Article pubs.acs.org/Langmuir
Ion-Specific and Thermal Effects in the Stabilization of the Gas Nanobubble Phase in Bulk Aqueous Electrolyte Solutions Stanislav O. Yurchenko,† Alexey V. Shkirin,‡,§ Barry W. Ninham,∥ Andrey A. Sychev,†,⊥ Vladimir A. Babenko,⊥ Nikita V. Penkov,# Nikita P. Kryuchkov,† and Nikolai F. Bunkin*,†,‡ †
Bauman Moscow State Technical University, Second Baumanskaya str. 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 ∥ The Australian National University, Acton ACT 2601, Australia ⊥ 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 ‡
ABSTRACT: Ion-stabilized nanobubbles in bulk aqueous solutions of various electrolytes were investigated. To understand the ion-specific mechanism of nanobubble stabilization, an approach based on the Poisson−-Boltzmann equation at the nanobubble interface and in the near-surface layer was developed. It has been shown that the stabilization of nanobubbles is realized by the adsorption of chaotropic anions at the interface, whereas the influence of cosmotropic cations is weak. With increasing temperature, it should be accounted for by blurring the interface due to thermal fluctuations. As a result, the adsorbed state of ions becomes unstable: the nanobubble loses its stability and vanishes. This prediction was proven in our experiments. It turned out that in the case of liquid samples being kept in hermetically sealed ampules, where the phase equilibrium at the liquid−gas interface is fulfilled for any temperature, the volume number density of nanobubbles decreases with increasing temperature and this decrease is irreversible.
1. INTRODUCTION Nanobubbles (gas particles with sizes ranging from tens to hundreds of nanometers) have recently become a subject of increasing research interest.1−4 There exists now much evidence that 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 pancakelike spatial structures. When considering gas nanobubbles in bulk liquid, the question of their stability inevitably arises and remains a challenging problem. Indeed, early theoretical calculations showed that the nanobubbles should persist only 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 be stable only if the liquid is supersaturated with dissolved gas and the surface tension © 2016 American Chemical Society
decreases with increasing degree of supersaturation. In addition, the rate of gas diffusion from both surface and bulk-phase nanobubbles into bulk liquid is relatively slow,19,20 and in the case of nanobubble clustering in bulk liquid, the diffusion yield of gas is even lower as a result of the screening effect of neighboring nanobubbles.21 In our opinion, the selective adsorption of dissolved anions at the nanobubble interface, the Coulomb repulsion of which can compensate for the pressure of surface tension 2Γ/R (R is the radius of the bubble, Γ is the surface tension), cannot be neglected while explaining the mechanisms of bulk-nanobubble stabilization. The adsorption of anions on the surface of aqueous solutions was confirmed in a series of experimental results including second-harmonic generation spectroscopy22,23 and high-pressure VUV photoelectron spectroscopy.24 The fact that basically negative ions are capable of adsorption at this interface is also supported by the data obtained in ref 25, where the Special Issue: Nanobubbles Received: May 6, 2016 Revised: June 27, 2016 Published: June 28, 2016 11245
DOI: 10.1021/acs.langmuir.6b01644 Langmuir 2016, 32, 11245−11255
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the nanobubbles were initially located. This can be treated as indirect evidence of the formation of the diffusion layer with a high concentration of ions around the nanobubbles. We have recently performed a series of experiments confirming the existence of bubstons in the bulk of aqueous NaCl solutions.41 The methodology of these experiments is based upon 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 42. 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 the 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 transparent particle (we assume, for simplicity, that the particle is spherical with radius R), then the phase difference between the object and reference waves is
negative density of the charge on the surface of a gas bubble in pure water was directly measured; in this case, the charge is caused by the adsorption of OH− ions onto the surface. The results obtained in these studies allow us to draw a conclusion about the essential possibility of the adsorption of some anions, for example, Cl−, I−, and Br−, at the water−gas interface. Ionic adsorption at a liquid interface was comprehensively investigated in numerous studies. In this brief review, we of course cannot cite the majority of such works. Here we are going to mention only the studies that guided us in developing our theoretic model. As was shown in refs 26−37, because of the strong effects of the interaction of polarizable ions with water molecules adjacent to the water droplet interface, large anions (halogen ions, for example) are attracted to the interface, but cations (which are fewer in number) are repelled from it. At the same time, the ionic adsorption should obviously depend not only on the type of dissolved ions but also on their concentration. Furthermore, we can encounter a situation where both anions and cations are adsorbed at the interface. Specifically, as was shown in ref 31, at high concentration of electrolytes, cationic adsorption can dominate. As was shown in ref 29, the polarizability effects of ions prevail for the surface effects, and the dispersion interactions are less pronounced. Nevertheless, the dispersion forces should be taken into account to improve the quantitative (but, generally speaking, not qualitative) accuracy of the theory. The contribution of dispersion forces to the adsorption of ions has been considered consistently in refs 31−37. Contributions to the dispersion solvation energies of some simple ions and the noble gas atom effect has been explored in refs 32−35. A new continuum model for calculating the total solvation energies of ions and neutral molecules, based on macroscopic quantum electrodynamics, was suggested in ref 34. The contribution of the cavitation energy, which is associated with the deformation of the hydrogen bond network around the ion, to the ionic adsorption was considered in refs 26−29 and also in refs 33, 36, and 37. As was hypothesized in ref 38, the ionic adsorption at the water−gas interface leads to the formation of stable gas nanobubbles in aqueous electrolyte solutions that were called bubstons (an abbreviation of bubbles stabilized by ions); it was assumed that the solution is in thermodynamic equilibrium with the external atmosphere at a certain pressure p and temperature T. In a subsequent study,39 also dedicated to theoretical analysis of the bubstons problem within the Coulomb model, it was shown that to explain the stability of a gas nanobubble of radius R an additional (negative) pressure is required to compensate for the Laplace pressure 2Γ/R. Then, the condition of mechanical equilibrium takes the form
Pg + Pe = Patm +
2Γ R
δ=
4π R (n − n 0 ) λ
(2)
where n is the refractive index of the particle and n0 is the refractive index of the surrounding liquid. Therefore, by measuring δ, it is possible to separate colloidal particles with high or low (with respect to water) refractive indexes. In experiments with phase microscopy,41 it was found that longlived micrometer-sized particles with a refractive index of less than that of the surrounding liquid arise spontaneously in aqueous NaCl solutions. The refractive index of these particles, n = 0.92 ± 0.05 ≈ 1, corresponds to a uniform spherical gas particle. Phase microscopy shows that the characteristic size of nanobubbles is ∼100 nm and almost independent of ion concentration in the solution. Additionally, data on the size distribution of scatterers in aqueous solutions of NaCl, obtained in ref 41 by means of dynamic light scattering (DLS), revealed the presence of particles of the same size; the theoretical basis for this experimental technique was presented in refs 43 and 44. It was shown in DLS experiments that the dependence of the volume number density nb of bubstons can be approximated empirically by the function nb ≈ 4.5 × 107(C − C0)1/4, where the constant C0 ≤ 10−7 M can be considered to be a certain threshold concentration. Absolute measurements of nb also revealed that the presence of bubstons in liquid does not basically violate Henry’s law, which should be formulated without taking into account the bubston phase. Finally, DLS experiments indicated that bubstons are not a thermodynamic equilibrium phase in aqueous salt solutions; as the solutions are settled for a long time in hermetically sealed and thermally stabilized cells, the concentrations of these particles essentially decrease. This was associated with the suppression of convection flows in sealed cells, which indicates the impossibility of bubston nucleation. As was shown for the first time in ref 41 at extremely low volume number densities of bubstons, when the intensity of light scattering by these particles is less than the level of the molecular Rayleigh scattering (this takes place when the liquid samples are settled for a long enough time in sealed vials without access to atmospheric air and the mechanism of bubston nucleation is suppressed by the absence of convective flows), the only relevant technique for investigating bubstons is based on the optical (laser-induced) breakdown. We demonstrate below that the
(1)
where Pg is the pressure of gas inside the bubble, Patm is the atmospheric pressure, and Pe is this additional (ponderomotive) pressure caused by the presence of adsorbed ions at the nanobubble interface. 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, where ng is the volume number density of gas molecules inside the bubble. In this regard, it is worth mentioning the work40 that describes an experiment with nanobubbles on a solid hydrophobic substrate in an aqueous solution of NaCl. In this experiment, after drying out the solution, ringlike NaCl crystal clots appeared around the areas on the substrate where 11246
DOI: 10.1021/acs.langmuir.6b01644 Langmuir 2016, 32, 11245−11255
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The potential, which corresponds to the ion−interface interaction, takes the form46
experiments with the optical breakdown on separate bubstons (which serve as the optical breakdown centers) have allowed us to find a number of features in the temperature dependence of the bubston volume density. Finally, in ref 41 we restricted ourselves to the investigation of aqueous NaCl solutions, whereas in the experiments described in the present study, we consider aqueous solutions of different cations and anions from the Hofmeister series.
⎧ −2κ(r − R − a) ⎪ βWa e , r−R≥a r−R ⎪ ⎪ βUi(r ) = ⎨ r−R , 0≤r−R R and ε = ε0 otherwise, and εw and ε0 are the dielectric permittivities of water and gas inside the bubble of radius R with the center at r = 0. ρ0 is the volume concentrations of ions, ρ± is the local concentrations of cations or anions, and U±(r) is the effective mean-field potential, which exhibits the features of ionic interaction with water. Equation 3 should be solved with the following boundary conditions for the sought potential ϕ(r )|r →∞ = 0,
λB 2
where p = k 2 + κ 2 . The energy (eq 5) accounts for the violation of spherical symmetry of the Coulomb screening field near the interface. The cavitation potential Uc(r) plays an essential role for chaotropic ions because of their efficient interaction with the hydrogen bond network and can be described as follows
4πq [ρ (r ) − ρ− (r )], ε (r ) +
⎡ qϕ(r ) U±(r ) ⎤ ρ± = ρ0 exp⎢ ∓ − ⎥ kT ⎦ ⎣ kT
(5)
(4)
where the first condition corresponds to the neutrality of the medium and the second one implies the absence of the electric field in the center of the spherical bubble (but not at the bubble interface from the side of the gas phase). We note that eq 3 is essentially nonlinear; therefore, its solution depends significantly on the boundary conditions. In previous works,26−29 the solutions to eq 3 were obtained for small liquid droplets, and other boundary conditions were thus taken into account in those studies. To the best of our knowledge, the problem formulated by eqs 3 and 4 has not yet been considered in analyzing the charged surface of bubbles. Here, we should note that the boundary conditions given by eq 4 are crucially important in the resultant solution to the problem of bubston stabilization. Ion-specific term U(r) includes (i) Ui(r), the ion−interface interaction, (ii) Uc(r), the cavitation potential associated with the interaction of an ion with the network of hydrogen bonds of water molecules, and (iii) Up(r), which accounts for the effects of ionic polarizability; the competition between the contributions of these terms results in the redistribution of the volume number density of ions close to the bubble interface. The ion−interface interaction and cavitation potentials and the effects of polarizability have different contributions for various ions. Below, we describe briefly particular profiles of these potentials employed in our calculations for cations and anions.
(7)
where x is the hydrated part of the ionic charge that minimizes the polarization energy, given by eq 7, x(r ) =
λBπεw + g[1 − cos[θ(r )]] aε0[π − θ(r )] λBπ λ πε + aε [πB− θw(r)] + 2g aθ(r ) 0
θ(r) = arccos(−(r − R)/a), γ is the polarizability of the ion, g = (1 − α)/α, and α = γ/a3 is the relative polarizability. In our calculations, we used for the chaotropes the potential U = Ui + Uc + Up, and for the kosmotropes, the cavitational and polarization effects can be neglected. Note also that eq 3 is written for aqueous solutions of univalent ions but it can be generalized to the solutions of multivalent ions. The parameters of ions, which were used in the calculations, in particular, ionic radii and relative polarizabilities, are presented in Table 1. 2.2. Results of Calculations. Figure 1a−d presents a numerical solution to eq 3 for NaCl at different concentrations. A characteristic feature of the anion behavior is manifested in a clearly pronounced peak in the ionic density distribution localized completely inside the bubble; see panels a−c. The 11247
DOI: 10.1021/acs.langmuir.6b01644 Langmuir 2016, 32, 11245−11255
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analytically. We note that these potentials have such a form because of the strong nonlinearity of eq 3. Using the total charge spatial distribution found, one can obtain the surface density of charge, localized at the interior (i.e., from the gas-phase side) interface of the bubble,
Table 1. Parameters of Ions Used in Theoretical Calculations ion −
Cl Br− I− NO3− ClO3− Na+ K+ Cs+ Mg2+ Ca2+ a
c/ka
a, Å
α
c c c c c k c c k k
2.0,28 1.6426 2.05,28 1.826 2.26,28 2.0526 1.9828 2.1628 2.528 2.028 1.7330 4.2847 4.1247
3.7726 5.0728 7.428 4.0928 5.428
σ=
1 R2
∫0
R
dr r 2[ρ+ (r ) − ρ− (r )]
(8)
The results of calculating the surface charge density at room temperature for different electrolytes at various concentrations are presented in Figure 2. One can see some trends, which emphasize the importance of the polarization effects for understanding the ionic stabilization of bubstons: the location of these curves in the XY plane generally corresponds to the Hofmeister series of anions, but the influence of kosmotropic cations is weak. For univalent ions, we have obtained the following series; here the ions are arranged in order of decreasing surface charge density for the same volume concentration of electrolyte: I− > ClO3− > Br− > Cl− > NO3−. We found that the relation between the effects of anions Cl− and NO3− depends significantly on the hydrated anion radius, used in eqs 3−7. For these anions, such radii can be quite different, depending on the particular conditions. All of the electrolytes in Figure 2, apart from CsCl, include kosmotropic cations. Because these cations are supposed to be strongly hydrated, they cannot penetrate the water surface. In the
2.3448
c and k denote chaotropic and kosmotropic ions, respectively.
characteristic behavior of the ionic concentration and potentials is almost the same for the electrolytes, provided that the anions are chaotropic. The ionic density distribution practically does not depend on the bubston radius R, which is assumed to be much greater than the cation and anion radii. The ionic density distribution at the interface is controlled by the volume concentration of the electrolyte; see panels a−c. The cation cloud in liquid provides diffusive screening of the negative charge, associated with the absorbed anions. Figure 1d presents the mean-field potentials for those concentrations. The linear dependencies are related to the screened Coulomb interaction, ϕ ∝ r−1 exp(−κr), where the inverse Debye length was calculated
Figure 1. Spatial distribution of the ionic density in aqueous NaCl solution near the bubston interface for the bubston radius R ≫ aCl−, aNa+ at (a) C = 10−2 M, (b) C = 10−1 M, and (c) C = 1 M. (d) Mean-field potentials near the bubble interface, found for the same concentrations. Far from the surface, the potentials decay in accordance with the screened Coulomb law (shown by thin black lines), whereas these are constant inside the bubble. 11248
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practically the same as that for pure water. The straight lines corresponding to the bubstons with radii R = 20, 100, and 500 nm are also depicted in Figure 2. From these graphs, we can specify the condition of bubston charging in solution. Also, one should bear in mind that the bubble can survive for a long time in bulk water, provided only that the gravitational Peclet number is 4 4π ρ gR
very small, Pe = 3 wkT <
