Modeling of an atmospheric pressure plasma-liquid anodic interface: Solvated electrons and silver reduction

Plasma-liquid interactions have become an increasingly important research topic due to their importance for a variety of existing and emerging applications, ranging from wastewater treatment,^1,2 plasma medicine,^3,4 and nanoparticle synthesis.⁵ At the plasma-liquid interface, various reactive species, including electrons, photons, and charged and neutral reactants, are injected from the gas-phase plasmas to the liquid being treated. The hydroxyl radical (OH), hydrogen peroxide (H₂O₂), and other reactive oxygen species (ROS) such as HO₂, O₂⁻, O₃, and atomic O are reported to play an important role in plasma medicine and wastewater treatment.⁶ The injection of gas-phase free electrons in water leads to hydrated electrons or solvated electrons, e_aq⁻. Solvated electrons are suggested to play a key role in Ag⁺ reduction leading to nanoparticle formation.⁷ Past research has demonstrated that solvated electrons might also enable perfluorooctanoic acid (PFOA) transformation with free electrons and argon ions proposed as additional active compounds, while the hydroxyl and superoxide radicals are not effective in this case.⁸ 

Because of their large reducing power and many interesting scientific questions regarding their structure, solvated electrons have drawn significant attention both experimentally and theoretically in the last few decades. The first experimental identification of solvated electrons e_aq⁻ was reported in 1962 when a broad structureless absorption band centered at 720 nm was found by radiolysis.⁹ Radiolysis has been instrumental in advancing our understanding of the physical mechanisms behind electron solvation and free radical chemistry in aqueous solutions. Photolysis can also be a source of solvated electrons. Assel et al.¹⁰ measured the solvated electrons in neat water generated by an intense laser pulse in the ultraviolet (UV) region. Gas discharge plasmas provide an interesting alternative for generating near-surface solvated electrons in water. Rumbach et al.¹¹ measured the spatially and time-averaged concentration of solvated electrons generated by an atmospheric pressure argon direct current (dc) glow discharge in contact with the surface of an aqueous solution using total reflection absorption measurements.

Several modeling studies of solvated electrons have been reported. The computations of low-energy electron stopping and penetration in water in the field of radiation chemistry have been studied in detail.¹² Monte Carlo simulations have also been used to track the low-energy electrons in liquid water.¹³ Modeling efforts focused on solvated electrons at the plasma-liquid interface have only been recently published. Gopalakrishnan et al.¹⁴ used a particle-in-cell/Monte Carlo model of an atmospheric pressure argon dc discharge coupled with a fluid model of an aqueous electrolyte acting as anode to the plasma to calculate the interfacial structure of the plasma-electrolyte interface. These modeling results were in excellent agreement with the experimental results reported by Rumbach et al.¹¹ Rumbach et al.¹⁵ also analyzed the interfacial behavior of solvated electrons delivered into an aqueous solution by an atmospheric pressure low-temperature plasma using a reaction-diffusion model.

As plasma-produced reactive species can reach large concentrations at the plasma-liquid interface, they have the potential to strongly impact the e_aq⁻ concentration at the interface by various reactions including fast reactions with radicals. Nonetheless, the previous published work did not consider the possible effects of plasma-produced reactive species transferred to the liquid, such as OH, O, H, O₃, H₂O_2, and vacuum ultraviolet (VUV) photons, on the concentrations of the solvated electrons near the plasma-liquid interface in detail.

As mentioned above, plasma-produced (solvated) electrons have been suggested to be responsible for electrolytic reduction reactions in aqueous solution. For example, the metallic cations can be reduced in solution by plasma electrons to form suspended metallic nanoparticles.^7,16–18 Shirai et al.¹⁹ used a Hoffman electrolysis apparatus with two atmospheric glow discharge plasmas as electrodes to synthesize metal nanoparticles in aqueous solution. They found that Ag nanoparticles were only produced at the anode and attributed the reduction of Ag⁺ to electron injection. The formation of silver clusters by pulse radiolysis has been well studied.^20,21 The agglomeration of silver clusters was shown to be influenced by the dose and the concentration of Ag⁺ ions in the solution. However, a detailed knowledge of how plasma conditions impact the reduction of silver ions is currently missing.

In this paper, we focus on the near interfacial liquid phase concentration profiles of reactive species produced by species fluxes typical for a pulsed atmospheric pressure argon dc plasma jet in contact with an anodic liquid. As this is a very challenging environment for diagnostics, we use a fluid model to assess near interfacial concentration profiles in the solution. One of the goals of this work is to compare the interfacial plasma-produced reactive species concentration profiles in NaCl and AgNO₃ solutions. NaCl was chosen because of its obvious importance to medical applications, while AgNO₃ solutions have been extensively used to synthesize nanoparticles by plasma.¹⁸ A second goal of the paper is to explore the effects of important parameters on the early products of the silver cluster formation. The parameters considered include the plasma current denisty, the plasma pulse width, and the concentration of AgNO₃. A final goal is to identify the effects of the reactive species transferred from the plasma to the aqueous solutions on the plasma-produced liquid phase species concentration profiles with emphasis on the e_aq⁻ and the products of Ag⁺ reduction.

A 1D model was used to represent the aqueous phase, as shown in Fig. 1, including the electrical double layer. The liquid acts as an anode for the plasma with electrons driven from the gas-phase plasma into the solution. In this work, we report on NaCl and AgNO₃ solutions. The NaCl and AgNO₃ solutions initially contain only salt of 1 mM, i.e., the NaCl and AgNO₃ are fully dissociated into Na⁺, Cl⁻, Ag⁺, NO₃⁻, and O₂ [at its saturation concentration of 0.1 mM (Ref. 14)]. All solutions are assumed to be at pH 7 initially and are, therefore, having both H⁺ and OH⁻ present at a concentration of 10⁻⁷M.

The model represents a direct current (DC) pulsed argon discharge operated at atmospheric pressure and near room temperature. The study was limited to the first 10 μs allowing to obtain insights into the initial reduction products of Ag⁺ while being able to ignore convective transport. Two cases have been studied: a constant electron flux is applied for 10 μs, and electrons are injected into the liquid for 1 μs, after which the electron flux at the interface is zero. The latter allows us to study the recombination of the plasma-induced reaction products up to 10 μs without further electron injection. The silver species considered in the first 10 μs include Ag⁺, Ag, Ag²⁺, Ag₂, Ag₂⁺, Ag₄, Ag₄²⁺, and AgOH⁺. These elementary silver species and processes of the reduction of Ag⁺ are chosen based on studies of pulse radiolytic reduction of Ag⁺.^20–23 In addition to the silver species, we include all liquid phase reactions involved for H₂O and NaCl. Reactions and the corresponding reaction rate coefficients are shown in Table I. The products of reactions (R62), (R63), and R65) are not reported in the literature. Additional products that ensured charge conservation were included in the model. Nonetheless, the reaction rates of these three reactions are much smaller than the main reactions and the unidentified product densities remain negligible and do not impact the reported results. In the case of NaCl, only the initial radical scavenger reactions for NaCl have been incorporated in the model. This is motivated by the short simulation times and the interest in e⁻_aq. A more detailed reaction set incorporating a more extensive amount of possible reaction products can be found in Ref. 38, although this reaction set does not include reactions driven by solvated electrons.

The governing equations consist of the drift-diffusion equation for the mass conservation and Poisson’s equation for the electric field, as follows:

where $ci$ (mol m⁻³) is the molar concentration of species i in the liquid region, $Di(m2s−1)$ is the diffusion coefficient in the aqueous solution, $μi(m2V−1s−1)$ is the mobility of the charged species in solution, $Ri(molm−3s−1)$ is the aqueous reaction rate, and $εa$ is the permittivity of the aqueous solution. $N+(1/m3)$ and $N−(1/m3)$ are the number density of the sum of the positive charge and the negative charge, respectively. The molar concentration, $ci$ is related to number density $Ni$ by Avogadro’s number: $ci=Ni/NA$⁠. The diffusion coefficients of the aqueous molecules considered are listed in Table II, and the mobility of charged species was obtained from the Einstein relation.⁴⁸ The diffusion coefficients of Ag₂, Ag₂⁺, Ag₄, Ag₄²⁺, and AgOH⁺ have not been reported and are assumed to be 1 × 10⁻⁹ m² s⁻¹ similar to the diffusion coefficient of Ag⁺.⁴⁴ 

The boundary conditions are as follows. The position x = 0 is taken to be the plasma-liquid interface and x = L is the grounded anode electrode position in the aqueous electrolyte. The Poisson equation boundary condition at x = 0 is

where $Ea(Vm−1)$ is the electric field on the aqueous side of the interface, $ϕa$ (V) is the corresponding value of the electric potential, $Eg(Vm−1)$ is the electric field on the gas-phase side, and σ is the surface charge. The relative liquid permittivity is $εa/ε0=78.5$⁠. The electric field on the gas-phase plasma side of the plasma-liquid interface is on the order of 10⁵ to 10⁶ V/m,^3,49 nonetheless the surface charge density at a plasma-liquid interface is unknown. For the modeling, we combined the effect of surface charge and electric field into one electric field parameter E_p with a typical value of 5 × 10⁵ V/m for the baseline model. We show in the results section that changing E_p does not significantly impact the calculated solvated electron densities.

The corresponding boundary condition at x = L is

While fully coupled plasma-liquid interface calculations have been explored by Lindsay et al.,⁵⁰ the effect of varying the unknown electron boundary condition (i.e., surface loss coefficient) was found to be mainly impacting the plasma phase while the liquid phase was predominantly determined by the current which we used in this work as boundary condition. The boundary conditions for the chemical species are listed as follows for the plasma-liquid surface. The electron flux entering the liquid from the plasma is determined by the plasma discharge current density as

where $Γe$ (mol m⁻² s⁻¹) is the electron molar flux and $jp$ is the plasma current density (A/m²). The current density at the interface is calculated as⁵¹ 

where $ip$ (A) is the plasma current magnitude, and it is usually in the range of 1–100 mA for DC glow discharge.³ The discharge radius $rp$ (m) is usually several millimeters, so the current density $jp$ is typically of the order from 10³ to 10⁴ A/m².⁵¹ $jp=5×103A/m2$ is chosen for the baseline model. For neutral reactive species transferred from plasma to liquid, such as H, OH, and H₂O₂, the net flux of the species into the liquid side of the interface is as follows:⁵² 

where $ng$ (m⁻³) is the bulk gas-phase density of the species, $na$ (m⁻³) is the density in the aqueous solution, $α$ is the accommodation coefficient, $υ¯$ (m s⁻¹) is the mean molecular speed of the species in the gas phase, H is Henry’s law coefficient for the species, R is the gas law constant, and T is the solution temperature. The mass accommodation coefficient and Henry’s law constant of H, OH, and H₂O₂ are listed in Table III. As the mass accommodation coefficient of H is unknown and Henry’s law coefficient of H is extremely small, the H concentration on the liquid side of the interface is assumed to reach equilibrium immediately overestimating the effect of H on liquid phase reactions.

The change in the concentration of species as a result of photoprocesses was taken into account as follows:⁵⁶ 

where $Φ$ is the reaction quantum yield, I(x) = I(0) × 10^−ax is the intensity of passed light at the point x of the medium, a is the absorption coefficient, and $hν$ is the photon energy. The VUV emission of an Ar plasma jet is dominated by the emission of argon excimer Ar₂ (⁠$λ=126nm$⁠).⁵⁷ 90% of the VUV radiation is absorbed by a water layer with a thickness of 10⁻⁶–10⁻⁵m as the absorption coefficient of water for VUV wavelengths $λ<172nm$ is between 10⁵ and 10⁶ m⁻¹.^56,58

To ensure current continuity through the electrolyte, we followed the approach of Gopalakrishnan et al.¹⁴ We assumed either Cl⁻ (NO₃⁻) or OH⁻ to carry the current through the bulk liquid. The boundary conditions at x = L for the negative ions as well as electrons are assumed to have zero concentration at x = L. All other species have no flux at this boundary. The grounded electrode is in the experiment often relatively far away from the region of major interest near the plasma-liquid interface. Considering the penetration length of VUV and the diffusion length (⁠$d≈Dt$⁠) within 10 μs for reactive species in liquid is a few hundreds of nanometers (with a typical diffusion coefficient of 10⁻⁹ m²/s), the domain length L is chosen to be 20 μm. The effect of the boundary at x = L on the calculated species profiles with a domain length L from 20 to 100 μm was compared and confirmed that the position of the boundary at x = L does not impact the results significantly. The above model was solved using comsol multiphysics.

Only electrons injected from the plasma to the aqueous solutions are considered for simplicity when comparing the near plasma-liquid interface for NaCl and AgNO₃ solutions. The plasma current density and electric field were fixed at 5 × 10³ A/m² and 5 × 10⁵ V/m, respectively. Figure 2 shows the spatial distribution of the main charged species concentrations within 2 μm of the plasma-liquid interface at 1 and 10 μs in a 1 mM NaCl solution. As the plasma treatment time increases from 1 to 10 μs, the penetration depth of the plasma-induced OH⁻ in the liquid phase, primarily formed through reaction (R2) (Table I), increases. Simultaneously, an enhancement of the main cation (Na⁺) and a depletion of Cl⁻ is observed near the interface due to the plasma-induced current in the solution as these ions are the main charge carriers in the bulk of the liquid. The change in ionic species concentrations near the interface is responsible for the formation of a space charge layer near the plasma-liquid interface. The e_aq⁻ concentration saturates at 0.11 mM at the interface and the solvated electrons have a penetration depth of 13 nm.

Figure 3 shows the spatial distribution of the main charged species concentrations within 2 μm of the plasma-liquid interface at 1 and 10 μs in 1 mM AgNO₃ solution. The key difference with the NaCl case shown in Fig. 2 is that Ag⁺ is reduced by e_aq⁻ at a rate that is 6 orders of magnitude larger than Na⁺; hence, Ag⁺ is significantly consumed near the plasma-liquid interface. The Ag⁺ reduction near the plasma-liquid interface results in the formation of various silver cluster species in the AgNO₃ solution. The time evolutions of the interfacial e_aq⁻ concentration (i.e., the concentration at x = 0) in the NaCl solution and the AgNO₃ solution are compared in Fig. 4. The interfacial e_aq⁻ concentration reaches a steady-state after 60 ns in the NaCl solution with a maximum interfacial concentration of 0.11 mM, while it continues to increase within 10 μs in the AgNO₃ solution. Nonetheless, the e_aq⁻ concentration in the AgNO₃ solution is similar but smaller than that in the NaCl solution.

As the plasma current density in the NaCl solution is the same as in the AgNO₃ solution, the main difference of the e_aq⁻ concentration in these two solutions is caused by the e_aq⁻ consumption reactions. The consumption rate of the e_aq⁻ concentration is defined as $(ks[S]+2k2ceaq−)ceaq−$⁠, where $ks$ is the rate constant for the scavenging reaction, $k2$ is the rate constant for second order recombination reaction [(R2) in Table I], $[S]$ is the density of the scavenger S, and $ceaq−$ is the concentration of e_aq⁻. Figure 5 shows the contribution of various e_aq⁻ consumption reaction rates to the total e_aq⁻ consumption rate at 1 and 10 μs in the NaCl and AgNO₃ solutions. 92% of the e_aq⁻ consumption in the NaCl solution is caused by the second order recombination reaction [(R2) in Table I]. Since the rate constants between e_aq⁻ and Na⁺ or Cl⁻ [(R63) and (R66) in Table I] are both several orders smaller than the the second order recombination reaction rate constant, less than 0.01% of the e_aq⁻ consumption is caused by the scavenger reaction of e_aq⁻ by 1 mM Na⁺ and Cl⁻. However, the dominant e_aq⁻ consumption reaction changes to scavenging reactions of e_aq⁻ by Ag⁺ and NO₃⁻ [(R44) and (R50) in Table I] in the AgNO₃ solution at 1 μs, causing 54% of the total e_aq⁻ consumption. As the Ag⁺ and NO₃⁻ concentrations decrease from 1 to 10 μs, the proportion of the scavenging reactions of e_aq⁻ by Ag⁺ and NO₃⁻ decreases to 26.7% at 10 μs, making the second order recombination reaction again the dominant e_aq⁻ consumption reaction at longer time scales in the AgNO₃ solution. Hence, the interfacial e_aq⁻ concentration in the AgNO₃ solution gradually approaches the interfacial e_aq⁻ concentration in the NaCl solution due to the local depletion of Ag⁺ and NO₃⁻ (Fig. 4). The significant reduction in the Ag⁺ concentration found at the plasma-liquid interface causing a shift in the dominant reactions of e_aq⁻ might make a detailed quantitative interpretation of scavenger measurements as used to assess the impact of solvated electrons on plasma-induced reactions complex.^10,18

The above results have been obtained for a given electric field boundary condition. While Gopalakrishnan et al.¹⁴ previously showed that the plasma electric field boundary condition does not significantly impact the species distribution in the NaCl solution, it is important to confirm this also for AgNO₃. Figures 6(a) and 6(b) show the spatial profiles of the electric field in the two solutions at 1 and 10 μs, respectively, for the plasma electric field E_p varied from 5 × 10⁴ to 5 × 10⁶ V/m. Figure 6 shows that changing the plasma electric field by a factor of 100 only affects the electric field within 30 nm of the interface. Two differences in the electric field distribution between AgNO₃ and NaCl are also observed. First, AgNO₃ has a higher bulk electric field than NaCl solution. As the salt concentrations are the same, this is due to the smaller mobility of Ag⁺ and NO₃⁻ compared to Na⁺ and Cl⁻. Second, the gradient in the electric field near the plasma-liquid interface is larger for the AgNO₃ solution compared to the NaCl solution. This correlates with steeper ion concentration gradients at the near plasma-liquid interface enabled by the faster e_aq⁻-ion reactions. In spite that the electric field varies significantly particularly in the first 30 nm where the majority of the e_aq⁻ are present, changing the plasma electric field by a factor of 100 has a negligible effect on the concentration and spatial profiles of the e_aq⁻ concentration in the two solutions (not shown). Note that the model assumes that electrons when entering the solution are solvated on time scales much faster than considered, so any effects of the change in electric field on the solvation dynamics that could potentially impact penetration depth of the electrons is not considered in the model.

While the plasma electric field boundary condition has no impact on the e_aq⁻ concentration, the current density directly relates to the source of e_aq⁻. Figure 7 shows the effect of a varying plasma current density in the range of 1 × 10³–4 × 10⁴ A/m² on the interfacial solvated electron concentration at 10 μs. The maximum e_aq⁻ concentration shows a linear relationship with j_p^2/3 in both NaCl and AgNO₃ solutions at 10 μs. Rumbach et al.¹⁵ showed with a simplified analysis that the interfacial e_aq⁻ concentration scales with j_p^2/3 and j_p for neat water and water containing high concentrations of scavengers. As shown in Fig. 5, although the e_aq⁻ is dominantly consumed by the scavengers Ag⁺ and NO₃⁻ at the beginning, the concentration of scavengers is not high enough to play a dominant role in the depletion of the e_aq⁻ concentration at 10 μs when the depletion of Ag⁺ and NO₃⁻ near the interface. Therefore, results shown in Fig. 7 are the same with the results in neat water from Rumbach et al.¹⁵ with reaction (R2) being dominant for these experimental conditions at 10 μs.

Both Figs. 2 and 3 show a significant increase in the OH⁻ concentration, leading to a rapid basification of the near plasma-liquid interfacial solution. Figure 8 shows that the pH at the interface rises in the NaCl and AgNO₃ solutions for the conditions of Figs. 2 and 3. A pH of 11.2 and 11 after 10 μs of plasma treatment is found for NaCl and AgNO₃ solutions, respectively. The OH⁻ moves further into the solution over time. The smaller amount of OH⁻ formation in the AgNO₃ solution compared to the NaCl solution is because a part of e_aq⁻ is converted by other reactions than (R2), the main responsible reaction for OH⁻ formation (see Fig. 5).

Silver reduction in aqueous solutions has been previously studied by pulsed radiolysis.^20,21,59,60 Species identified include Ag₂⁺ and Ag₄²⁺, which were formed in aqueous solution with an excess of silver ions. When pulsed radiolysis experiments were conducted with low Ag⁺ concentrations leading to full reduction of Ag⁺ into Ag⁰, neutral clusters such as Ag₂ and Ag₄ were formed.^20,21 The formation of different clusters can lead to different growth mechanisms of nanoparticles from solution potentially affecting the final morphology and the size (distribution) of the synthesized nanoparticles.⁶¹ Hence, an increased understanding of the initial cluster formation in plasma-induced reduction is of interest. In this section, we investigate the impact of j_p, plasma pulse duration, and Ag⁺ concentration on the cluster formation. In particular, we will show that the relative concentrations of e_aq⁻ and Ag⁺ ions controlled by these two parameters have a critical impact on the early products of the Ag⁺ reduction by the plasma-liquid interaction. The effect of plasma-produced species other than solvated electrons is described in Sec. III C.

Figure 9 shows the time evolution of the products of the Ag⁺ reduction for a plasma pulse of 1 μs including 9 μs of recombination time at the interface for three different plasma current densities in 1 mM AgNO₃ solution. The e_aq⁻ concentration shown in the figure is a good representation of the plasma pulse duration as the e_aq⁻ concentration has a very fast rise time and drops very quickly when the electron injection is switched off at 1 μs. With increasing current density j_p from 10³ to 10⁴A/m², the amount of Ag⁺ conversion during the pulse is larger, leading to larger concentrations of reduction products. Nonetheless, Ag⁺ remains the dominant species and the Ag concentration decreases within less than 1 μs after the current injection stops due to the fast formation of silver clusters [(R51) and (R58) in Table I]. The concentration of the ionic silver clusters (Ag₂⁺ and Ag₄²⁺) is larger than the concentration of the corresponding neutral silver clusters (Ag₂ and Ag₄) under all these conditions. Since the largest e_aq⁻ concentration in Fig. 9(c) is still much smaller than the Ag⁺ concentration, less neutral silver clusters are formed.

To further enhance the reduction of Ag⁺, the pulse width of the plasma voltage was extended to 10 μs. Figure 10 shows the time evolution of the early products of Ag⁺ reduction at the interface for AgNO₃ concentrations ranging from 0.01 to 1 mM in this case. Comparing Fig. 10(a) with Fig. 9(b), while the maximum e_aq⁻ concentration is similar to the 1 μs case, significantly more silver clusters are formed with a 10 μs pulse width. This increased production of silver clusters is enabled by a continued reduction of Ag⁺ during the plasma pulse. The initial Ag⁺ concentration is reduced by a factor 5 at the end of the plasma pulse. Nonetheless, the Ag⁺ concentrations remain significantly larger than the Ag concentration during the entire plasma pulse and the agglomeration processes still occur in the presence of excess Ag⁺ ions. This results in the charged clusters, Ag₄²⁺ and Ag₂⁺ being the dominant cluster.

Figure 10(b) shows the same reduction process but for a reduced AgNO₃ concentration of 0.1 mM. This AgNO₃ concentration is chosen as it is equal to the solvated electron concentration. While less silver clusters are formed than in the 1 mM Ag⁺ case, the Ag⁺ drops below the Ag⁰ concentration after 235 ns. This results in the neutral silver cluster (Ag₂, Ag₄) concentrations becoming larger than the corresponding ionic silver cluster concentrations (Ag₂⁺, Ag₄²⁺). Nonetheless, a significant amount of Ag₂⁺ clusters remains. Figure 10(c) shows the possibility of a consumption of Ag⁺ to less than 2% of its initial concentration in a single plasma pulse by further reducing the AgNO₃ concentration down to 0.01 mM. In this case, the initial Ag⁺ concentration is ten times lower than the concentration of e_aq⁻. The concentration of Ag⁺ becomes more than 1 order of magnitude smaller than the Ag concentration within less than 2 μs, and Ag₂ becomes the dominant cluster with the concentration of the dominant ion cluster Ag₂⁺ one order smaller than the dominant neutral cluster. Figure 10 also shows that the e_aq⁻ concentration is in steady-state in 0.01 and 0.1 mM AgNO₃ solutions, while it increases slowly in 1 mM AgNO₃ solution up to the end of the pulse. The smaller concentrations of Ag⁺ make reaction (R2) the dominant loss reaction for solvated electrons in this case and suggest that the Faradaic efficiency will be significantly reduced with reducing Ag⁺ concentration.

The results in Figs. 9 and 10 show that the reaction of neutral clusters with one another or with silver ions is in competition, and the experimental conditions determine the dominant path. The dominant effect that is revealed in this study seems to be the ratio between the e_aq⁻ and Ag⁺ concentrations. The initiating reaction is the production of Ag atoms,

In the case that $[eaq−]≪[Ag+]$⁠, i.e., with excess of Ag⁺, the Ag atoms react with Ag⁺ ions and produced Ag₂⁺ species as proposed by Ershov et al.,²¹ 

which could progressively lead to the formation of silver charged clusters in the solution.

However, in the case of $[eaq−]≫[Ag+]$ where the majority of the Ag⁺ ions are reduced during the plasma-liquid interaction, the following cluster growth mechanisms likely occur,

which could lead to the formation of neutral silver clusters in the solution. Neutral clusters can easily react with one another or agglomorate to nanoparticles, while charged clusters are anticipated to have a slower agglomeration due to Coulomb repulsion. While further research in cluster growth mechanisms is needed, the potential of two different cluster growth mechanisms depending on plasma conditions could impact the particle size distribution of plasma-synthesized nanoparticles in solution. Interestingly for typical plasma current densities, [e_aq⁻] is between 0.1 and 1 mM as shown in Fig. 9, while in many cases, AgNO₃ concentrations in this same range are used in reported Ag nanoparticle synthesis work.^15,17,19 This suggests that both neutral and charged clusters could be present at significant concentrations during the reduction process for these conditions.

In Secs. III A and III B, we only considered electron injection as a source of plasma-induced liquid phase reactions. Besides electrons, the plasma also transfers ions, long-lived species, radicals, and UV/VUV photons to the liquid resulting in a complex plasma-induced liquid chemistry.³ The H atom, a dominant radical in plasmas in contact with liquids, has a similar reducing potential to e_aq⁻, and it may also play a role in the Ag⁺ reduction process.¹⁸ Modeling shows that when the plasma is in direct contact with the solution, plasma-produced liquid phase reactive species can reach large concentrations near the plasma-liquid interface.⁴⁹ While the OH and H₂O₂ radicals cannot reduce Ag⁺, they may shift balances between the oxidizing and reducing capacity at the plasma-liquid interface. VUV photons also produce H and OH at the interface.⁵⁶ In this section, we analyze the effects of these reactive species, including H, OH, H₂O₂, and VUV photons, on the concentration of solvated electrons in NaCl and AgNO₃ solutions, as well as on the Ag⁺ reduction processes. The current density in this section is fixed at 5 × 10³A/m².

The gas-phase OH radical density in pulsed plasma jets has been measured or simulated to be 10¹⁹–10²¹m⁻³.^3,49,62 Nonetheless, much higher densities of gas-phase OH radicals have been measured in atmospheric pressure air plasma with water anode discharge.⁶³ Here, the reference OH density in the argon plasma jet is chosen to be 10²¹ m⁻³, and the gas-phase H₂O₂ density at the interface is assumed to be the same as the gas-phase OH density.⁶⁴ The H radicals density in the plasma phase has been measured to be on the order of 10²²m⁻³ by two-photon absorption laser-induced fluorescence,¹⁸ so an upper limit for the gas-phase H density at the interface is assumed to be 10²³ m⁻³ in this study. According to Brandenburg et al.,⁵⁷ the VUV emission of an Ar plasma jet is dominated by the emission of argon excimer Ar₂ (⁠$λ=126nm$⁠), and the photon irradiance is less than 100 W/m² at 5 mm away from the plasma jet source. Hence, the VUV intensity at the interface in the model is assumed to be 100 W/m² with λ = 126 nm.

Figures 11 and 12 show the effects of the radical species transferred from the plasma to the liquid on the spatial profiles of the e_aq⁻ concentration at 1 and 10 μs in NaCl solution and AgNO₃ solution, respectively. The VUV photons can impact the e_aq⁻ concentration in two ways. First, the solvated electrons can be produced directly by VUV photons by the reaction (R68) in Table I but the quantum yield of this reaction is only 0.05 at 126 nm waveform, hence the e_aq⁻ concentration produced by photolysis with 100 W/m² VUV intensity has a negligible effect on the total e_aq⁻ concentration. Second, the main products of photolysis by 126 nm photons are H and OH radicals [(R67) in Table I] which both react with Ag⁺. However, the concentrations of H and OH induced by photolysis for 100 W/m² VUV intensity remain about 2 orders of magnitude smaller than the e_aq⁻ concentration. Hence, the consumption reactions of e_aq⁻ by H and OH [(R3) and (R4) in Table I] produced by photolysis do not affect the e_aq⁻ concentration. It would require a photon flux that is 10³ times larger (10⁵ W/m²) to have a 20% reduction in e_aq⁻ concentration.

In spite of a gas phass plasma density of 10²³ m⁻³ H radicals, small Henry’s law constant of H only yields a liquid phase H radical concentration of 1 μM (not shown in figures) in the liquid phase at the interface in the NaCl solution. This concentration is too small to have a significant effect on the concentrations of other radical species at the plasma-liquid interface. Consequently, as shown in Figs. 11 and 12, the plasma-produced VUV and H radicals have a negligible effect on the e_aq⁻ concentration both in NaCl and AgNO₃ solutions.

The spatially integrated e_aq⁻ concentration in the NaCl solution decreases by 35% at 1 μs and by 61% at 10 μs with OH diffusion from a gas-phase concentration of 10²¹m⁻³, and it decreases by 8% at 1 μs and by 29% at 10 μs with H₂O₂ diffusion from the same gas-phase concentration of 10²¹m⁻³. On the other hand, the OH and H₂O₂ generation has negligible effects on the spatially integrated e_aq⁻ concentration in the AgNO₃ solution at 1 μs [Fig. 12(a)]. However, the integrated e_aq⁻ concentration in the AgNO₃ solution at 10 μs is reduced by 44% considering OH diffusion from the gas phase, while it is reduced by 18% with H₂O₂ diffusion considered. The smaller effect of OH during a 1 μs compared to a 10 μs exposure is surprising because the OH flux is actually larger than the electron flux in the calculation. The reason is that Ag⁺ is quenching the OH radical effectively in this case. More details will be provided below. The above results show that the OH radicals produced by plasma have the greatest impact on the e_aq⁻ concentration but it has a more significant effect on the e_aq⁻ concentration in the NaCl solution than it does on the e_aq⁻ concentration in the AgNO₃ solution. Both H₂O₂ and OH are hydrophilic and have similar gas-phase density. Nonetheless, the scavenger reaction rate of e_aq⁻ by OH [(R4) in Table I] is about three times larger than that by H₂O₂ [(R7) in Table I], leading to two to three times larger e_aq⁻ concentration reduction due to reaction (R4) compared to reaction (R7) in both NaCl and AgNO₃ solutions at 10 μs.

The e_aq⁻ and H can both reduce the Ag⁺ ions to produce Ag atoms,¹⁸ and the OH radical and H₂O₂ can oxidize the metal ions. Figure 13 shows the effects of these species injected from the plasma on the reduced concentration of Ag⁺ ions. The reduced amount of Ag⁺ ions is defined as the concentration of the consumed Ag⁺ ions by adding the concentration of the product species as follows: [Ag] + 2 × [Ag₂] + 4 × [Ag₄] + [Ag₂⁺] + 2 × [Ag₄²⁺]. The spatially integrated concentration of the reduced Ag⁺ ions is decreased by 70% at 1 μs and 96% at 10 μs with OH diffusion from the gas-phase plasma. Figure 14 shows the time evolution of the early products of the plasma-induced reduction of Ag⁺ ions at the interface with the consideration of electron and OH injection from the plasma to the liquid compared to electron injection only in Fig. 10(a). The concentrations of Ag²⁺ and AgOH⁺ dominate the silver clusters in 1 mM AgNO₃ solution. More OH radicals are consumed by reacting with Ag⁺ [(R53) and (R55) in Table I] compared to e_aq⁻ [(R4) in Table I] at 1 μs. Hence, OH radicals transferred from the plasma can significantly impact Ag⁺ reduction with limited impact on the e_aq⁻ concentration at 1 μs. As the Ag⁺ concentration decreases about 2 orders of magnitude at 10 μs, the reaction rate of OH with Ag⁺ decreases, and the OH radicals reduce the e_aq⁻ concentration at 10 μs, as shown in Fig. 12(b). The H₂O₂ can also suppress the plasma-induced Ag⁺ reduction. Assuming a gas-phase concentration of 10²¹ m⁻³ H₂O₂ at the plasma-liquid interface, the spatially integrated reduced Ag⁺ concentration decreases by 10% at 1 μs and by 39% at 10 μs.

In summary, while plasma can produce a multitude of reactive species, OH radicals have the highest potential to impact plasma-induced Ag⁺ reduction. The presence of OH also leads to the formation of AgOH⁺ and possible oxidation of the precursor, which could impact the silver nanoparticle formation. This process might prove particularly important as it might be challenging to suppress OH formation when the plasma is in direct contact with the aqeous solution.

A numerical simulation of the near interfacial liquid phase chemistry induced by species fluxes typical for a pulsed argon atmospheric pressure plasma jet in contact with an anodic liquid has been performed. The liquid phase species, electric fields, and pH spatial distributions and their difference for NaCl and AgNO₃ solutions including the early products of the plasma-induced Ag⁺ reduction, and the effects of the radical species injected from plasma to the aqueous solutions on the interfacial structures have been reported. With the same current density injected from the plasma to the liquid, the magnitude and the penetration depth of the e_aq⁻ concentration in the AgNO₃ solution are smaller than that in the NaCl solution because of the scavenger reactions of e_aq⁻ by Ag⁺ and NO₃⁻. In addition, a significant reduction in the Ag⁺ concentration is found at the plasma-liquid interface due to the electron-induced reduction of Ag⁺ on a microsecond time scale. This leads to a shift in the dominant recombination reaction of e_aq⁻ over time.

The relative concentrations of e_aq⁻ and Ag⁺ ions controlled by current density and AgNO₃ concentration have a critical impact on the early products of the Ag⁺ reduction by plasma-liquid interaction. In the case that $[eaq−]≫[Ag+]$ (at high current densities and low Ag⁺ concentrations), mainly neutral silver clusters are formed. Dominantly, ionic silver clusters are formed in the presence of excess Ag⁺ ions. Interestingly for several previously reported experimental conditions used for Ag nanoparticle production, the [e_aq⁻]/[Ag⁺] ∼ 1. The results suggest that it might be worthwhile to experimentally assess the impact of the plasma current density and the AgNO₃ concentration on silver nanoparticle growth.

Furthermore, the gas-phase OH radicals transferred from the plasma to the liquid can have an impact on the e_aq⁻ concentration and the Ag⁺ reduction products. For the same plasma current density, the gas-phase OH radicals have less impact on the e_aq⁻ concentration in the AgNO₃ solution than on the e_aq⁻ concentration in the NaCl solution. OH radicals do cause a 95% drop of the plasma-induced Ag⁺ reduction ability. VUV photons and H radical fluxes for typical plasma conditions are found to have a negligible effect on the dominant reactive species concentrations near the plasma-liquid interface. On the other hand, H₂O₂ can also decrease the e_aq⁻ concentration and the reduction ability but has a smaller impact compared to OH radicals, at least on the microsecond time scales investigated in the paper.

P.B. was supported by the University of Minnesota and the Army Research Office under Grant No. W911NF-20-1-0105. Y.Z. acknowledges the support of the Chinese Scholarship Council that enabled her research Sintay at the University of Minnesota. Y.Z. and P.B. acknowledge the help of Santosh Kondeti in constructing the reaction set used in this work. The authors acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the results reported in this paper.

 Peter J. Bruggeman is currently Professor and Associate Head of Mechanical Engineering at the University of Minnesota. He serves as the Director of the High Temperature and Plasma Laboratory and Associate Director of the Department of Energy Center on Plasma Interactions with Complex Interfaces consisting of eight institutions. He also leads a MURI on “Plasma-driven solution electrochemistry.”

Professor Bruggeman obtained his Ph.D. from Ghent University, Belgium, in 2008 and was an Assistant Professor of Applied Physics at the Eindhoven University of Technology, the Netherlands, from 2009 until he joined the University of Minnesota in 2013. A significant part of his research is focused on the fundamental physical and chemical processes of low-temperature nonequilibrium plasmas enabling many environmental, biomedical, and renewable energy applications and technologies. He has published over 110 papers in peer-reviewed journals and delivered invited and keynote lectures at over 80 international meetings. His research has been recognized by several awards including the 2012 Hershkowitz Early Career Award, the 2013 Institute of Pure and Applied Physics Young Scientist Medal and Prize in Plasma Physics, the 2016 U.S. Department of Energy Early Career Award, the 2018 Peter Mark Memorial Award of the American Vacuum Society, and the 2020 George W. Taylor Award for Distinguished Research of the College of Science and Engineering of the University of Minnesota.

Professor Bruggeman is an active member of his research community. He is currently the Section Editor for Low Temperature Plasmas of the Journal of Physics D: Applied Physics (Institute of Physics Publishing, UK) and serves as an editorial board member of several other journals. He also served on the committee charged by the National Academies with the Decadal Study of Plasma Science (Plasma 2020) and coedited the “2017 Plasma Roadmap” giving directions for the future development of the field of low temperature plasma. Professor Bruggeman is also an elected member of the board of directors of the International Society of Plasma Chemistry. He has been a member of more than a dozen international scientific and organizing committees of meetings in his research field. Professor Bruggeman was the elected chair of the 2018 Gordon Research Conference on Plasma Processing Science and organized the conference “Frontiers in Low Temperature Plasma Diagnostics X” in 2013 in the Netherlands.