Plasma Formation during Acoustic Cavitation: Toward a New Paradigm for Sonochemistry

Nikitenko, Sergey I.

doi:https://doi.org/10.1155/2014/173878

Advances in Physical Chemistry

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Review Article | Open Access

Volume 2014 | Article ID 173878 | https://doi.org/10.1155/2014/173878

Plasma Formation during Acoustic Cavitation: Toward a New Paradigm for Sonochemistry

Sergey I. Nikitenko¹

Academic Editor: Samir K. Pal

Received12 Feb 2014

Accepted09 Apr 2014

Published04 May 2014

Abstract

The most recent spectroscopic studies of single bubble (SBSL) and multibubble (MBSL) sonoluminescence reveal that the origin of extreme intrabubble conditions is related to nonequilibrium plasma formed inside the collapsing bubbles. Analysis of the relative populations of OH(A²Σ⁺) vibrational states observed during MBSL in water saturated with noble gases shows that in the presence of argon at low ultrasonic frequency weakly excited plasma is formed. At high-frequency ultrasound the plasma inside the collapsing bubbles exhibits Treanor behavior typical for strong vibrational excitation. Plasma formation during SBSL was observed in concentrated H₂SO₄ preequilibrated with Ar. The light emission spectra exhibit the lines from excited Ar atoms and ionized oxygen . Formation of species is inconsistent with any thermal process. Furthermore, the SBSL spectra in H₂SO₄ show emission lines from Xe⁺, Kr⁺, and Ar⁺ in full agreement with plasma hypothesis. The photons and the “hot” particles generated by cavitation bubbles enable the excitation of nonvolatile species in solutions increasing their chemical reactivity. Secondary sonochemical products may arise from chemically active species that are formed inside the bubble but then diffuse into the liquid phase and react with solution precursors to form a variety of products.

1. Introduction

When studying the action of 100–500 kHz ultrasound on aqueous solutions, Richards and Loomis [1] discovered that the ultrasonic waves accelerate the hydrolysis of dimethylsulfate and the reduction of potassium iodate by sulfurous acid (iodine “clock” reaction). Two years later, Schmitt et al. [2] reported the oxidation of iodide ions in aqueous solutions under the effect of 750 kHz ultrasound. These seminal works have introduced a new field of chemistry called “sonochemistry” by Neppiras [3]. Large amounts of research papers and detailed critical reviews have been published since that time describing different ultrasonic processes, such as cleaning and degassing [4], extraction of biologically active compounds [5], food processing [6, 7], advanced oxidation processes [8, 9], synthesis of nanostructured materials [10], and redox reactions of actinide ions [11].

Ultrasound spans the frequencies of roughly 15 kHz to 1 GHz. As a rule, the sonochemical effects are observed in the range of 15 kHz–2 MHz. The ultrasound of higher frequency is used for medical and material diagnostics [4]. The acoustic wavelengths of chemically active ultrasound (1–10⁻⁴ cm) are much higher than the molecule size. Therefore, the sonochemistry arises not from a direct action of ultrasonic waves on molecules, but rather from the acoustic cavitation. Simply put, cavitation is a set of consequent events: nucleation, growth, and violent collapse of microbubbles in liquids submitted to ultrasonic vibrations. There is a general consensus that the chemical and physical effects of power ultrasound are related to extremely rapid implosion of the cavitation bubbles occurring at the final stage of collapse.

It is important to emphasize that the acoustic cavitation leads not only to the chemical transformation of the medium, but also to the light emission, known as sonoluminescence (SL). In 1933 Marinesco and Trillat have accidentally observed the darkening of photographic plates submitted to ultrasound in water [12]. They attributed this finding to the ultrasonic acceleration of Ag⁺ chemical reduction at the surface of plates. However, one year later, Frenzel and Schultes [13] have shown that photographic plate darkening is due to the light emission from sonicated water rather than from chemical reaction. In modern literature, two different types of SL can be distinguished: light emission from a cloud of bubbles (multibubble sonoluminescence (MBSL) and light emission from a single cavitation bubble trapped in a standing acoustic wave of relatively weak acoustic pressure (single bubble sonoluminescence (SBSL). For the first time SBSL was reported by Yosioka and Omura [14]. Eight years later, Temple described the same phenomenon in his MS thesis [15]. However, both observations did not attract the attention of scientific community and only in 1990 Gaitan and Crum independently rediscovered and studied more in detail the SBSL in water/glycerin mixtures [16]. In degassed water, the SBSL was bright enough to be visible to the naked eye. The experiments demonstrated the unique properties of this system: the light emission occurs at every acoustic cycle at the final stage of collapse and the pulse duration of the light flash is below 200 ps [17–19]. Note here that single collapsing bubbles can be produced in liquids also by focused laser beam [20] but the sonoluminescence of such kind of bubbles is less studied than that of ultrasonic bubbles. In the years since SBSL was discovered, more than thousand papers have been published on this topic. The most significant results in sonoluminescence obtained before 2005 have been summarized in the monograph of Young [21]. This review will be focused on more recent results in sonoluminescence and sonochemistry which provided the new insights into the origin of the processes occurring during acoustic cavitation.

2. Sonoluminescence as a Probe of Intrabubble Conditions

The nonlinear oscillations of a bubble driven in liquids by acoustic waves are generally described by Rayleigh-Plesset equation [23–26]: where is the bubble radius, and are the bubble wall velocity and the acceleration, respectively, is the equilibrium bubble radius at ambient pressure , is the polytropic index, is the bulk density, is the surface tension, is the viscosity, and is the far-field acoustic pressure. Numerous studies of bubble dynamics reviewed recently by Lauterborn and Kurz indicate that the Rayleigh-Plesset equation works well over most of the range of bubble radius [27]. However, this equation fails at the final stage of bubble implosion where the density of compressed gas inside the bubble is comparable with that of the bulk liquid [28]. It is noteworthy that the SL flash occurs only in the last stage of collapse. Consequently, the theoretical description of conditions required for SL based on Rayleigh-Plesset equation becomes somewhat uncertain. Despite this limitation, (1) is very useful for calculations of several practically important parameters of cavitation bubbles. For example, Table 1 summarizes the calculated values of maximal bubble radius and the time of total collapse as a function of ultrasonic frequency presuming Minnaert’s acoustic resonance conditions [29]. One can see that the bubbles are much smaller and their implosion is much more rapid at higher ultrasonic frequency. It should be emphasized that the distribution of the cavitation field is also different between low- and high-frequency ultrasound. A 20 kHz horn system yields a limited conical cavitation zone near the horn tip while high frequencies (≥100 kHz) tend to give a more diffuse, widely distributed zone of cavitation [4]. Therefore, at high frequency, a larger volume of solution is directly submitted to ultrasonic irradiation compared to 20 kHz ultrasound. On the other hand, as the frequency increases, the generation of cavitation bubbles becomes more difficult to achieve in the available time and that greater sound intensity is needed to provide bubble formation.

In the pioneering work on acoustic cavitation, Rayleigh suggested that the rapid bubble implosion should lead to adiabatic heating of the gas inside the cavity [30]. This idea was further developed by Noltingk and Neppiras [31] and later by Flynn [32]. Using Rayleigh-Plesset equation and presuming adiabatic conditions during bubble implosion, they calculated the temperature and the pressure within the bubble at the moment of total collapse. For nitrogen-filled bubble in water, there calculations provided 4200 K and 975 atm, respectively. Note here that this calculation does not take into account electronic and vibrational excitation of N₂ molecules or their possible high temperature dissociation. Despite the numerous contradicting points noted by Margulis [33], the adiabatic heating model based on simple physical principles was quite rapidly accepted by sonochemists since it allowed interpreting the most of sonochemical phenomena in terms of easily understandable flame-like processes.

Spectroscopic studies of sonoluminescence offer a powerful experimental tool to probe the intrabubble conditions and to confirm or to improve the theoretical models of cavitation. The SBSL spectra of degassed water did not reveal any structures as lines and bands. Early SBSL studied attributed these spectra to blackbody emission which is in line with adiabatic heating model. However, Gompf at al. [34], Hiller et al. [35], and Moran and Sweider [36] have not found any significant difference between the pulse width in the UV part of SBSL spectrum (300–400 nm) and in the red part (590–650 nm). This contradicts a thermal model which suggests that the red pulse of the black body emission should be about twice as long as the UV part. Moreover, the intensity of the pulse predicted by blackbody model is about two orders of magnitude larger than the experimental values for studied experimental parameters [37]. Today many researches believe that the featureless SBSL spectra originated from bremsstrahlung rather than from blackbody emission [21, 37]. Bremsstrahlung emission is produced by the deceleration of an electron by an atomic nucleus in plasma. Plasma formation in single cavitation bubble was observed in concentrated H₂SO₄ preequilibrated with 50 mbar of argon at the driven frequency of 20 kHz [38]. Spectral analysis revealed light emission from excited Ar atoms and ionized oxygen . Formation of species is inconsistent with any thermal process. The ionization energy of O₂ molecules is more than twice its bond dissociation energy. Therefore, the strong heat should lead to O₂ homolytic dissociation rather than to ionization. By contrast, the species can be formed by electron impact in plasma [39]. Furthermore, the SBSL spectra in sulfuric acid in the presence of noble gases show emission line from Xe⁺, Kr⁺, and Ar⁺ with the energies ranging from 26.0 eV to 34.2 eV [40]. On the other hand, the effective gas temperature calculated from line widths at the same conditions is only about 1 eV (ca. 11000 K). Such a discrepancy cannot be understood by presuming only adiabatic heating during bubble collapse. The time-resolved spectra of SBSL in H₂SO₄ preequilibrated with Kr measured using streak camera revealed the spectrum evolution with time of collapse [41]. At 0.5 ns the SBSL spectrum exhibits line emission from excited Kr atoms centered at 810 nm (5s-5p). With evolution of time, the lines of Kr* disappear, the central wavelength moves from infrared to ultraviolet monotonously, and at 8.5 ns the spectrum shows featureless emission in the UV range. Emission from excited Kr () at the early stage of collapse is incompatible with the adiabatic heating model as a possible mechanism of SBSL.

In contrast to SBSL, the MBSL spectra in different solvents exhibit molecular lines emission in a wide range of conditions. Spectroscopic analysis of emission bands (Swan band d³Π_g–a³Π_u) during sonolysis at 20 kHz of argon-saturated silicon oil gives the effective cavitation temperature of about 5000 K [42]. However, the interpretation of this spectroscopic temperature is not without complications since is the product of a set of chemical reactions, and the relative band intensities might reflect the kinetics of these reactions rather than the intrabubble temperature. The MBSL spectra of H₂SO₄ at 20 kHz in the presence of argon revealed the emission lines from excited atoms [43]. However, like in the case of SBSL, the calculated effective gas temperature (~8000 K) was much lower than the energy of species (~13 eV~150900 K).

The MBSL spectra of pure water preequilibrated with Ar, Kr, and Xe are composed of the emission lines of excited OH^∙ radicals in A²Σ⁺ and C²Σ⁺ states and a broad continuum ranging from UV to near-infrared spectral range, which probably results from the superposition of several emission bands: H + OH^∙ recombination, water molecule de-excitation, and OH(B²Σ⁺-A²Σ) emission [22, 44]. Figure 1 shows the experimental SL spectra in argon measured at different ultrasonic frequencies normalized on the most intense OH(A²Σ⁺-X²Π_i) (0-0) transition. In the spectral range of 280−350 nm, the vibrational bands (0-0), (0-1), (1-0), (1-1), (2-1), (2-2), (3-2), and (4-3) of the OH(A-X) system can be identified. These spectra clearly demonstrate the dramatic effect of ultrasonic frequency on the relative populations of vibrational levels. In addition, for high-frequency ultrasound, OH(C²Σ⁺-A²Σ⁺) emission can be seen around 250 nm. The OH(C²Σ⁺) state cannot be populated by any thermal process since excited water molecule required for formation of such species must possess an excitation energy of at least 16.1 eV. The most probable mechanism of OH(C²Σ⁺) species production involves electron impact of water molecules. It was concluded that the observation of OH(C²Σ⁺-A²Σ⁺) emission indicates the formation of nonthermal plasma inside the cavitation bubble [44]. Spectroscopic analysis of OH(A²Σ⁺-X²Π_i) vibrational transitions supports this hypothesis [22]. The relative populations of OH(A²Σ⁺) vibrational states have been calculated using an optical thin plasma model. Figure 2 shows that, in contrast to a thermalized system, the relative population distribution obtained from MBSL spectra deviates strongly from the equilibrium Boltzmann distribution. At 20 kHz, the vibrational population distribution of OH(A²Σ⁺) state appears to follow a Brau distribution function typical for weak vibrational excitation [39]. At higher ultrasonic frequencies, it follows a Treanor distribution function which describes strong vibrational excitation [39]. It is noteworthy that the spectroscopic analysis based on the determination of the relative vibrational level populations of excited species does not depend on total intensity of sonoluminescence. Consequently, this method is sensitive to intrabubble conditions rather than to the total number of light emitting bubbles. Obviously, plasma far from equilibrium cannot be characterized by average gas temperature around 5000 K usually referred to multibubble cavitation in water [28]. Such kind of plasma is described by multiple temperatures related to different plasma particles and different degrees of freedom. The electron temperature often significantly exceeds the vibrational , rotational , and translational temperatures: [39]. Table 2 summarizes the optimized values of and estimated from the simulated MBSL spectra [22]. It shows that the nonequilibrium plasma generated during the sonolysis of water sparged with argon obeys the classical inequality . The value increases with the ultrasonic frequency from ~8000 K (~0.7 eV) at 20 kHz to ~12000 K (~1 eV) at 1057 kHz. These data clearly indicate that the acoustic collapse creates more drastic conditions at higher ultrasonic frequency. Another interesting phenomenon described in the literature is that the shape of OH^∙ radical SBSL spectrum obtained in water preequilibrated with 70 mbar of Ar is very similar to that observed in MBSL spectra of argon-saturated water at 20 kHz, indicating the strong similarity of intrabubble conditions for SBSL and MBSL under certain experimental conditions [45].

The MBSL is strongly influenced by saturating noble gas. In xenon, the vibrational population distribution for OH^∙ radicals exhibits strong vibrational (Treanor) behavior even at low ultrasonic frequency. Moreover, the MBSL spectra of water exhibit much stronger OH(C²Σ⁺-A²Σ⁺) emission bands in the presence of Xe compared to those in Ar [46]. In terms of nonequilibrium plasma model, the higher vibronic temperatures in Xe are the result of lower ionization potential of Xe compared to Ar (12.13 eV for Xe, 15.76 eV for Ar). Lower ionization potential provides plasma with higher electron density or in other words with higher electron temperature.

The formation of nonequilibrium plasma inside the cavitation bubble is in strong correlation with the isotope effects in MBSL spectra of heavy and light water observed recently by Ndiaye et al. [46]. Despite a very small variation in physicochemical properties of H₂O and D₂O, their MBSL spectra exhibit a striking difference whatever the ultrasonic frequency. The OH/OD(A²Σ⁺-X²Π_i) emission bands exhibit not only the isotope shift but also spectral profile modifications indicating differences in the populations of the OH/OD(A²Σ⁺) vibrational levels. The strong emission from OH(C²Σ⁺) excited state observed in light water is dramatically reduced in heavy water. The spectroscopic analysis of OH/OD(A²Σ⁺-X²Π_i) transitions revealed overpopulation of both OH^∙ and OD^∙ vibrational levels compared to Boltzmann equilibrium distribution. Moreover, the isotope effect for relative OD/OH(A²Σ⁺) vibrational populations () does not follow an exponential Boltzmann function. The trend followed by can be explained by formation of “hotter” nonequilibrium plasma in D₂O than in H₂O. Finally, the nonequilibrium model can contribute to an understanding of SBSL in sulfuric acid. Actually, the electron temperature is an average energy of the electrons in plasma [39]. The electron energy distribution function (EEDF) in nonequilibrium plasma is quite different from the quasiequilibrium Boltzmann distribution. Usually, the EEDF is described by Maxwellian or by Druyvesteyn distributions [39]. In both cases, for nonequilibrium plasma can contain the electrons with an energy of tens of eV. This would explain the emission bands of highly energetic ionized and excited species in SBSL spectra of H₂SO₄. In water, these species most probably are quenched by H₂O molecules.

3. Activating Molecules, Ions, and Solids with Acoustic Cavitation

Finding of nonequilibrium plasma formation during acoustic cavitation represents a paradigm shift for sonochemistry. Instead of simplistic adiabatic heating model, the sonochemical processes can be considered in terms of more sophisticated plasma chemical approach allowing explaining the new effects in sonochemistry as well as in sonoluminescence. One of such processes is a carbon isotope effect during sonochemical carbon monoxide disproportionation in water [49]. The prolonged sonication of water with 20 kHz ultrasound in the presence of 20% CO/Ar gas mixture yields a tiny amount of solid carbon-containing product. It was found that the composition of this product has some similarity with hydrated poly(carbon suboxide) which is known to be formed during CO disproportionation in plasma [39]. Moreover, the product of sonolysis was enriched with the ¹³C isotope ( = 1.053–1.055). This effect is inconsistent with equilibrium isotope effects described by Bigeleisen-Mayer theory which predicts the enrichment of reaction products with light isotopes [50]. By contrast, vibrational excitation of CO molecules in nonequilibrium plasma leads to reverse isotope effect or in other words to the enrichment of reaction products with heavy isotopes [39]. The population of highly vibrational states of CO molecule occurs through an anharmonic vibration-to-vibration pumping mechanism, known as Treanor effect. It is noteworthy that the nonequilibrium vibrational excitation of OH^∙ radicals discussed above is related to the same phenomena. One can conclude that observed isotope effects clearly indicate that the nonequilibrium plasma inside the cavitation bubbles can influence not only the MBSL spectra but also the sonochemical reactions.

In principal, each cavitation bubble can be considered as a plasmochemical microreactor providing highly energetic processes at almost room temperature of the bulk solution. The photons and the “hot” particles produced inside the bubble enable exciting the nonvolatile species in solutions, thus increasing their chemical reactivity. For example, power ultrasound enables the excitation of lanthanide ions [51, 52] and uranyl ions [53] in aqueous acidic solutions. The mechanism of excitation involves two stages: sonophotoluminescence (excitation with photons emitted by collapsing bubble) dominates in diluted solutions, and collisional excitation with “hot” particles would add its contribution at higher metal ions concentration. It should be emphasized that the nonradiative deexcitation pathways play more important role in MBSL of Ln(III) and U(VI) ions compared to photoluminescence due to the quenching with sonolytical products (H₂O₂, H₂, etc.).

Oxidizing properties of power ultrasound in aqueous solutions related to the sonochemical production of OH^∙ radicals and hydrogen peroxide are known for a long time [8]. The sonochemical reduction processes are less common. Recently, the reduction of Pt(IV) under the action of 20 kHz ultrasound in pure water has been reported [47]. In the presence of argon, reduction occurs by hydrogen issued from hemolytic water molecule split. However, Pt(IV) ion reduction appears to be slow at these conditions due to the formation of oxidizing species (OH^∙, H₂O₂) leading to reoxidation of intermediate Pt(II) ions. Sonochemical reduction is accelerated manifold in the presence of formic acid or CO/Ar gas mixture. Both CO and HCOOH act as OH^∙ radical scavengers and reducing agents. Sonolysis of Pt(IV) in aqueous solutions provides an innovative synthetic route to obtain monodispersed Pt nanoparticles without any templates or capping agents. The sonochemical process with CO/Ar gas mixture in pure water yields Pt nanoparticles within the range of 2-3 nm highly stable towards sedimentation (Figure 3). It noteworthy that the high efficiency of the reduction process at low frequency ultrasonic irradiation is a further benefit for the controllable Pt nanoparticles deposition on various specific supports even on thermosensitive materials like polymer beads [54]. The sonochemical reduction of Au(III) ions to Au⁰ in argon-saturated water also has been observed by Caruso et al. [55].

The acoustic cavitation is accompanied not only by generation of chemically active species but also by strong shear forces arising around violently imploding bubbles. Ultrasonic chain scission of polymers in solutions under the effect of these forces is known for a long time [56]. Recently the ultrasonic activation of homogeneous latent catalysts has been reported [57, 58]. It was shown that the mechanochemical scission of a metal-ligand bond triggered with low-frequency ultrasound may be used to release the innate catalytic activity of either the ligand or the metal.

Actually, the mechanical forces generated by cavitation play much more important role in heterogeneous systems than in homogeneous solutions. The first observation of cavitation erosion has been reported by Thorneycroft and Barnaby [59] much earlier than any data on sonochemistry or sonoluminescence. They observed that the propeller of torpedo-boat destroyer became pitted and eroded over a relatively short operation period. This phenomenon is explained by asymmetric bubble collapse near interface which generates microjets and shock waves proving intense pressure and temperature gradients in the local vicinity. Today, the use of power ultrasound to enhance the reactivity of solids has become a routine technique in heterogeneous catalysis and various cleaning [4] and extraction [5] processes. In general, the mechanical effects of ultrasound are much stronger at low-frequency ultrasound compared to high ultrasonic frequency which is related to the decrease of bubble size with the increase of ultrasonic frequency. Recently it was found that the light emitted by an acoustically driven cloud of cavitation bubbles enables exciting Tb(III) contained in a (Ce,Tb)PO₄ solid extended matrix [48]. The MBSL spectrum shown in Figure 4 demonstrates the Tb(III) light emission resulting from ⁵D₄-⁷F_j f-f transitions along with OH(A-X) and continuum emission typical for MBSL in water saturated with argon. Finally, the strong luminescence and even soft X-Ray emission (0.7–1.2 keV) have been recently reported during cavitation generated by high-pressure spindle oil jet at bar using narrow dielectric channels [60]. Detailed study of this phenomenon allowed concluding that the X-Ray emission originates from the excitation of the jet surface atoms by the cavitation-induced shock waves. Note here that the latter process is triggered by hydrodynamic cavitation. In contrast to the acoustic cavitation, hydrodynamic cavitation can be produced by passing a liquid through a constricted channel at a specific velocity or by mechanical rotation of an object through a liquid. The effects of hydrodynamic cavitation are generally recognized as similar to those of low-frequency power ultrasound [4].

4. Conclusions

In summary, the recent spectroscopic investigations of sonoluminescence provide the strong evidence for nonequilibrium plasma formation during the acoustic collapse. The MBSL spectra of water saturated with noble gases reveal OH(A²Σ⁺-X²Π_i) and OH(C²Σ⁺-A²Σ⁺) emission bands and a broad continuum ranging from UV to NIR part of the emission spectra. The most probable mechanism of the OH(C²Σ⁺) state production involves excitation of the water molecule by electron impact which is inconsistent with adiabatic heating model of cavitation dominated today in sonochemistry. The detailed analysis of OH(A²Σ⁺-X²Π_i) emission bands revealed vibrational overpopulation of OH(A²Σ⁺) state. At low ultrasonic frequency, weakly excited plasma with Brau vibrational distribution is formed. By contrast, at high-frequency ultrasound, the plasma inside collapsing bubbles exhibits Treanor behavior typical for strong vibrational excitation. The vibronic temperatures (, ) increase with ultrasonic frequency indicating more drastic intrabubble conditions at high-frequency ultrasound. In xenon, the vibrational population distribution for OH^∙ radicals exhibits Treanor behavior even at low ultrasonic frequency. Moreover, the MBSL spectra of water exhibit much stronger OH(C²Σ⁺-A²Σ⁺) emission bands in the presence of Xe compared to those in Ar. In terms of nonequilibrium plasma model, the higher vibronic temperatures in Xe are the result of lower ionization potential of Xe compared to Ar (12.13 eV for Xe, 15.76 eV for Ar). Lower ionization potential provides plasma with higher electron density or in other words with higher electron temperature.

The spectroscopic study of SBSL in sulfuric acid in the presence of noble gases revealed emission lines from ionized atoms Xe⁺, Kr⁺, and Ar⁺ with the energies ranging from 26.0 eV to 34.2 eV. However, the gas temperature obtained at the same conditions is only about 1 eV. Such a discrepancy cannot be understood by presuming adiabatic heating during bubble collapse, but it can be explained by the formation of nonequilibrium plasma with an electron temperature higher than the gas temperature. The future research should be focused on the understanding of physical process leading to the intrabubble plasma formation.

In principal, each cavitation bubble can be considered as a plasma chemical microreactor providing highly energetic processes at almost room temperature of the bulk solution. The photons and the “hot” particles produced inside the bubble enable the excitation of nonvolatile species in solutions, thus increasing their chemical reactivity. For example, the mechanism of ultrabright sonoluminescence of uranyl ions in acidic solutions is influenced by uranium concentration: photons absorption/reemission in diluted solutions and excitation via collisions with “hot” particles contributes at higher uranyl concentration. Chemical species produced by cavitation bubbles can be used for the synthesis of metallic nanoparticles without any templates or capping agents.

Conflict of Interests

The author declares that there is no conflict of interests regarding the publication of this paper.

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Copyright © 2014 Sergey I. Nikitenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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