Large-Scale Inhomogeneities in Solutions of Low Molar Mass

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Large-Scale Inhomogeneities in Solutions of Low Molar Mass Compounds and Mixtures of Liquids: Supramolecular Structures or Nanobubbles? Marián Sedlák* and Dmytro Rak Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia ABSTRACT: In textbooks, undersaturated solutions of low molar mass compounds and mixtures of freely miscible liquids are considered as homogeneous at larger length scales exceeding appreciably dimensions of individual molecules. However, growing experimental evidence reveals that it is not the case. Large-scale structures with sizes on the order of 100 nm are present in solutions and mixtures used in everyday life and research practice, especially in aqueous systems. These mesoscale inhomogeneities are long-lived, and (relatively slow) kinetics of their formation can be monitored upon mixing the components. Nevertheless, the nature of these structures and mechanisms behind their formation are not clear yet. Since it was previously suggested that these can be nanobubbles stabilized by adsorbed solute at the gas/solvent interface, we devote the current study to addressing this question. Static and dynamic light scattering was used to investigate solutions and mixtures prepared at ordinary conditions (equilibrated with air at 1 atm), prepared with degassed solvent, and solutions and mixtures degassed after formation of large structures. The behavior of large structures in strong gravitational centrifugal fields was also investigated. Systems from various categories were chosen for this study: aqueous solutions of an inorganic ionic compound (MgSO4), organic ionic compound (citric acid), uncharged organic compound (urea), and a mixture of water with organic solvent freely miscible with water (tert-butyl alcohol). Obtained results show that these structures are not nanobubbles in all cases. Visualization of large-scale structures via nanoparticle tracking analysis is presented. NTA results confirm conclusions from our previous light scattering work.

1. INTRODUCTION Solutions of ordinary low molar mass compounds and mixtures of freely miscible liquids are usually considered as homogeneous at larger length scales exceeding appreciably dimensions of individual molecules. In other words, such solutions and mixtures are assumed to be structureless on given length scales with homogeneous distribution of the particular components. Nevertheless, a growing experimental evidence has emerged during recent years which shows that it is not the case. Solutions and mixtures as used in everyday life and research practice possess long-lived, large-scale inhomogeneities with sizes much larger than the dimensions of individual molecules and much smaller than macroscopic (can be therefore referred to also as mesoscale, typically on the order of 100 nm). This evidence is coming mainly from static and dynamic light scattering, which are methods very sensitive to association, but also from other techniques such as small angle neutron scattering or nanoparticle tracking analysis. While observation of inhomogeneities in a single specific system could be attributed to some system-specific type of interaction/ aggregation/microphase separation, it appears that the existence of large-scale, long-lived inhomogeneities is a rather universal phenomenon occurring in a vast number of systems, including those where it is really not expected (well soluble solutes and freely miscible liquids). In 2000, Georgalis et al.1 © XXXX American Chemical Society

published a short communication regarding the observation of a slow dynamic mode in dynamic light scattering (DLS) experiments on three different types of electrolytes in aqueous solutions. This mode was interpreted as due to submicrometer size clusters of ions. At this time, we had a number of published works2−6 on large-scale inhomogeneities in solutions of macroions but also a solid amount of unpublished data on similar effects in solutions of low molar mass ions. We later on conducted very detailed research in this direction and investigated around 100 different solute−solvent pairs, including inorganic salts, organic ionic and nonionic molecules, and various liquid mixtures. A series of three papers on this topic was published in 2006.7−9 In summary, long-lived structures of sizes on the order of 100 nm were clearly found in the majority of the systems investigated. The first paper7 of this series dealt with a detailed characterization of these largescale structures by both static and dynamic light scattering. It was concluded that we deal here with real objects (not fluctuations) and that these are discrete objects (not bicontinuous phases with large correlation lengths). They are usually polydisperse, with smaller or larger polydispersities, in Received: January 7, 2013 Revised: February 1, 2013

A

dx.doi.org/10.1021/jp4002093 | J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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distinctly. We also present results on a direct visualization of the long-lived large-scale structures by NTA (nanoparticle tracking analysis). NTA data confirm our conclusions from the original light scattering work:7−9 (i) that these are real objects, not fluctuations, (ii) that these are discrete objects (not bicontinuous phases with large correlation lengths), and (iii) that a good agreement can be found between size distributions obtained from light scattering and NTA.

certain cases with sizes spanning up to a decade (radii from ∼30 to ∼300 nm). Sizes are usually concentration-dependent. The second paper8 dealt with the kinetics of the structure formation as well as with its long-time stability. The time scale on which the large-scale structures develop upon mixing the components of the solution or mixture varies from minutes to weeks, depending on the concrete system. Importantly, a truly homogeneous mixture is obtained at the beginning, and only af terward, a buildup of large structures begins. The long-time stability of large-scale structures was also studied in detail in experiments where samples were monitored in long time intervals ranging up to 15 months. In some systems, the structures appeared virtually infinitely stable; in others, a very slow ceasing was observed with time (weeks to months). The third paper9 of this series was focused on giving a detailed classification of systems with respect to the capability of formation of the large-scale structures as well as to trying to shed some light on the mechanism of its formation. The presence and intensity of the large-scale structures was correlated with properties of constituent molecules and ions such as their charge, dipole moment, protic vs aprotic character, etc. Electrolytes of both inorganic and organic origin exhibited large-scale structures in aqueous solutions (in all cases) and in organic solvents (selectively). Solutions of nonelectrolytes including mixtures of liquids exhibit large-scale structures in aqueous solutions (in all cases) and in organic solvents (selectively). Nonaqueous mixtures did not exhibit large-scale organization in the case of nonpolar and weakly polar components. Large-scale structures were observed in systems where at least one component had the ability to form hydrogen bonds, especially the ability of spatial networking by hydrogen bonding. Shortly after this series of papers, the presence of large structures was confirmed by Jin et al.10,11 in aqueous solutions of several common well-soluble compounds (urea, α-cyclodextrin, tetrahydrofuran, ethanol), but these structures were interpreted as nanobubbles stabilized by solute adsorbed at the gas/water interface. The nanobubble nature of observed large structures in mixtures of water with several organic liquids was later questioned by Häbich et al.12 who came to the conclusion that the large structures cannot be nanobubbles. Their conclusion was supported by light scattering, infrared spectroscopy, and atomic force microscopy. Several other recent papers13−15 dealt with the observation of large structures (objects) in aqueous solutions. They were not interpreted as nanobubbles, but these papers were not focused specifically on addressing the question of whether these structures can be nanobubbles or not. In the current paper, we address directly the question whether the long-lived submicrometer structures naturally occurring in solutions and mixtures are nanobubbles or not. We chose systems from various categories: aqueous solution of an inorganic ionic compound (MgSO4 salt), aqueous solution of an organic ionic compound (citric acid), aqueous solution of an uncharged organic compound (urea), and mixture of water with organic solvent freely miscible with water (tert-butyl alcohol). Static and dynamic light scattering experiments were performed on solutions prepared with regular solvent (equilibrated with air at 1 atm) and on solutions prepared with degassed solvent. Then, the whole solutions (not solvents only) were degassed and results were compared with nondegassed solutions. Solutions were then exposed to centrifugation experiments, since, due to a huge difference in densities between air and solution, the nanobubbles should behave very

2. EXPERIMENT Materials. Experiments were performed on analytical grade chemicals (mostly from Sigma). Water was purified by reversed osmosis, activated carbon TOC reduction, freshly doubledistilled in a quartz apparatus, and subsequently deionized by analytical grade mixed-bed ion exchange resins (Bio-Rad, Richmond, CA). The resistivity of water was above 15 MΩ cm. Centrifugation tests were performed with well-defined particle standards: polystyrene latex particles from Invitrogen (Grand Island, NY) and silica particles from Bangs Laboratories (Fishers, IN), Static Light Scattering (SLS). SLS measurements were made using a 25LHP928 HeNe laser (CVI Melles Griot, Albuquerque, NM) with a 632.8 nm vertically polarized beam. Laser power was 40 mW. No change of data with laser power was observed in the range 1−40 mW. A laboratory made goniometer with angular range from 30°to 135° was used to collect data for both static and dynamic light scattering experiments. The scattering cell was thermostatted with a precision of ±0.03 °C. Scattering intensities were measured by photon counting. Solvent scattering I0 was subtracted from total solution scattering It to obtain excess scattering intensity I I = It − I 0

(1)

The subtraction of solvent scattering was done separately for each angle. Excess scattering intensities were normalized using doubly distilled and filtered benzene as a standard and expressed as ratios I/IB, where IB is the benzene total scattering. Great attention was paid to the purity of samples. Scattering cells were thoroughly cleaned from dust. All solvents were filtered through 0.2 μm filters because of the same reason. Experiments on blank samples (nonstructured mixtures or pure liquids) showed a complete dust removal. An optimized regularization technique (ORT)16,17 was used for the calculation of particle size distributions from static light scattering data. The size distribution function is searched as a linear combination of cubic B splines ϕi(R) in a window delimited by Rmin and Rmax n

D(R ) =

∑ ciϕi(R) i=1

(2)

where the natural limits 2Rmin = π/qmax and 2Rmax = π/qmin may be exceeded to a certain extent16,17 (qmax and qmin are the maximum and minimum experimentally available scattering vectors). Scattering vector is defined as q = |q⃗| = (4πn/λ0) sin(θ/2), with n being the refractive index of the medium, λ0 the light wavelength in a vacuum, and θ the scattering angle. Scattering intensity is expressed via coefficients ci, which are the unknowns that can be determined by a constrained leastsquares condition. In our particular case, the amplitude of the slower mode As calculated by eq 4 (scattering contribution from large-scale structures) was used as the input scattering intensity for the ORT calculation of large-scale structure size B



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distributions. The relative refractive index of particles with respect to solvent, which comes into calculation, is in our case an unknown parameter, since the scattering contrast of domains is not exactly known. However, very similar results are obtained irrespective of concrete values of refractive index used in the calculation. Dynamic Light Scattering (DLS). An ALV5000E correlator with a fast correlation board option (ALV, Langen, Germany) was used for photon correlation measurements. Characteristic decay times of dynamic modes τi and their relative amplitudes Ai(τi) were evaluated through the moments of distribution functions of decay times A(τ) obtained by fitting correlation curves using CONTIN18 and GENDIST19,20 programs as g(1)(t ) =

∫0

∞

A(τ )e−t / τ dτ

(3)

Diffusion coefficients were calculated as Di = (1/τi)q−2. Two diffusive modes were detected. They were characterized by diffusion coefficients Df, Ds and amplitudes Af, As (subscripts f and s refer to faster and slower, respectively). Amplitudes were calculated as A s (θ ) =

I(θ )/IB(θ ) 1 + A f (θ )/A s(θ )

(4)

A f (θ ) =

I(θ )/IB(θ ) 1 + A s(θ )/A f (θ )

(5)

Figure 1. Schematic of the centrifugation experiment. Samples are centrifuged directly in glass light scattering tubes capable to withstand RCFs up to 22 000g using a swing-out rotor with elastic protective rubber pads in the buckets. Particles need to be translocated (migrate) a well-defined distance to disappear from the position where detected by laser beam in a light scattering setup.

assuming that I(θ)/IB(θ) = Af(θ)/As(θ). Dimensionless ratios As(θ)/Af(θ) and Af(θ)/As(θ) were taken from DLS spectra of relaxation times. Nanoparticle Tracking Analysis (NTA). NTA was carried out with an LM10 Nanoparticle characterization system from Nano Sight (Amesbury, United Kingdom) with trinocular microscope and LM12 viewing unit with a 40 mW laser working at λ = 638 nm. Video sequences were recorded via CCD camera operating at 30 frames per second (fps) and evaluated via the NANOSIGHT NTA 2.0 Analytical Software Suite. A blank NTA experiment with pure water was performed to exclude a possible contamination of water or viewing unit with parasitic scatterers. Centrifugation. Samples were centrifuged in a microchipcontrolled Jouan KR22i centrifuge (Jouan, France). This centrifuge enables one very precisely to set not only the relative centrifugal force (RCF) and centrifugation time t but also the product RCFt including the acceleration and braking by definition of the integral of the dependence of RCF on t. This allows one to exactly and reproducibly apply centrifugal gravitational separation. As follows from theory, a certain product of RCF and time t is necessary to translocate the particles over the desired distance. In order to set a desired product of RCFt, both RCF and t were varied proportionally with the aim to avoid extreme situations such as very high RCF during very short t or very low RCF during extremely long times. In agreement with theory, identical results were obtained for the same RCFt product irrespective of the particular RCF and t chosen along the above-mentioned guideline. Temperature was controlled during centrifugation by cooling. A swingout rotor (SWK100.13, Jouan, France) was used in which the scattering cell is positioned perpendicular to the axis of rotation during centrifugation so that the gravitational force acts along the cell axis toward its bottom (see Figure 1). Samples were

centrifuged directly in glass light scattering tubes capable of withstanding RCFs up to 22 000g due to special glass and elastic protective rubber pads in the buckets. This avoided any possible contamination, since no transfer of samples from centrifugal tubes to light scattering cells was needed. Light scattering was measured immediately before and after centrifugation. No kinetic changes were observed during the time necessary to perform light scattering measurement after carefully removing the cell from the centrifuge. Equations for data evaluation are described in the Results section. Prior to measuring our samples, successful tests were performed with well-defined particle standards of various sizes, namely, polystyrene latex particles and amorphous silica particles. Latexes have a small density difference with respect to water (Δρ = 55 kg/m3), while silica particles have a substantial difference (Δρ = 960 kg/m3), in absolute value quite comparable to the density difference between air and water (Δρ = −996 kg/m3).

3. RESULTS Figure 2 shows typical NTA images of an aqueous solution of urea (concentration c = 45 g/kg). Such urea solutions were previously investigated in detail by light scattering.7 NTA images and data confirm our conclusions from the original light scattering work,7−9 that a solution comprised of large-scale structures appreciably exceeded the dimensions of individual molecules and that these are (i) real objects with macroscopic lifetimes, not fluctuations, and (ii) discrete objects (not bicontinuous phases with large correlation lengths). Largescale structures are clearly visualized in NTA images as individual bright spots. It should be stressed, however, that these structures/particles are not being directly imaged. For the C



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Figure 2. Nanoparticle tracking analysis images of an aqueous solution of urea (c = 45 g/kg), room temperature. Two still images from a video sequence are shown where the captured area is 80 × 100 μm while the focal depth is approximately 20 μm. Below are individual tracks of several selected particles as monitored and evaluated by the NTA software. The number concentration of particles is 3.4 × 108 mL−1.

nanoscale particle range to which the Nano Sight system is best suited, the particles act as point scatterers whose dimensions are below the Abbé limit, only above which can structural information and shape be resolved. The image captures individual particles present in the approximately 80 μm wide laser beam (volume approximately 80 × 100 × 20 μm3). Some spots are larger, some smaller, which can be due to either different sizes of particles or different positions in the beam. Some particles exhibit Airy patterns (diffraction rings) due to the diffraction limit of visible light, which is a common feature for this method. The image shown in Figure 2 can be considered as a typical NTA image. This method permits one to further track the Brownian motion pathways of individual particles over a suitable period of time (typically several seconds), compute their diffusion coefficients based on their mean square displacements, and subsequently compute their hydrodynamic radii via the Stokes−Einstein formula. The inset in Figure 2 shows an example of pathways of several selected individual particles. The computed size distribution is shown in Figure 3 together with the size distribution obtained by the ORT (optimized regularization technique16,17) method from static light scattering measurement on the same sample. Angular dependence of scattering intensity (slow mode scattering amplitude) from which this distribution was calculated is shown in Figure 4. For comparison purposes, both distributions are shown as volume size distributions. Volume size distribution of particle sizes Dv(R) means that Dv(R) dR represents the volume fraction of particles with radius from the interval (R, R + dR). The distribution from NTA is obtained natively as the number distribution based on the number fraction of particles with radius from the interval (R, R + dR). The distribution from light scattering is obtained natively as the so-called intensity distribution. Dashed lines correspond to regions where the reliability of the distribution is becoming lower due to the physical nature and limitations of the respective methods.21 Nevertheless, a good agreement between the two methods is obtained. We have similarly visualized other systems by NTA with a good agreement with our previous light scattering work.7−9

Figure 3. Volume size distribution of mesoscale structures in an aqueous solution of urea (c = 45 g/kg, room temperature) obtained by quantitative analysis of the nanoparticle tracking analysis data (orange line) and by quantitative analysis of static light scattering data by the optimized regularization technique (black line). R is the radius.

Figure 4 summarizes results of experiments focused on the verification of the eventual nanobubble nature of the large structures, namely, on the question of what happens if we prepare an aqueous solution of urea not at ambient conditions (equilibrated with air at 1 atm). The solution was prepared with degassed deionized water instead of non-degassed deionized water. Water was degassed by three cycles of the F−P−T method (freeze−pump−thaw). Water was first frozen by liquid nitrogen, then the pressure was pumped down to 1 mbar, and subsequently the solvent was thawed under a vacuum. This method allows the removal of 99.999% of gases from liquids.22,23 As can be seen from Figure 4, the light scattering result was identical. Then, the whole solutions (not solvent only) was degassed by exposure to a vacuum. The strength of the vacuum as well as the time of exposure had again no effect on the light scattering data. Practically identical curves were obtained after correction for a slight increase in solute concentration due to partial solvent evaporation during degassing. Finally, the whole solutions (not solvent only) D



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steeper angular dependence of the slow mode scattering intensity that corresponds to slightly bigger structures in solution. In agreement with static light scattering, diffusion coefficients from dynamic light scattering measured at angle 45° are identical no matter whether degassed or non-degassed water is used as solvent and are slightly lower after the F−P−T cycle due to the increased size of the structures giving rise to the slow mode (Ds = 10.6 × 10−9 cm2 s−1 before the F−P−T cycle vs Ds = 8.3 × 10−9 cm2 s−1 after the F−P−T cycle). In conclusion, degassing of solvent or the whole solution does not lead to disappearance or at least suppression of the slow mode scattering which is contradicting the notion of nanobubble character of the large structures/objects that we identify in solutions by light scattering or nanoparticle tracking analysis. In principle, the adsorbed solute at the gas−water interface could hinder efflux of the gas outside the bubble even upon degassing; however, experiments with degassed solvent (water) compared to non-degassed solvent should show less nanobubbles. This is, however, not observed. In the next section of the paper we present results of centrifugation experiments. Due to a huge difference in densities between air and aqueous solution, nanobubbles should behave very distinctly under stronger gravitational fields. A schematic of the principle of centrifugation experiments is shown in Figure 1. Light scattering measurements are performed in round-bottom glass cylindrical cells (tubes) which are filled with a liquid sample such that the meniscus is located around 19 mm above the bottom of the tube. The laser beam in a light scattering experiment is passing 12 mm above the bottom of the tube. Light scattering cells are placed into a swing-out rotor of a centrifuge where they are capable of withstanding relative centrifugal forces (RCFs) up to 22 000g due to a special glass material and elastic protective rubber pads in the buckets. Particles in the sample need to be translocated (migrate) a well-defined distance during centrifugation in order to disappear from the position where they are detected by the laser beam in a light scattering experiment. In the case of sedimenting particles, the maximum needed translocation distance is equal to r2 − r1. In the case of buoyant particles, it is r3 − r2. The meaning of r1, r2, and r3 follows from the scheme in Figure.1: r1 is the distance from the axis of rotation to the meniscus, r2 is the distance from the axis of rotation to the position where the laser beam passes through the tube in a light scattering experiment, and r3 is the distance from the axis of rotation to the bottom of the tube. Migration of a particle from r1 to r2 in a centrifuge is described by the sedimentation equation24,25

Figure 4. Angular dependencies of the slow mode scattering amplitude. Aqueous solution of urea (c = 45 g/kg). (○) Sample prepared with non-degassed deionized water, (●) sample prepared with degassed deionized water, (△) sample prepared with degassed deionized water plus the whole solution after dissolution of urea was degassed again by exposure to a vacuum, (□) sample prepared with degassed deionized water plus the whole solution after dissolution of urea was degassed again by three cycles of freeze−pump−thaw (F−P− T). Intensities corrected for slight changes of urea concentration after degassing.

were degassed by three cycles of the F−P−T method (freeze− pump−thaw). Again, no removal or at least decrease of the slow mode scattering occurred. Oppositely, a slightly higher intensity was obtained, even after correction for a slight increase in solute concentration. It was checked by separate experiments that this increase is caused solely by the freezing of the solution: solutions just frozen and thawed without vacuum showed also such increase in intensity. Figure 5 shows results from a similar

Figure 5. Angular dependencies of the slow mode scattering amplitude. 0.4 M aqueous solution of magnesium sulfate heptahydrate (net concentration of MgSO4, c = 48.1 g/kg). (○) Sample prepared with non-degassed deionized water, (●) sample prepared with degassed deionized water, (□) sample prepared with degassed deionized water plus the whole solution after dissolution of salt was degassed again by three cycles of freeze−pump−thaw (F−P−T). Intensities corrected for slight changes of salt concentration after degassing.

ln

r2 2R2Δρ 2 = ωt 9η r1

(6)

where R is the particle radius, Δρ is the difference between the density of the particle and the density of the surrounding liquid, η is the suspension viscosity, ω is the angular frequency of the rotor, and t is the duration of centrifugation. The term (2R2Δρ)/9η is known as the sedimentation coefficient. Instead of the angular frequency ω, the centrifugal acceleration or relative centrifugal force (RCF) is used in practice

set of experiments on a different system, 0.4 M aqueous solution of magnesium sulfate heptahydrate (net concentration of MgSO4, c = 48.1 g/kg). Again, no difference is seen between solutions prepared with degassed and non-degassed water. After degassing the whole solutions by the F−P−T method, a small increase in intensity is observed, accompanied by a slightly

RCF = rω 2

(7)

where r is the distance between the center of rotation and the particle experiencing RCF. Conveniently, RCF is expressed in units of Earth’s gravitational acceleration g. As can be seen from E



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eq 6, a certain product of RCF and time t is necessary to translocate the particle over the desired distance |r2 − r1|. This is because the particle moves with a constant terminal velocity, which is proportional to RCF. This terminal velocity is inversely proportional to viscous friction, which under laminar flow at low Reynolds numbers can be taken as the Stokes friction factor f = 6πηR

(8)

which for nonrigid spheres such as bubbles or drops adopts the form24 ⎛ 3η + 2η ⎞ ⎟⎟ f = 6πηR ⎜⎜ 0 ⎝ 3η0 + 3η ⎠

(9)

where η0 is the viscosity of the gas or liquid inside the drop and η is the viscosity of the solvent outside the drop. If we consider possibly air bubbles, then η0 ≪ η, f = 4πηR, and eq 6 adopts the form ln

r2 R2Δρ 2 = ωt 3η r3

(10)

Figures 6 and 7 show results from the centrifugation of the urea sample described in Figures 2 and 3. As can be seen from Figure 7. Scattering from an aqueous solution of urea (c = 45 g/kg). (A) Dependence of the slow mode scattering amplitudes on the applied relative centrifugal force (RCF) for time t. Scattering angle θ = 90° (○) and 45° (●). (B) Dependence of the slow diffusion coefficient Ds on the applied relative centrifugal force RCF for time t, θ = 90°.

Angular dependencies of scattering intensity in Figure 6 are gradually flatter and less curved with increasing RCFt, which corresponds to smaller sizes and narrower and narrower size distributions. Due to the technical limitations of the method (max. 22 000g), it was not possible to centrifuge out the smallest particles; even 11 h of centrifugation at 22 000g was not enough. Figure 7 shows the dependence of scattering intensities As and the slow diffusion coefficient Ds on the applied RCFt. Ds is inversely proportional to the hydrodynamic radius of particles; hence, the increase of Ds corresponds to a decrease of the radius. Measured Ds reflects an average radius of particles, namely, the intensity-weighted z-average, and is quite strongly angularly dependent in this particular case due to a broad size distribution. Nevertheless, it is qualitatively well correlated with static light scattering data. The strongest effect on both static intensities and the diffusion coefficient is obtained around RCFt ∼ 6 × 106 g min. In conclusion, nanoparticles/nanostructures giving rise to the slow mode and visualized by NTA do not behave as nanobubbles. Oppositely, the density difference between the inside and outside of the particles is very small. Exact determination of the density difference is not possible mainly due to the large polydispersity, but it comes out semiquantitatively that Δρ is on the order of 1 kg/m3 or even less. This is in contrast to Δρ = 996 kg/m3 for air nanobubbles. Figures 8 and 9 summarize the results of a similar experiment performed with 1 M aqueous solution of citric acid. The largescale structures are also polydisperse here but slightly smaller than in the case of the urea sample. A large portion of particles that dominates contributions to the light scattering signal

Figure 6. Influence of centrifugation on large-scale structures in an aqueous solution of urea (c = 45 g/kg). Angular dependencies of the slow mode scattering amplitude after applying relative centrifugal force (RCF) for time t. Products RCFt in units of 103 g min: 0 (○), 42 (●), 400 (□), 2679 (△), 6203 (◇), and 14 427 (▽).

Figure 3, the solution contains a substantial portion of particles with radii in the range R = 250−350 nm that dominate the light scattering signal. If these particles would be nanobubbles, then according to eq 10 (taking R = 300 nm, Δρ = −996 kgm−3) we would need RCFt = 615 g min to translocate them such that the laser beam would not detect them anymore in a light scattering experiment. Figure 6 shows, however, that we need a RCFt value 3−4 orders of magnitude higher. Namely, we need RCFt = 2.68 × 106 g min to cut the size distribution such that particles with R > 250 nm are eliminated from the sample (up triangles in Figure 6). The overall trend in the centrifugation experiment is exactly what we expect; i.e., by centrifugal force increasing RCFt, we gradually cut more and more from the size distribution, naturally starting from the largest R. Hence, particles larger than 220 nm are eliminated from the sample after applying 6.2 × 106 g min (diamonds in Figure 6), and particles larger than 150 nm are eliminated from the sample after applying 1.44 × 107 g min (down triangles in Figure 6). F



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especially at small angles exhibits radii around 180 nm. Again, if these particles would be nanobubbles, then we can calculate according to eq 10 (taking R = 180 nm, Δρ = −996 kg/m3) RCFt needed to translocate them such that the laser beam would not detect them anymore in a light scattering experiment (RCFt = 1708 g min). However, orders of magnitude higher RCFt is needed. An interesting feature can be seen by detailed inspection of angular dependencies in Figure 8. In contrast to the experiment with urea, the shape of angular dependencies changes very little in spite of the fact that the scattering intensity gradually decreases. This means that the size distribution changes very little. In the case of sedimentation of solid polydisperse particles, a gradual change of size distribution should be seen because the largest particles sediment first and then smaller and smaller ones, so that the distribution is gradually being cut from the large-size end. This was basically observed with the urea sample. In general, if the scattering intensity decreases while the size distribution is maintained, it can be due to two effects: (i) decreasing number of particles of each size in an identical manner or (ii) decreasing scattering contrast. While the first one is physically evidently incorrect for centrifugal sedimentation, the second one seems quite realistic. It looks that during the enforced movement under strong gravitational drag force our particles (large-scale structures) in citric acid solution gradually lose scattering contrast, which is given by a different composition inside and outside the particles. In other words, these compositions are gradually being equalized. In fact, subtle changes of angular dependencies (and hence size distributions) are still present (Figure 8B). Therefore, it can be concluded that a combination of a size-dependent centrifugal translocation and a “contrast washing out” are simultaneously operative, the latter effect being more dominant. Figures 10 and 11 show results on the centrifugation of 0.4 M aqueous solution of magnesium sulfate heptahydrate (net

Figure 8. Influence of centrifugation on large-scale structures in a 1 M aqueous solution of citric acid. (A) Angular dependencies of the slow mode scattering amplitude after applying relative centrifugal force (RCF) for time t. Products RCFt in units of 103 g min: 0 (○), 41.6 (●), 124 (□), 253 (△), 472 (◇), 828 (▲), and 1362 (+). (B) Angular dependencies are shifted vertically (normalized to the last point) to demonstrate subtle changes in shape.

Figure 10. Influence of centrifugation on large-scale structures in a 0.4 M aqueous solution of magnesium sulfate heptahydrate (net concentration of MgSO4, c = 48.1 g/kg). Angular dependencies of the slow mode scattering amplitude after applying relative centrifugal force (RCF) for time t. Products RCFt in units of 103 g min: 8.2 (black), 51.2 (blue), 137 (red), 344 (green), 550 (orange), 898 (magenta), and 1959 (cyan). Figure 9. Scattering from a 1 M aqueous solution of citric acid. (A) Dependence of the slow mode scattering amplitude on the applied relative centrifugal force (RCF) for time t. (B) Dependence of the slow diffusion coefficient Ds on the applied relative centrifugal force (RCF) for time t. Scattering angle θ = 90° (○) and 45° (●).

concentration of MgSO4, c = 48.1 g/kg). In this case, the largescale structures (particles) are almost monodisperse, giving a linear angular dependence in the Guinier plot (Figure 10). The slope of this dependence yields a radius of gyration of 129 nm, which corresponds to radius R = 166 nm under the assumption G



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Figure 12. Influence of centrifugation on large-scale structures in a mixture of tert-butyl alcohol (TBA) and water (cTBA = 150 g/kg). Angular dependencies of the slow mode scattering amplitude after applying relative centrifugal force (RCF) for time t. Products RCFt in units of 103 g min: 0 (○), 347 (●), 1513 (□), and 6194 (△).

Figure 11. Scattering from a 0.4 M aqueous solution of magnesium sulfate heptahydrate. (A) Dependence of the slow mode scattering amplitude on the applied relative centrifugal force (RCF) for time t. (B) Dependence of the slow diffusion coefficient Ds on the applied relative centrifugal force (RCF) for time t. Scattering angle θ = 90° (○) and 45° (●).

of spherical homogeneous particles. This size does not change upon centrifugation; the shape and slope of angular dependencies remains the same. However, as can be seen from Figure 11B, the diffusion coefficient increases. Increase of the diffusion coefficient of scattering objects with constant size means decreased friction. This is rather consistent with the notion of washing out the scattering contrast. Particles become looser and looser with more and more solvent inside. This means that they may also become more drainable. Increased drainage leads to decreased friction and increased diffusion coefficient. The concept of drainability is well-known, for instance, from polymer research. In every case, findings related to a gradual ceasing of contrast at constant size are inconsistent with the nanobubble notion. Also, the critical RCFt needed to remove nanobubbles with R = 166 nm is equal to 2008 g min. In reality, RCFt = 1 × 107 g min is necessary to remove completely As (Figure 11A). Figures 12 and 13 show results on the centrifugation of a sample from another class, a mixture of two liquids, namely, tert-butyl alcohol and water (TBA concentration, c = 150 g/kg). In this case, the large-scale structures (particles) are significantly smaller (R = 78 nm). They are very resistant to the migration in a gravitational centrifugal field. No changes are seen up to RCFt = 4 × 105 g min and then only very subtle changes up to the maximum RCFt used (6 × 106 g min). If these particles would be nanobubbles, then according to eq 10 (taking R = 78 nm and Δρ = −996 kg/m3) we would need RCFt = 9 × 103 g min to translocate them such that they would not be detected anymore by light scattering. This experiment also confirms that the large-scale structures (particles) in the mixture are not nanobubbles.

Figure 13. Scattering from a mixture of tert-butyl alcohol (TBA) and water (cTBA = 150 g/kg). (A) Dependence of the slow mode scattering amplitude on the applied relative centrifugal force (RCF) for time t. (B) Dependence of the slow diffusion coefficient Ds on the applied relative centrifugal force (RCF) for time t. Scattering angle θ = 90° (○) and 45° (●).

Finally, we would like to add that the findings presented here do not imply anything about the possibility of formation of nanobubbles in general, especially under external stimuli such as, for instance, sonication.

4. CONCLUSIONS No difference was observed between solutions prepared at ordinary conditions (equilibrated with air at 1 atm) and those prepared with degassed solvents. Similarly, no decrease of scattering intensity was seen upon degassing the whole solutions where large structures were already developed. H



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Centrifugation experiments showed that orders of magnitude higher relative centrifugal forces and times must be applied to translocate these objects as if they were nanobubbles. This means that the density difference between the inside and outside of these objects is contrary to nanobubbles very small. In certain cases, a gradual decrease of scattering contrast (equalization of different compositions inside and outside these objects) was observed upon centrifugation, while their size remained constant. All of these results are inconsistent with the presence of nanobubbles in solutions and mixtures investigated. Our conclusions are in agreement with the recent work on mixtures of water and organic solvents where the nanobubble nature of observed large structures was excluded.12 Several systems were chosen for this work, one from each category: aqueous solution of an inorganic ionic compound, organic ionic compound, uncharged organic compound, and a mixture of water with an organic solvent freely miscible with water. Nanobubbles can be excluded in all cases. The observed inhomogeneities should be therefore classified rather as supramolecular structures. Questions related to the exact nature and mechanisms of formation of these structures need to be answered yet, including the question of whether other minor components (other than dissolved gas) are necessarily needed to create such structures or these structures can be formed only by the two major components (solute and solvent). The work in this direction is in progress. Visualization of large-scale supramolecular structures via nanoparticle tracking analysis was also presented in the current paper. NTA results confirm conclusions from our previous light scattering work,7−9 namely: (i) that these are real objects with macroscopic lifetimes, not fluctuations, (ii) that these are discrete objects (not bicontinuous phases with large correlation lengths), and (iii) that a good agreement is seen between size distributions obtained from light scattering and NTA.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support of the Slovak Research and Development Agency (Grant No. 048610) and Scientific Grant Agency VEGA (Grant No. 2/0215/10) is acknowledged. This work was realized within the frame of the project “Centre of Excellence for Advanced Materials With Nano- and Submicrometer Structure”, which is supported by the Operational Program “Research and Development” of the Slovak republic financed through European Regional Development Fund. The authors would like to thank J. Borovský for technical assistance in some experiments. The authors are also thankful to Dr. P. Štěpánek from Institute of Macromolecular Chemistry, Prague, for providing NTA equipment.

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REFERENCES

(1) Georgalis, Y.; Kierzek, A. M.; Saenger, W. Cluster Formation in Aqueous Electrolyte Solutions Observed by Dynamic Light Scattering. J. Phys. Chem. B 2000, 104, 3405−3406. (2) Sedlák, M.; Koňaḱ , Č .; Štěpánek, P.; Jakeš, J. Semidilute Solutions of Poly(Methacrylic Acid) in the Absence of Salt: Dynamic Light Scattering Study. Polymer 1987, 28, 873−880. I



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(22) Armarego, W. L. F.; Chai, C. L. L. Purification of Laboratory Chemicals, 7th ed.; Elsevier: Oxford, UK, 2013; p 37. (23) Pashley, R. M. Effect of Degassing on the Formation and Stability of Surfactant-Free Emulsions and Fine Teflon Dispersions. J. Phys. Chem. B 2003, 107, 1714−1720. (24) Allen, T. Particle Size Measurement, 5th ed.; Chapman & Hall: London, 1997; Vol. 1, pp 223−268. (25) Bernhardt, C. Particle Size Analysis; Classification, and Sedimentation Methods; Chapman & Hall: London, 1994.

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Large-Scale Inhomogeneities in Solutions of Low Molar Mass

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