Formation and Dynamics of Ion-Stabilized Gas Nanobubble Phase in

Article pubs.acs.org/JPCB

Formation and Dynamics of Ion-Stabilized Gas Nanobubble Phase in the Bulk of Aqueous NaCl Solutions Nikolai F. Bunkin,*,†,§ Alexey V. Shkirin,#,§ Nikolay V. Suyazov,§ Vladimir A. Babenko,‡ Andrey A. Sychev,†,‡ Nikita V. Penkov,⊥ Konstantin N. Belosludtsev,$ and Sergey V. Gudkov§,$,& †

Bauman Moscow State Technical University, second Baumanskaya 5, Moscow, 105005 Russia A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, ul. Vavilova 38, 119991 Russia # National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409 Russia ‡ P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskiy prospekt 53, Moscow, 119991 Russia ⊥ Institute of Cell Biophysics, Russian Academy of Sciences, Institutskaya ul. 3, Pushchino, Moscow region, 142290 Russia $ Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Institutskaya ul. 3, Pushchino, Moscow region, 142290 Russia & Lobachevsky State University of Nizhni Novgorod, pr. Gagarina 23, Nizhni Novgorod, 603950 Russia §

ABSTRACT: Ion-stabilized gas nanobubbles (the so-termed “bubstons”) and their clusters are investigated in bulk aqueous solutions of NaCl at different ion concentrations by four independent laser diagnostic methods. It turned out that in the range of NaCl concentration 10−6 < C < 1 M the radius of bubston remains virtually unchanged at a value of 100 nm. Bubstons and their clusters are a thermodynamically nonequilibrium phase, which has been demonstrated in experiments with magnetic stirrer at different stirring rates. Different regimes of the bubston generation, resulting from various techniques of processing the liquid samples, were explored.

1. INTRODUCTION Experimental and theoretical studies of nanobubbles (gas particles with sizes ranging from tens to hundreds of nanometers) have grown significantly in recent years; see, for example, refs 1−4. There exists now much evidence that submicrometer-sized gas-filled nanobubbles can persist for significant periods of time both in aqueous solution5−10 and at surfaces submerged in an aqueous environment.11−15 Surface nanobubbles can be detected by a number of different techniques, prominent among which is tapping mode atomic force microscopy (AFM).16 Nanobubbles are commonly found on solid hydrophobic substrates in solutions open to the air, where the nanobubbles appear to be quite stable17 and may spread out to form pancake-like structures. When considering gas nanobubbles in bulk liquid, the question of their stability inevitably arises. Indeed, early theoretical calculations showed that the nanobubbles should only persist for a few microseconds.18 Therefore, considerable effort has been spent on the search for mechanisms of nanobubble stabilization in liquids. In a survey,3 various mechanisms of the stabilization of gas nanobubbles in bulk liquid and at solid substrates are theoretically considered; it is claimed that the nanobubbles may only be stable provided that the liquid is supersaturated with dissolved gas and the surface © 2016 American Chemical Society

tension decreases with increasing the degree of supersaturation. Additional to this, the rate of gas diffusion from both surface and bulk-phase nanobubbles into bulk liquid is relatively slow19,20 and in the case of clustering the nanobubbles in bulk liquid, the diffusion yield of gas is even lower due to the screening effect of neighboring nanobubbles.21 In our opinion, the selective adsorption of the dissolved anions at nanobubble interface, Coulomb repulsion of which can compensate for the pressure of surface tension 2σ/R (R, radius of the bubble; σ, the surface tension), must also be considered in explaining the mechanisms of bulk-nanobubble stabilization. The adsorption of the anions on the surface of aqueous solutions was confirmed by numerical MD simulation with regard for the effect of the polarization of water molecules,22 and also series of experimental results including, e.g., second harmonic generation spectroscopy,23,24 highpressure VUV photoelectron spectroscopy,25,26 and X-ray photoelectron spectroscopy combined with scanning electron microscopy.27,28 The results, obtained in these studies, allow us to make a conclusion about the possibility of the adsorption of Received: November 12, 2015 Revised: January 11, 2016 Published: February 5, 2016 1291

DOI: 10.1021/acs.jpcb.5b11103 J. Phys. Chem. B 2016, 120, 1291−1303

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The Journal of Physical Chemistry B some anions, for example, Cl−, I−, and Br− at the water−gas interface. The fact that basically negative ions are capable of adsorption at this interface is also supported by the data obtained in ref 29, where the negative density of the charge on the surface of gas bubble in pure water was directly measured: for pH = 6.9 its value is α = −18 × 10−6 C/m2; in this case, the charge is caused by the adsorption of OH− ions to the surface. In ref 30, the existence of stable gas nanobubbles in aqueous electrolyte solutions that were called bubstons (an abbreviation of Bubbles stabilized by ions) has been predicted; it was basically assumed that the solution is in thermodynamic equilibrium with the external atmosphere at a certain pressure p and temperature T. In subsequent studies,31,32 also dedicated to theoretical analysis of “bubstons problem” within Coulomb model, it was shown that for explaining the stability of a gas nanobubble of radius R, an additional pressure, equilibrating the Laplace pressure 2σ , is required. Then, the condition of R mechanical equilibrium takes the form: Pg + Pe = Patm +

2σ R

transparent particle (we assume, for simplicity, the particle is spherical with radius R), then the phase difference between the object and reference waves is

δ=

∂We ∂V T

( )

=−

(1)

∂We ∂R

( )( ) = 1 4πR2

4 1 Q0 4 , 8πε R

(2)

where n is the refractive index of the particle, n0 is the refractive index of the surrounding liquid (water, in this case). Therefore, by measuring δ, it is possible to separate colloidal particles with high or low (with respect to water) refractive index. In experiments with phase microscopy,37 it was found that longliving micrometer-sized particles with a refractive index less than that of the surrounding liquid arise spontaneously in aqueous NaCl solutions. Provided that these particles have spherical form, their refractive index is nb = 1.28. This suggests that they cannot be monolithic gas spheres. Such particles can rather be interpreted as micrometer-sized clusters consisting of bubstons with the refractive index n = 1; the presence of liquid films between the gas cores in the cluster results in a slight increase in the refractive index; i.e., nb > n = 1. Additionally, data on the size distribution of scatterers in aqueous solutions of NaCl, obtained in ref 37 by means of dynamic light scattering (DLS), revealed the presence of particles with the size ∼100 nm. On the basis of laser polarimetric scatterometer data, also presented for these aqueous solutions in ref 37, we have solved an inverse scattering problem by a numerical simulation of various ensembles of scattering clusters. In the present study, the solution to the inverse scattering problem has been significantly refined, and the resulting cluster models have been processed numerically to find the dependence of the volume-averaged refractive index as a function of the cluster’s gyration radius; the refractive index measured for a bubston cluster37 and the results of the numerical simulations presented here are in a good agreement. In addition, this paper develops the DLS experiments. In particular, it has been found that the minimum radius of the scatterers is about 100 nm and practically independent of the ionic concentration and the volume number density of the scatterers is controlled by the gas content in the sample. We interpret these scatterers as bubstons. Finally, in this work, the technique of phase microscopy has been substantially improved; as a result, we were able to resolve not only bubston clusters but also individual bubstons.

where Pg is the pressure of gas inside the bubble, Patm is the atmospheric pressure, Pe = −

4π R (n − n 0 ) λ

is this additional

(ponderomotive) pressure, caused by the presence of adsorbed ions at the nanobubble interface and the diffusive electrical double layer. The pressure Pe “expands” the bubble, and at a certain radius R, is capable of equilibrating the compressive force of the surface tension, providing the diffusion equilibrium: Pg = ngkT = Patm. Here, We is the electrostatic component of the r 1 free Helmholtz energy, We(r ) = 2ε ∫ [Q 2(x)/x 2] dx V = (4π/ R 3)(r3 − R3) is the volume of the ion cloud around the nanobubble, Q(r) is the charge distribution at a distance r from the nanobubble center, Q(R) ≡ Q0 is the charge at the nanobubble interface, which is screened by the diffusion cloud of counterions. In this regard, it is worth mentioning the work,33 which describes an experiment with nanobubbles on a solid substrate in an aqueous solution of NaCl. In this experiment, after drying out the solution, ring-like NaCl crystal clots appeared around the areas on the substrate where the nanobubbles were located. This can be treated as an indirect evidence of the formation of the diffusion layer with a high concentration of ions around the nanobubbles. It should be noted that in accordance with the theoretical model, developed in refs 30−32, bubstons coagulate with each other, which leads to the formation of bubston clusters. We have previously conducted a series of experiments confirming the existence of bubston clusters in aqueous solutions of electrolytes.34−38 The methodology of these experiments is based on laser phase microscopy in conjunction with dynamic light scattering and measuring the angular dependence of the scattering matrix elements. The operating principle of the phase microscope is described in detail in ref 34. The main advantage of such a device is that it combines a conventional far-field microscope with a laser interferometer working at a wavelength of 400 nm. The device allows us not only to determine the size of objects at microscopic scale, but also to find their refractive index profile relative to the refractive index of ambient liquid. Actually, the phase microscope measures the optical path difference between the reference and object waves in the laser interferometer. Thus, if the object wave passes through a

2. LASER PHASE MICROSCOPY Hereinafter, distilled water with a resistivity of 5 MΩ·cm and pH = 5.7, and analytical grade NaCl (BioXtra, mass fraction 99.5%, Sigma-Aldrich) was used for preparing the aqueous solution samples. These samples were filtered by a pressure filtration device using a Teflon membrane with a pore size ≈200 nm. In accordance with theoretical estimates,31 the bubston radius is Rb ∼ 100 nm. This means that bubstons in bulk liquid sample with a height h ≫ 100 nm (in our case, h = 30 μm) can stochastically move with an average speed v ∼ D/ Rb ∼ 10 μm/s (where D ∼ 10−8 cm2/s is a theoretical estimate of the bubston diffusivity). Since, the acquisition time of an interference pattern with a resolution of 1280 × 1024 pixels in our case is τ = 0.2 s, we find that during this time bubston moves on the average over a distance of R = vτ ≈ 200 nm > Rb. Thus, the phase profile of individual bubstons, which allows us to determine their size and refractive index, can be obtained only if the bubstons are nearly motionless. 1292


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The Journal of Physical Chemistry B Individual bubstons can be detected near the inner surface of the cover glass of the cell used in the phase microscopy experiment. In fact, the viscosity of liquid increases dramatically in the near-surface layer, so that the bubston mobility decreases up to zero. We performed an experiment with a sample of 1 M NaCl aqueous solution of the height h = 30 μm by the use of an objective with a numerical aperture of 0.9 (100× magnification) that provides the maximum resolution achievable for nonimmersion objectives. By measuring the spatial refractive index distribution (in terms of the optical path difference), we managed to visualize stationary structures at the submicrometer scale with a refractive index lower than the refractive index of the ambient liquid, see Figure 1, where an interference pattern

Figure 2. Two-dimensional distribution of the optical path difference for a nanometer-sized particle near the cover glass in 1 M aqueous NaCl solution (a) and its profile along the axis Y (b), obtained using an objective with a numerical aperture of 0.9. Figure 1. 2D-distribution of the optical path difference in 7.5 × 7.5 μm2 area. The pattern was obtained using an objective with a numerical aperture of 0.9.

where n0 = 1.332 (for water), Δh is the difference between the maximum and minimum values of the optical path difference, expressed in nm, γ is a dimensionless correction factor. From calibration experiment with monodisperse polystyrene latex particles, having a known refractive index, it was found that γ ≈ 2.5. For the particle in Figure 2b, we have Δh ≈ −50 nm. According to (3), the refractive index for this particle n = 0.92 ≈ 1, which corresponds to a uniform spherical gas particle, i.e. it is gas nanobubble. Phase microscopy shows that the characteristic size of nanobubbles is almost independent of ion concentration in the solution. In fact, Figure 4 shows the distribution of the optical path difference in a 7.5 × 7.5 μm2 area for 0.1 M NaCl solution. It is seen that with decreasing the ion content by an order of magnitude (in comparison with Figure 1), the size of nanobubbles is practically not changed (as in Figure 1, separate small cavities represent nanobubbles). It should be noted that particles with a refractive index n < 1.33 emerge only in the presence of ionic components in the sample. In accordance with the theoretical model,31 such particles can be treated as bubstons and bubston clusters. As is known, one of the most common techniques for studying nanoscale particles in liquid is DLS. So, naturally, the question arises: to what extent do the data of phase microscopy correspond to the results of DLS? Recall that in ref 37, we also carried out experiments with DLS. In the present work, we have refined our earlier data. Furthermore, in the following experiments, it is proved that the bubstons and bubston

of 7.5 × 7.5 μm2 area is shown. In this figure, the vertical axis corresponds to the optical path difference in the units of λ h = 2π δ , where λ = 400 nm is the laser wavelength, and δ is the phase difference between the reference and object waves of the interferometer. As is seen in Figure 1, the interference pattern has a spatial resolution sufficient to detect nanometer-sized particles, which look as tiny cavities on the phase distribution and thus can be discerned along with large branched cavities corresponding to micrometer-scale particles. An example of the phase distribution in the vicinity of the nanometer-sized particle is shown in Figure 2, parts a and b. The radius of this particle, evaluated as the half width of the profile at its half height, is approximately 150 nm, see Figure 2b. An analysis of the phase profiles of these particles suggests that with a good accuracy they have the same radius of 150 nm in 1 M NaCl solution. As an illustration of such monodispersity, the phase profile of a dimer composed of such nanoparticles is shown in Figure 3. It must be borne in mind that the measured profiles are broadened due to diffraction, i.e. the real size of these particles is slightly smaller. As was shown in ref 37, the refractive index for particles in a liquid is calculated by the formula ⎛ Δh ⎞ ⎟ + n n = γ⎜ 0 ⎝ 2R ⎠

(3) 1293


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3. DYNAMIC LIGHT-SCATTERING SPECTROSCOPY The DLS method is based on photon correlation spectroscopy.39,40 Here, the intensity I of light, scattered at a specific angle θ in a liquid sample, is measured. Since the particles obey the diffusion law, the frequencies of the interfering waves are shifted due to the Doppler effect. Thus, the scattering spectrum is inhomogeneously broadened, and the scattering intensity I can be represented as a random process I(t), whose time correlation function G(2)(τ) can be found in a direct experiment in the form: G(2)(τ ) = ⟨I(t )I(t + τ )⟩ = lim

tm →∞

1 tm

∫0

tm

I ( t ) I (t + τ ) d t (4)

where tm is the time of accumulating the correlation function. In accordance with Onsager’s hypothesis,41 the relaxation of fluctuations of the scattering particles volume number density can be described by the diffusion equation: ∂P(r, t )/∂t = −DΔP(r, t )

(5)

where P(r, t) is the probability density function, r is the coordinate of a particle, time t is a parameter, and D is the particle diffusion coefficient. As follows from the Wiener− Khinchin theorem (see, for example, ref 42), the correlation function of a relaxation process (the spectrum of which is described by a Lorentzian contour) is a decaying exponential function. Specifically, if the system is characterized by a single diffusion coefficient (i.e., we deal with a suspension of monodisperse particles in liquid), P(r, t) can be written as Figure 3. Two-dimensional distribution of the optical path difference for a nanoparticle dimer near the cover glass in 1 M aqueous NaCl solution (a) and its profile along the axis Y (b), obtained using an objective with a numerical aperture of 0.9.

P(r, t ) =

⎛ (Δr)2 ⎞ 1 exp ⎜− ⎟ ⎝ 4Dt ⎠ (4πDt )3/2

(6)

Averaging over the distribution P(r, t) gives the correlation function G(2)(τ) in the form: ⎛ 2|τ | ⎞ G(2)(τ ) = a exp⎜ − ⎟+b ⎝ tc ⎠

(7)

where b = ⟨I⟩ , a is a dimensional constant, and tc is the correlation time. It follows from (5), (6), and (7) that the inverse correlation time is 2

1/tc = Γ = Dq2

(8)

Here q is the wave scattering vector, which is related to the wave vectors of scattered and incident waves by the Bragg condition. The modulus of this vector, as is known, is described by the expression: q=

⎛ 4πn0 ⎞ ⎛ θ ⎞ ⎜ ⎟ sin⎜ ⎟ ⎝ λ ⎠ ⎝2⎠

(9)

As previously, n0 is the refractive index of the liquid, where the scatterers are suspended. For solid spherical particles with a radius R, moving with a velocity u and subjected to Stokes friction F = 6πηRu, where η is the dynamic viscosity of liquid, one can use the Stokes − Einstein formula for the particle diffusion coefficient:

Figure 4. 2D-distribution of the optical path difference in 7.5 × 7.5 μm2 area for 0.1 M NaCl solution.

clusters arise not only in the presence of ions, but also in the presence of dissolved gas and under the condition of stirring the liquid sample. A DLS apparatus has been described in detail in ref 37; for the convenience of presentation, below we briefly explain the foundations underlying the DLS technique.

D=

κBT 6πηR

(10)

where κB is the Boltzmann constant and T is absolute temperature. If one deals with a gas bubble in a liquid, the 1294


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Figure 5. Scattering intensity distributions over particle sizes in a sample of 1 M NaCl aqueous solution for scattering angles θ = 45° (a) and 120° (b).

Figure 6. Scattering intensity distributions over particle sizes in a sample of 1 M NaCl aqueous solution (scattering angle θ = 45°) after a long-term settling in a vertical hermetically sealed cell (compare to Figure 5, parts a and b).

Stokes friction force is F = 4πηRu, see ref 43; therefore, the corresponding formula is κT D= B 4πηR

(tc)i =

1 ; Diq2

the results can be represented as histograms of

scattered light intensity over the scatterer radii R. Parts a and b of Figures 5 show such hystograms for 1 M NaCl solution and scattering angles θ = 45° and 120°, respectively. The histograms are normalized to their integral values. The plots presented here demonstrate rather broad distribution over radii ranging from 70 to 3000 nm. At the same time, one can clearly see two peaks in the plot in Figure 5a, with maxima at 120 and 1500 nm. The choice of scattering

(11)

In the case polydisperse suspension (actually, we deal with such a system), we should analyze a set of exponentials in the form (7) with the corresponding set of correlation times 1295


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Figure 7. Scattering intensity distribution for the freshly prepared 10−6 M NaCl aqueous solution.

angle θ is of no fundamental importance, although the scattered intensity obviously decreases with an increase in θ (see, e.g., refs 44 and 45). The reproduction of peak positions in the size distributions obtained at different θ confirms additionally the assignment of these peaks to real particles. Note that the distribution I(r) is not identical to the scatterer size distribution because the dependence of the scattering cross section on the particle size must be taken into account here. Since the sizes of the scatterers, detected by DLS, coincide approximately with the sizes of the particles observed by phase microscopy, it is reasonable to suggest that these are the same particles (the same NaCl solution was studied simultaneously by both methods). Therefore, the peaks in the distribution (Figure 5a) must be associated with separate bubstons and bubston clusters. A natural question of the stationarity of bubstons and bubston clusters arises. Let us consider again Figure 5 (a). The size distribution, depicted here, turned out to be not quite stationary: large particles (bubston clusters) disappeared after settling the sample for a very long time (six months) in a hermetically sealed (without access to air) cell, whereas single bubstons survived (Figure 6). Figure 7 shows scattering intensity distribution over bubston sizes in a freshly prepared 10−6 M NaCl solution; a freshly prepared sample is one, settled open to the atmosphere for no more than two −3 h immediately after pouring in the cell for letting the micrometer-sized bubbles, appeared in the process of pouring, float up. Note that, during sample preparation, various shear flows arise in the liquid as a result of stirring and pouring the sample, which, as will be shown below, facilitate the bubston nucleation. It can be seen that the size distribution is fairly narrow and has a peak at about 80−90 nm. Comparing plots in Figures 6 and 7, one can claim that the equilibrium bubston radius does not depend (or depends very weakly) on the ion content. Therefore, we can assume that the equilibrium bubston radius in NaCl aqueous solutions is about 100 nm. The phase microscopy experiment also revealed that the bubston radii amount to 150 nm and are independent of the ion content (see Figures 2−4); as was noted above, an increase of bubston size in phase microscopy experiments can be caused by diffraction effects. Furthermore, by comparing the scattering coefficients, we can conclude that the volume number densities of bubstons in the freshly prepared 10−6 M solution and in the 1 M solution, which was settled for 6 months in a sealed cell, are approximately the same.

A comparison of the scattering intensities measured in freshly prepared NaCl solutions and in toluene, whose scattering coefficient is known (see, e.g., ref 46), allowed us to estimate the bubston number density nb in these solutions as a function of salt concentration on a double logarithmic scale (Figure 8).

Figure 8. Variation of the number density of bubstons nb with the ion content in freshly prepared NaCl aqueous solutions.

Note that these calculations were performed on the assumption of bubston size Rb being constant and independent of the ion concentration, that is, the scattering cross section for individual bubstons Ccsa is also implied to be constant (for a spherical bubston of Rb = 100 nm in water, Ccsa = 0.004 μm2 at the light wavelength λ = 633 nm). As is seen in the graph in Figure 8, there exists a quite clear relationship between the bubston number volume density nb and the concentration of NaCl, so we can claim that the presence of this salt is indeed necessary for the generation of bubstons. Of course, it would be interesting to explore other pairs of cations and anions in the context of the stabilization of bubstons; we are currently conducting experiments with anions and cations in the Hofmeister series, i.e., ions, which are differently hydrated and, consequently, are “kosmotropes” or “chaotropes”. As follows from the graph, the experimental points can be approximated by the function nb ∼ 4.5 × 107(C − C0)1/4, where the constant C0 ≤ 10−7 M can be considered as a certain threshold concentration, necessary for bubston nucleation. 1296


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conditions for bubston nucleation are met. Note that the content of dissolved gas and ions in both cells is equal, but in the open cell the liquid evaporates, while in the sealed cell the evaporation does not occur. The evaporation in the open cell results in a slight cooling of the liquid interface, due to which the convective counter-flow is generated, while this mechanism is obviously absent in the sealed cell. We of course can imagine the convective counter-flow in the sealed cell, associated with bubston clusters, which float up to the surface and entrain ambient layers of liquid due to the viscous forces, but this process will eventually stop. It can be concluded that the system of bubstons and bubstons clusters is not a thermodynamic equilibrium phase: for their stable existence in an aqueous salt solution, contact with the atmosphere is needed to ensure the presence of convective counter-flow through the evaporation. Generally, as noted in the work of Ball and Ben-Jacob,48 “water at room temperature under ordinary conditions (open to the atmosphere) is a nonequilibrium open system that exchanges heat and gases with the environment.″ The evaporation may result in different possible types of Rayleigh and Marangoni convective flows (see, for example, ref43). The different modes of Rayleigh convection in the presence of a temperature gradient are described for real liquids

Unfortunately, because of a large dispersion of the data in these experiments, we can determine only the upper boundary of ion concentration C0. Furthermore, bubston detection, in the scattering experiments, is limited by the level of conventional molecular scattering. It is also seen that saturation occurs at high ion concentrations, i.e., nb barely changes with a further increase in the ion content. It is seen that nb actually stops growing at the ion concentration C = 10−1 M = 6 × 1019 cm−3. At this concentration, we have nb ∼ 6 × 107 cm−3, while in accordance with theoretic estimate in ref 31, the surface density 14 −2 of ions, adsorbed at the bubston interface γAD i ≈ 6 × 10 cm , 6 i.e., the bubston of radius Rb = 100 nm contains ∼10 ions. Thus, the relative share of the ions, associated with bubstons ΔC

6 × 107 × 106

can be estimated as C = 6 × 1019 ∼ 10−6 , i.e., the saturation in the dependence nb(C) cannot be associated with deficit of ions, associated with the bubston stabilization. It is clear that the mobility of ions, adsorbed at the bubston interface, should be essentially lower than that for the ions in the nonadsorbed state. Therefore, after removal of bubstons (e.g., as the result of degassing), the conductivity of liquid should slightly increase, which indeed was observed in experiments, see, e.g., ref 47. According to our model, bubstons are in a state of local thermodynamic equilibrium with the ambient liquid, which corresponds to the diffusion equilibrium of the chemical potential of dissolved gas molecules at the bubston interface. Thus, under normal conditions, the pressure inside bubstons is p = 1 Atm. If the liquid is subjected to degassing, the diffusion equilibrium at the bubston interface is violated, and the gas molecules, via the diffusion kinetics, go out of the bubstons toward the bulk of the liquid that eventually leads to the collapse of bubstons. On our assumption, the dissolved gas molecules can be subdivided into free molecules inside the bubstons, and “intrinsically dissolved gas molecules”; this term was first introduced in ref 32 and means that individual gas molecules are surrounded by water molecules, and, probably, hydrated. Let us now estimate the value nf of the volume number densities of the free gas molecules at C ≥ 10−1 M. The total volume number density of dissolved molecules of the atmospheric air in water under normal conditions is nd = KNL ≈ 6 × 1017 cm−3 = nf + ni, where NL ≈ 3 × 1019 cm−3 is Loschmidt number, K ≈ 0.02 is the effective dimensionless Henry constant for atmospheric air, ni and nf are the volume number densities of intrinsically dissolved and free gas molecules, respectively. Thus, each bubston with the radius 4 Rb = 100 nm contains N = NL 3 πR b 3 ≈ 12.6 × 104 free gas molecules, i.e. nf = Nnb ≈ 7.6 × 1012 cm−3, nf ≪ nd. Thereby nd ≈ ni ≈ KNL, and Henry law can be formulated specifically for the intrinsically dissolved gas molecules. Note finally that the graph in Figure 8 is not stationary; we further explain qualitatively such a behavior. As shown in ref 38, bubston nucleation occurs as a result of local shear stresses in a liquid, saturated with dissolved gas and containing an ionic impurity. Obviously, the shear stresses arise while stirring the sample. This can be verified by vigorous shaking the cell with a transparent solution: small bubbles appear in the sample, and the solution remains turbid for several minutes. Different results for the volume number density of bubstons in the open to the atmosphere and sealed cells may be explained by the lack of the mechanisms of bubston nucleation in the sealed cell, while in the open cell, the

using Rayleigh numbers Ra =

gβ ΔTL3 νχ

where g is the gravita-

tional acceleration, β is the thermal expansion coefficient for water, ΔT is the temperature difference between the surface and the bulk of water, L is the characteristic linear scale of the heat transfer surface, ν is the kinematic viscosity of water, χ is its thermal conductivity. In the following, we estimate the Rayleigh number for ΔT = 0.2 °C, which was calculated by a program simulating the evaporation of water. Assuming that in our experimental situation L = 3 cm, we obtain Ra = 62253. The Rayleigh number is usually compared to its critical value Racrit; for water Racrit = 1100−1700. When Ra < 7.4Racrit, there are no convective counter-flows. When 7.4Racrit < Ra < 9.9· Racrit, a laminar convection with a single circulation rate occurs. In the interval 9.9Racrit < Ra < 11.01Racrit, there appear laminar counter-flows with different rates. Finally, when Ra > 11.01Racrit, the convection becomes turbulent. In our case, the turbulent convection threshold is exceeded, therefore we can say that such a convection actually becomes possible. In connection with the above-described matter, the mechanism of the bubston nucleation in the bulk of a liquid looks as follows. A liquid sample is implied to be poured into a cell; as is known,43 the boundary layer, where the liquid is immobile, is formed near the surface of the cell. If a shear counter-flow is excited in the vicinity of this layer, there arise the shear stresses that lead to local microruptures of the liquid in this region. The characteristic size R of the cavities, formed in such way, can be estimated from the condition R ≫ R0, where R0 = 3 1 is the mean distance between the liquid molecules, nl is nl

the volume number density of the liquid molecules. For water, which has nl = 3 × 1022 cm−3, we obtain R0 ≈ 3.2 Å, i.e., R ∼ (10−100)R0 = 30−300 Å. The intrinsically dissolved gas molecules occupy this cavity via diffusion kinetics and form a short-living “proto-bubston” (note that the term “proto-bubble” is widely used in the studies, devoted to bubble chambers). Actually, such proto-bubston quickly collapses due to huge surface tension force, i.e., its lifetime is very small. However, if a certain amount of ions is capable of adsorbing on the protobubston surface before it completely collapses, the proto1297


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bubstons arise. The proto-bubstons in the filtered sample are being filled with the intrinsically dissolved gas molecules, and therefore the value of ni becomes markedly lower compare to that before the filtration. The question of the sizes and dynamics of proto-bubstons and their typical lifetime remains unexplored, but we can assume that they captured a significant amount of intrinsically dissolved gas molecules ni. This, on the one hand, qualitatively explains the graph in Figure 9, and, on the other hand, does not strongly contradict to the inequality ni ≫ nf in the steady state, because apparently only a very small part of proto-bubstons can survive. This question, however, requires a more detailed study. Immediately after filtration the liquid samples were poured into cylindrical vials with a diameter of 25 mm and a height of 30 mm and kept open to the atmosphere for a day; the dissolved gas content certainly turned back to its equilibrium level for that time, so that the initial number density of bubstons in the samples was nb = 4.5 × 106 cm−3. Then the samples were subjected to centrifugation with a magnetic stirrer at variable circulation rate (TA Instruments, USA) for a certain time t at room temperature and then studied by the DLS technique. In the process of centrifugation we controlled the surface of the liquid: the surface retained a fixed (approximately parabolic) shape, no liquid droplets were torn off the surface and no droplets fell on the surface in the process of centrifugation, thus the growth of dissolved gas content resulted from trapping gas particles by such droplets was excluded. DLS measurements of centrifuged samples showed that the size distribution remains unchanged at short times and expands slightly toward larger sizes at long times, while the scattering coefficient grows at short times and reaches a constant value at long times. Having known the scattering cross section of a separate bubston, we can plot the time dependence of the volume number densities of bubstons nb(t), which for the stirring rates ω1 = 150 and ω2 = 1500 rpm are shown in Figure 10.

bubston appears to be stabilized by the mechanism described in the Introduction. Note, however, that the model of ionic adsorption, described in ref 31, is valid only for the equilibrium situation and cannot in principle be applied to the case of the adsorption on the proto-bubston surface, so that our arguments should be considered only as qualitative ones. Nonetheless, intuition suggests that the higher the ion content, the higher the volume number density of viable proto-bubstons. The possibility of such a nonequilibrium mechanism of the bubston nucleation was confirmed in the following experiment. Samples of aqueous NaCl solution with concentration C = 0.16 M (physiological solution) saturated with atmospheric air were filtered by a Teflon membrane with a pore size of 200 nm, which is close to the bubston size. It turned out that the filtration partially reduces the dissolved air content; for the first time, we have compared the content of dissolved oxygen in freshly prepared liquid samples and in the same samples immediately after the filtration. The content of dissolved oxygen was measured with OROBOROS Oxygraph-2k highresolution respirometer. Figure 9 shows the time variation of

Figure 9. Time variation of the dissolved oxygen content in aqueous NaCl 0.16 M solution before and after filtration carried out at t = 0.

the dissolved oxygen content; the sample was subjected to filtration at t = 0. We observed approximately 20 percent reducing the oxygen content compare to its equilibrium value N0 = 271 μM, which is obviously related to the value nd ≈ ni for the dissolved oxygen. The filtration effect is completely reversible: while the filtered sample is settled in the cell of height h ≈ 10 mm, open to the atmosphere, the initial concentration of dissolved oxygen is completely recuperated for t ≈ 3 h. Note that the recuperation process is not controlled by a diffusion kinetics of saturating with oxygen solely from the liquid surface, otherwise we should have obtained the estimate

Figure 10. Time dependence of nb(t) for the centrifugation at the stirring rates 1500 rpm (red graph) and 150 rpm (black graph).

h2

t = D ≈ 14 hrs, where D ≈ 2 × 10−5 cm2/s is the diffusion coefficient of oxygen in water.49 We attribute this effect to the following. In this experiment we actually study the dynamics of ni; the bubstons cannot penetrate into the filtered sample, while the intrinsically dissolved gas molecules can go through the membrane pores. It is clear, nonetheless, that in the process of forcing a liquid through a porous membrane fairly complex pattern of shear microvortices is realized, i.e., in accordance with our model, the conditions for the nucleation of new proto-

The experimental points in these graphs were approximated by the function nb(t) = (nb)0 − c exp(−at), where, for the stirring rate, ω1 we have (nb)0 = 2.1 × 107 cm−3, c = 1.6 × 107 cm−3, and a = 3 × 10−3 s−1 while for ω2 these parameters are (nb)0 = 2.3 × 107 cm−3, c = 1.8 × 107 cm−3, and a = 3.2 × 10−2 s−1. As follows from the graphs, for both stirring rates, the centrifugation results in the growth of nb by an order of 1298


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Figure 11. Scattered-light intensity distribution for initially degassed NaCl aqueous solution with concentration C = 0.16 M (physiological solution) after unsealing the cell and settling the sample open to the atmosphere for 24 h.

along the optical axis in the lens caustic; the total number of such flashes is controlled by the volume number density of the breakdown centers. It is convenient to use near-IR radiation in experiments with optical breakdown because this radiation is invisible, so it does not hinder the plasma flashes from visual observing. At the same time, the absorption of light (and laser heating) in this spectral range can still be ignored. These experiments were carried out with single pulses of Nd3+:YAG laser with pulse-width τ = 21 ps at a wavelength λ = 1.064 μm, the absorptivity in water is 0.17 cm−1. The pulse energy W can be varied in the range of 1−10 mJ. The radiation was focused into a cell with the sample: the focal length was 10 cm, the radius of the spot on the lens was 5 mm, the radius of the laser spot in the caustic was ∼100 μm, and the caustic length was 4 mm. The incident laser light is scattered by the plasma generated by laser shot. In the experiments we explored the dependencies of intensity Is of the scattered under 90° incident light versus the pulse energy W. Parts a and b of Figure 12 shows the dependence of Is(W) for aqueous NaCl solution, C = 0.16 M (physiological solution); each data point corresponds to a laser “shot” with a certain energy W. Case a corresponds to the freshly prepared sample, which was open to the atmosphere during the experiment, and case b is related to the same solution, which was preliminary degassed and prior to the experiment was kept for several months in the sealed cell under the pressure of 17 Torr; i.e., by our model, this is the bubston-free sample; we performed the DLS experiments (see previous section) exactly for this sample. The threshold energy Wthr corresponds to the intersection of the dependence Is(W) with the abscissa-axis. It is seen that for the bubston-free samples the value Wthr exceeds more than 30 times that for the freshly prepared samples. Furthermore, the dependence Is(W) for the freshly prepared samples has an obvious dispersion of the experimental points, while for the bubston-free samples such dispersion is not so prominent. We attribute this to the fact that the freshly prepared solutions contain not only the individual bubstons but also the bubstons clusters, for which the breakdown threshold Wthr is significantly lower than that for individual bubstons. At the same time, the bubston-free samples contain the bubstons only in the trace amounts and do not contain the bubston clusters at all, i.e., the breakdown occurs only due to the presence of individual bubstons (the breakdown centers), and the dependence Is(W) is more regular.

magnitude: the graphics nb(t)|ω1 and nb(t)|ω2 come to approximately the same stationary level (nb)0 ≈ (2−2.5) × 107 cm−3. Note that for ω2 the dependence nb(t) arrives at the steady-state level for t ≈ 300 s (5 min), while for ω1 this level is reached within t ≈ 14000 s (≈3.8 h); when the stirring rate grows by an order of magnitude, the parameter a, characterizing the rate of establishing the stationary level (nb)0, increases to the same extent. Note also that in accordance with the data in Figure 8, the value of nb for freshly prepared 0.16 M solution of NaCl is very close to (nb)0. The presence of the stationary level (nb)0 indicates that the magnetic stirrer does not introduce some additional impurities into the sample. At the same time, increasing the value of nb with a magnetic stirrer is a reversible process: if the sample with the bubston density (nb)0 is yet again subjected to the filtration using a membrane with a pore diameter ϕ ≤ 2Rb, and subsequent settling in an open to the atmosphere cell, we get the initial value of nb ≈ 4.5 × 106 cm−3. Now, the only thing to do is to make sure that the volume density of bubstons is determined by the content of dissolved gas. To this end, a sample of degassed 0.16 M NaCl solution in a hermetically sealed cell (the pressure in the free volume of the cell was 17 Torr, that is, the saturated vapor pressure at room temperature) was studied by the DLS technique. According to the experimental data, this sample did not contain any scatterers with radii from 100 to 1000 nm. At the same time, after unsealing the cell and opening it to atmosphere, particles with a size distribution maximum at 200 nm arose in the liquid after 24 h (Figure 11). This estimate corresponds to the time of the diffusion saturation with dissolved gas for a liquid sample of the height h = 1 cm.

4. OPTICAL BREAKDOWN Note that the key role of dissolved gas nanobubbles was also confirmed in experiments with optical breakdown. Indeed, as was shown in refs 50−53, bubstons and bubston clusters play the role of heterogeneous centers for optical (laser-induced) breakdown in transparent liquids free of solid impurities. In accordance with the model considered in ref 54, optical breakdown develops if a bubston or bubston cluster occurs in some volume V during laser pulse; this volume is determined by the pulse energy and focusing conditions. The light intensity in this volume should exceed certain threshold value, sufficient to induce the breakdown and generate plasma inside this bubston. Therefore, the pattern of optical breakdown on bubstons should look like a set of individual plasma flashes 1299


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density of the blackbody radiation, which is related to the heating of the electron gas in the process of breakdown inside individual bubstons, with the spectral maximum at λmax = 450 nm. As follows from Figure 13a, the bubston-free solution contains the breakdown centers only in trace amounts: we can discern on the average five breakdown flashes per one millimeter, which corresponds to the volume number density of such centers n = N2 ∼ 105 cm−3, where N = 5, l = 1 mm, and r πr l

= 100 μm is the laser beam radius in the caustic. Note that in the DLS experiment such small number densities of bubstons cannot be detected due to low sensitivity of the DLS setup. In the experiment on optical breakdown (in contrast to the phase microscopy experiment) we cannot say unambiguously if the breakdown centers are bubstons or solid nanoparticles. At the same time, the increase in the volume number density of the breakdown centers after the sample saturation with dissolved air (Figure 13b) indicates that breakdown centers are indeed bubstons. In accordance with the DLS experiment (see Figure 11), the scatterers, appeared in the sample after 24 h settling in the open air, are bubstons as well. Thus, the plasma flashes in Figure 13a are due to the breakdown inside the bubstons. Let us again consider the plot nb(C) in Figure 8. In this plot, at C = 0.16 M, we arrive at nb ≈ 2.5 × 107 cm−3. Thus, we can estimate the number of breakdown centers N = nbπr2l for the situation, illustrated in Figure 13b. For l = 1 mm we obtain N ≈ 103 mm−1. Bearing in mind that Rb = 100 nm, the mean distance between neighboring plasma flashes ⟨r⟩ ≈ 600 nm; this estimate neglects the fact that the bubstons filled with plasma are expanded due to the thermal heating; i.e., this distance is even smaller. The spatial resolution of the optical system along λmax ≈ 880 nm, where n is the the horizontal axis is δx = 0.61 n sin α refractive index of water and α is the viewing angle of an objective used by us. Since ⟨r⟩ < δx, two neighboring plasma flashes cannot be resolved in accordance with the theory of optical images, and one would expect to see a continuous bright line along the caustic lens in the far-field zone; specifically this is shown in Figure 13b. To sum up this section, we can claim that the bubstons found in the phase microscopy experiment and the scatterers of the same size revealed in the dynamic light scattering and optical breakdown experiments are the same entities. Below we report the results of experimental study of bubston clusters by laser polarization scatterometry: measurements of the angular dependences of scattering-matrix elements. The experimental setup and the experiments was described in ref 38.

Figure 12. Dependence of the energy, Is, of incident laser radiation scattered at an angle of 90° to the optical axis (in relative units) on the pulse energy for (a) freshly prepared physiological solution and (b) degassed physiological solution. The dots correspond to the experimental data.

Let us further analyze in more detail the breakdown stimulation in the bubston-free sample. The optical breakdown pattern for this case is shown in Figure 13a. The breakdown spark is just a set of separate bright points, which corresponds to an optical breakdown within individual bubstons that were not completely removed from the sample. The estimated intensity of light in the lens focus (the self-focusing effect was disregarded while calculating this value) is I = 1.3 × 1013 W· cm−2. If one opens the cell into the atmosphere and shoots the sample immediately after that (this experiment takes a few seconds), the breakdown pattern does not change, i.e., the external pressure practically does not influence the breakdown in individual bubstons. At the same time, if the sample is settled for a day open to the atmosphere (similar to the DLS experiment), the breakdown pattern changes dramatically, see. Figure 13b. In this case the plasma flash looks as a continuous bright line. For the latter case we specially investigated the plasma flash spectral intensity G(ω); for more detailed information about the emission spectrum at different modes of the optical breakdown see our previous work.54 It turned out that the function G(ω) can be interpreted as the spectral

5. THE INVERSE LIGHT-SCATTERING PROBLEM FOR BUBSTON CLUSTERS IN AQUEOUS NACL SOLUTIONS To make a computer simulation of bubston clusters, we used hierarchical model of clustering for spherical particles.37,55,56 We have found a solution to the inverse scattering problem in the form of a stochastic sample of 2 × 103 hierarchical-type clusters obeying exponential distribution p(N) ∼ e−aN over the number N of bubstons in a cluster (N ≥ 1, a > 0). To do this, we calculated a set of the scattering matrices as the averages over random cluster ensembles with the statistical parameters, taken on a uniform discrete grid. The solution was found by minimizing the divergence between the measured angular profiles of the scattering matrix and the same profiles, 1300


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Figure 13. Patterns of the optical breakdown (a) in a degassed NaCl solution with a concentration C = 0.16 M and (b) in the same solution but settled for 24 h in the cell open to the atmosphere.

Figure 14. Mutually perpendicular projections of a stochastic realization of hierarchic bubston cluster with the parameters N = 400, Rb = 100 nm, Df = 2.45.

calculated for a computer-generated sample of clusters. Numerical experiments have shown that it is possible to find a solution to the inverse scattering problem for the bubstons with radii Rb = 50−150 nm, i.e., to choose the appropriate values of the parameters of cluster ensemble; these parameters are the average number of bubstons per cluster ⟨N⟩ and the average fractal dimension ⟨Df⟩ of clusters. In modeling the clusters, the initial parameters of bubston phase were taken as the results of DLS and phase microscopy experiments, where the radius of bubstons and the effective width of the distribution over the sizes of bubston clusters were measured. We have found that the bubstons are practically monodisperse, and their size is Rb ≈ 100 nm. In view of this fact, we found the corresponding solution to the inverse scattering problem. The parameters of the cluster ensemble are ⟨N⟩ = 200 and ⟨Df⟩ = 2.45. Figure 14 shows a particular realization of the bubston cluster simulation. For comparison with phase microscopy data, obtained for bubston clusters (see Figure 4 in ref 37), we present the results of numerical modeling the effective refractive index for the

bubston cluster, depicted in Figure 14. The refractive index, averaged over a spherical volume with the radius r is shown in Figure 15 as a function of r. Here, the origin of coordinates corresponds to the cluster center of mass. The radius r has a physical meaning of the so-called radius of gyration rg relating to the instantaneous configuration of the growing fractal cluster N

rg =

N

∑ rj 2R j3(∑ R j3)−1 j=1

j=1

(12)

where Rj and rj are the radius of the jth bubston and the distance from its center to the origin of coordinates, respectively; the summation is carried out over all bubstons in the cluster. The dependence ⟨n⟩ = f (r) can be regarded as an evolution of the average refractive index of the entire cluster due to the fractal growth at a constant parameter of cluster−cluster aggregation α; see ref 56. With increasing r, the given dependence achieves the asymptote ⟨n⟩ → 1.33, which 1301


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■

4 The experimental results allow us to distinguish several types of liquid samples with respect to the bubston system: stirred samples, characterized by enhanced number density of bubstons (stirring also results in the generation of bubston clusters); filtered samples, where the number density of bubstons is substantially reduced; degassed samples, where the number density of bubstons is negligible.

AUTHOR INFORMATION

Corresponding Author

*(N.F.B.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by Russian Foundation for Basic Researches (Project Nos. 15-02-07586 and 16-52-540001) and Grant NSh-4484.2014.2 for Support of Leading Scientific Schools.

Figure 15. Refractive index ⟨n⟩ of the bubston cluster (Figure 11), averaged over a spherical volume of the radius r.

■

corresponds to the refractive index of water (in this simulation, we do not account for a slight increase in the refractive index of saline solution compared with pure water). It follows from the graph that the condition of fractal self-similarity is fulfilled for the radii of gyration r = rg ≥ 0.5 μm. Thus, using this graph, the value of ⟨n⟩ for the bubston clusters of size rg > 0.5 μm can be estimated. The cluster, shown in Figure 14, has the size rg = 1.25 μm, and, therefore, we obtain ⟨n⟩ ≈ 1.3. Large bubston clusters similar to that, shown in Figure 14, can be formed in liquid samples, where the number density of bubstons is raised significantly above some equilibrium level as a result of some external influence, such as stirring or shaking that usually accompany the preparation of aqueous solutions. The presence of large clusters is indicated by a broad size distribution of scattered intensity, for which second micrometer-scale peak may appear in addition to 100 nm one (see Figure 5). Summarizing, it is important to emphasize that the parameters of bubston clusters, which are found as the solution to the inverse scattering problem from the angular dependencies of the scattering matrix elements measured in ref 37, are fully consistent with the parameters, obtained in independent experiments with phase microscopy, optical breakdown, and dynamic light scattering.

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6. CONCLUSIONS 1 Experiments using four independent laser methods have revealed particles at the micrometer and submicrometer scale, which are generated spontaneously in bulk aqueous solutions of NaCl, free of solid impurities. These particles display the characteristic properties of bubstons and bubston clusters. 2 Phase microscopy and dynamic light scattering showed that the radius of bubstons in the bulk of liquid sample is about 100 nm and practically independent of ion content. 3 Bubstons and bubston clusters are not a thermodynamic equilibrium phase in aqueous salt solutions; as the solutions are settled for a long time in sealed and thermally stabilized cells, the concentration of these particles decreases. This is due to the suppression of convection flows in sealed cells, i.e., the impossibility of bubston nucleation. 1302


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Formation and Dynamics of Ion-Stabilized Gas Nanobubble Phase in

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