of particles andthe volume of the system were constant during thesimulations, while the temperature was allowed tofluctuate around a predefined value, which in our

2

case was 300 K. Henceforth, quantities related to thesystem were expressed in real units.

The total energy of a system includes harmonicinteractions described by the following relations,

U =bonds

kb(l l0)2 +angles

ka( 0)2, (1)

where kb and ka are stiffness parameters for bondand angle interactions, respectively; l0 and 0 arethe equilibrium distance and the equilibrium angle,while l and are the actual distance and angleduring the simulation at a particular time-step. Fornonbonded interactions, a pairwise potential con-sisting of LennardJones (LJ) 126 and Coulombinteractions was considered,

Uij = 4ij

[(ijrij

)12(ijrij

)6]+qiqjrij

, (2)

where ij expresses the strength of the interaction,rij the actual distance between the ith and thejth particles, ij the size of the particles, and qithe charge of the ith particle. Charges were takeninto account by using the particleparticle particlemesh (PPPM) method [37]. The SPC/E model wasemployed for the simulation of water molecules. Thedetails of the simulations are provided in Supplemen-tary Materials.

2.3 Properties of nanobubbles

The nanobubble was determined firstly by clusteranalysis from the trajectories of the molecules. Then,Voronoi analysis was performed to find the inter-face between the water phase and the air phase.The volume, the density, and the contact angle ofnanobubbles were calculated based on this interface(See Supplementary Materials for details). Thecontact angle of water nanodroplets on the HOPGsubstrate was also analyzed for comparison. Thevarious analysis was performed by using customizedMatlab programs.

To calculate the surface tension of nanobubble inwater, a new simulation configuration was used bysetting up a layer of water molecules in air at thenanobubble density (and a configuration with airat normal density for comparison). For a planarinterface between two phases (1 and 2) perpendicularto the z direction, the surface tension 12 can becalculated as follows [38],

12 =

phase2phase1

[(Pxx + Pyy)/2 Pzz]dz, (3)

where Pxx and Pyy are tangential pressure com-ponents, Pzz the normal pressure component, andthe integration is along the normal direction to theinterface.

3 Results and discussion

3.1 Formation and dissolution ofnanobubbles

The formation of nanobubbles is driven by a nucle-ation process (see Figure 3). Initially, air moleculesare dispersed randomly and uniformly in water.Later, they aggregate into clusters, which graduallygrow with the addition of nearby air molecules. Thisis due to the oversaturation of the air moleculesin water and the favorable interaction among airmolecules in comparison with the less favorable inter-action between air and water molecules. Moreover,the interaction between air molecules and the HOPGsubstrate is also more favorable in comparison withthe interaction between air and water molecules. Asa result, the energetically most suitable position ofair molecules within the aqueous phase is on thesubstrate. Therefore, the air molecules dispersed inwater diffuse towards the substrate, eventually form-ing one or more nanobubbles. Other air molecules,however, may have diffused towards the liquidvaporinterface without interacting with the substrate,in this way escaping from the aqueous phase andeventually reaching the gas phase above the aqueousphase.

During the formation of nanobubbles, severalclusters of air molecules may collide and coalesce,resulting in a larger nanobubble (See Figure 4).Some clusters of air molecules could also form inthe liquid phase far from the substrate. Theseclusters exhibit a random (Brownian-like) motion,and pop immediately once they reach the airwaterinterface (see Figure 5). In contrast, nanobubbles incontact with the substrate remain stable, in this wayunderlining the key role of the substrate in providingfurther stability to the nanobubbles.

The formation process realized by the aggregationof air molecules depends on the degree of saturationof the system. For the simulated systems in thisstudy, the size of a typical nanobubble, duringthe formation process, increases rapidly within 5ns until it reaches a plateau (see Figure 6a) andforms nanobubbles of about 200 air molecules. Inexperiments, this process would require more timedue to the lower concentration of air moleculesand the larger size of the nanobubbles than thatin the simulations. The coalescence and the popof clusters of air molecules happen in similar timescales (see Figures 6b and c for coalescence and poprespectively). The coalescence time scale depends onthe average distance between clusters, while the poptime scale depends on the average distance betweenthe clusters and the water surface. Since thesedistances are functions of the initial air concentrationand the air cluster size, they are much larger inexperiments and consequently the time scales of thecoalescence and the pop processes are also muchlarger in experiments than those in the simulations.

3

(a) 0 ns (b) 1 ns (c) 2 ns (d) 3 ns

(e) 4 ns (f) 5 ns (g) 7 ns (h) 9 ns

Figure 3: Formation of a nanobubble on the HOPGsubstrate illustrated by snapshots at different timesas indicated. The water/air mixture is initiallyhomogeneous, and the air molecules gradually aggre-gate into small clusters dispersed randomly in water.Then, some clusters collide to form larger ones.Finally, a large cluster form on the substrate due tothe interaction with the substrate. The nanobubbleexhibits a Brownian-like motion in contact with thesubstrate. The domain is periodic in the x and ydirections. A movie for the whole process is availableas Supplementary Material Video 1.

(a) 0 ns (b) 11.0 ns (c) 11.1 ns (d) 11.3 ns

(e) 15.2 ns (f) 15.3 ns (g) 15.4 ns (h) 15.6 ns

Figure 4: Coalescence of two nanobubbles to form alarge one and its subsequent spreading on the HOPGsubstrate illustrated with snapshots at different timesas indicated. Two bubbles form initially in thissystem, a small one on the substrate and a large onein the bulk. The large nanobubble eventually mergeswith the small one on the HOPG substrate, in thisway underlining the crucial energetic contribution ofthe substrate in the formation process. The domainis periodic in the x and y directions. A movie for thewhole process is available as Supplementary MaterialVideo 2.

(a) 0 ns (b) 2.02 ns (c) 3.02 ns (d) 5.49 ns

(e) 17.95 ns (f) 17.97 ns (g) 17.99 ns (h) 18.01 ns

Figure 5: Pop of a nanobubble towards the topwater surface illustrated with snapshots at differenttimes as indicated. A nanobubble produced in thebulk water phase approaches the top water surface,and pops immediately. Subsequently, all the gasmolecules escape from the bubble to the open space.The domain is periodic in the x and y directions. Amovie for the whole process is available as Supple-mentary Material Video 3.

During the formation of a nanobubble, the fastaggregation of air molecules indicates a collectiveprocess, where air molecules also reach diffusively theHOPG substrate. Then the nanobubble graduallydissolves at a pace that depends on its maximumsize in terms of the number of contained air molecules(see Figure 7a). In contrast to the formation process,the gradual dissolution of nanobubbles indicates anon-collective process, where the average numberof air molecules in nanobubbles smoothly decays.Interestingly, different simulations of nanobubbleswith the same size exhibit the same behavior asthey dissolve. The dissolution time of a nanobubbleprogresses linearly. For example, for a nanobubbleof 245 air molecules shown in Figure 7a, it is about96 ns. Large nanobubbles will have longer life time,but could not be simulated using the MD methodbecause of the high demand in CPU time. Moreover,longer lifetime of nanobubbles in experiments hasbeen mainly attributed to the pinning of contactlines on defects of substrates [2427], which is notconsidered in the current study on smooth sub-strates. Large nanobubbles are dominated by thebulk interactions among air molecules, instead ofthe unfavorable interactions between water and airmolecules at their interface, which tends to dissociatea small nanobubble. Hence, for a small nanobubble,these interfacial interactions lead to their gradualdissolution and the diffusion of air molecules to thetop gas phase, where the system eventually reaches

4

t (ns)0 5 10 15 20

N(-)

0

100

200

300

t (ns)0 2 4 6 8 10

N(-)

0

100

200

300

t (ns)0 5 10 15

N(-)

0

100

200

300

formation

(c)a b d e-hc

a b-d e-h

a b dc e f g h(a)

(b)

coalescence

pop

Figure 6: Time evolution of the three largest clustersof air molecules (in terms of number of molecules) inthe domain for three typical systems. (a) Formationof a nanobubble shown in Figure 3, (b) coalescenceof two large clusters shown in Figure 4, (c) pop ofthe largest cluster shown in Figure 5. Labels ah onthe axis of the plots correspond to the snapshots ahin Figures 3, 4, and 5, respectively.

its global thermodynamic equilibrium state.

3.2 Properties of nanobubbles

To understand the behavior of nanobubbles on sub-strates, we sought for additional information bymeasuring different properties of the nanobubblesduring our simulations. This would also assist inexplaining the intriguing stability of nanobubbles.From our analysis, we find that the properties, suchas density, contact angle, and surface tension, aresignificantly altered by the presence of the substrateand the size of the nanobubbles.

Density of nanobubbles We find that nanobub-bles are much denser than a typical gas phase, andthere densities are rather close to typical densities ofliquids. In particular, the density of air molecules innanobubbles is 409 10 kg/m3 (see Figure 7), of theorder of the density of liquids (e.g., the densities ofliquid nitrogen and liquid oxygen are 808 and 1141kg/m3 respectively, while the densities of nitrogenand oxygen at atmospheric state are 1.25 and 1.43kg/m3 respectively). A more detailed analysis ofthe simulation data reveals that the average distance

N(-)

100

200

300

(k

g/m

3 )

300

400

500 mean = 40910 kg/m3

t (ns)0 5 10 15 20

(

)

60

80

100 mean = 75.02.4

(a)

(b)

(c)

Figure 7: Properties of the surface nanobub-bles. (a) Size of nanobubbles in term of thenumber of molecules; the bubbles became smalleras air molecules is dissolved in water; (b) densityof nanobubbles; (c) contact angle of nanobubbles.Curves with different colors represent simulationswith different initial configurations (i.e. differentrandom positions of air molecules), and the blackcurves show the mean values of five simulations.

between air molecules is in the range of the van derWaals interactions indicating that air molecules arecondensed in the nanobubble phase. Hence, insteadof the standard collisions in gases, van der Waalsinteractions dictate the behaviors of the air moleculesin the condensed phase of a nanobubble. Therefore,air molecules in nanobubbles are dominated by thepotential interactions instead of the kinetic energy,providing in this way further stability for nanobub-bles. Many experimental measurements could previ-ously only confirm that nanobubbles entirely consistof air molecules [1]. In this study, we are able, forthe first time, to provide an estimate for the densityof nanobubbles, which was previously unknown.

Contact angle of nanobubbles From the con-tact angle analysis for nanobubbles, we find that thecontact angle measured in the case of nanobubbles isdifferent from that measured in the respective caseof nanodroplets, which we simulated for comparison(see Supplementary Material). In the case of anaqueous nanodroplet on the same HOPG substrateand in the air environment as in the case of nanobub-bles, the contact angle is about 65, which is smallerthan the contact angle in the nanobubble scenario,i.e., about 75 as shown in Figure 7c (both contactangles are measured from the water side). This showsthat the contact angle is not only a property of thesubstrate, but also depends on the configuration ofthe system (e.g., the ratio of water to air molecules).Moreover, in small systems the substrate interactswith the whole nanobubble/nanodroplet to affect

5

the interface shape, unlike in large scale systemswhere the contact angle is a local behavior near thecontact line. Nanobubbles are dominated by theinterfacial interactions between airwater interfaceand the substrate, rather than the interaction of theair molecules in the bulk with the substrate. Inagreement with previous findings [39], the contactangle of nanodroplets depends on their sizes up toa system-dependent threshold. Our conclusions areconsistent with experimental findings on the contactangles of nanobubbles, which argue that contactangles of nanobubbles are much larger than that ofbubbles at large scales [1].Surface tension Our analysis shows that the

surface tension of nanobubbles is smaller than thatin the corresponding bulk systems. We simulated theinterfacial tension of the waterair interface of thenanobubbles at the atmospheric density and at thenanobubble density, which represent the surface ten-sions for bulk systems and for nanobubbles, respec-tively. The results reveal that the interfacial tensionfor the nanobubble case (50.71.6 mN/m) is smallerthan that for waterair interface at atmosphericconditions (57.63.0 mN/m), where the latter valueis in agreement with the model prediction from MDsimulations [40, 41]. The relatively smaller surfacetension of nanobubbles than that in the equivalentsystem under atmospheric conditions indicates thestrong effect of the gas phase. This could beattributed to the higher density of air molecules innanobubbles. The surface tension results from thenet force produced by the greater attraction betweenwater molecules than that between water and airmolecules. A higher density of air can reduce theenergetic penalty for the formation of the liquidvapor interface.

Overall, our investigation of the density, contactangle, and surface tension of nanobubbles has un-derlined their dependence on the size of nanobubblesand the presence of the substrate. The air moleculesin nanobubbles are significantly condensed and con-straint into a small space, which affects the shapeand contact angle of the nanobubbles. The surfacetension is also suppressed due to the compression ofthe nanobubble. These are factors that contribute tothe unusual stability of nanobubbles, which adoptan optimum metastable state with an increaseddensity and contact angle, and a reduced surfacetension.

4 Conclusions

By using all-atom simulations, the present workhas clarified the role of the substrate in the forma-tion/dissolution and properties of surface nanobub-bles on HOPG substrates, which are challengingto investigate experimentally, but are important inunderstanding the intriguing stability of nanobub-bles. The formation process is driven by an initial

nucleation of air molecules and the subsequent coa-lescence of air clusters. The clusters favorably formon the substrate and are relatively more stable onthe substrate than those in the bulk, which eithermove randomly to the substrate and spread or moveto the liquid surface and pop immediately. Hence,the presence of the substrate is a crucial elementfor the enhanced stability of nanobubbles. Thenanobubbles are found to consist of a high-densitygaseous phase, an increased contact angle and areduced surface tension with respect to equivalentbulk systems. These properties are also found toincrease the stability of nanobubbles by providing anoptimum metastable state.

Our results also demonstrate the possibility ofaddressing some fundamental questions regardingthe field of nanobubbles by molecular dynamicssimulations based on atomistic force fields. Thereare many open questions worthy of numerical andexperimental investigation. The current approachcould be extended to the study of substrate wetta-bility, contamination [21], and pinning [2426], whichdeserve careful consideration in order to understandthe behaviors of nanobubbles. Direct measurementof the formation and the properties of nanobub-bles, such as density, surface tension, and contactangle, would be helpful. We anticipate that ourstudy will advance this field by providing insightsinto the physics of nanobubbles which are currentlyexperimentally inaccessible. The findings of thiswork will be valuable for the understanding of manyrelevant phenomena in nature, such as nucleation inboiling [42] and cavitation [43], because nanobubblescould act as nucleation sites in these processes. Thefindings of this study can also be used in a widerange of potential applications of nanobubbles, suchas material synthesis, microfluidics and nanofluidics,advanced diagnostics, and drug delivery.

Acknowledgements

This work is supported by National Natural ScienceFoundation of China (Grant No. 51676137) andthe National Science Centre, Poland (Grant No.2015/19/P/ST3/03541). This project has receivedfunding from the European Union?s Horizon 2020research and innovation programme under the MarieSk llodowska-Curie grant agreement No. 665778.

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1 Introduction2 Materials and methods2.1 System configuration2.2 MD simulation method2.3 Properties of nanobubbles

3 Results and discussion3.1 Formation and dissolution of nanobubbles3.2 Properties of nanobubbles

4 Conclusions