Effect of Competing Oxidizing Reactions and Transport Limitation on the Faradaic Efficiency in Plasma Electrolysis

Chloroacetate (sodium chloroacetate, 98%, Sigma Aldrich) and ferricyanide (potassium ferricyanide (III), powder or chunks, <10 μm, 99%, Sigma Aldrich) solutions were reduced in a glass H-cell electrochemical reactor (Adams & Chittenden) separated by a glass frit of P4 (ISO 4793) porosity, shown in Figure 1. In the ferricyanide (Fe(CN)₆³⁻) experiments, the catholyte consisted of 0.1−1 mM Fe(CN)₆³⁻ solutions dissolved in deionized (DI) water, using 82 mM of sodium perchlorate (NaClO₄ for molecular biology; DNase, RNase, and protease, none detected, 98%, Sigma Aldrich) as a background, non-reactive electrolyte. For ClCH₂CO₂⁻ experiments, solutions of 0.1−1 mM ClCH₂CO₂⁻ were prepared in 41 mM sodium tetraborate (Na₂Ba₄O₇), which provided the same conductivity (10.3 mS) as 82 mM NaClO₄, while maintaining the pH of the solution below 9; the pH was kept below 9 to prevent the interference of OH⁻, generated by Reaction 2, with Cl⁻ measurements (see Chemical analysis). The anolyte for both experiments was 82 mM NaClO₄ dissolved in DI water.

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In this configuration, an argon plasma functioned as a cathode, and a platinum electrode submerged in the solution functioned as the electrochemical anode, similar to our prior work.¹⁵ Air was purged out of the cathodic half-cell using a hose inserted through the lid of the cell, and a constant 250 cm³/min flow of Ar (UHP, Airgas) was used to pressurize the head space. An argon plasma was ignited between a stainless-steel capillary (Restek, 1.58 mm outer diameter, 0.017 mm inner diameter) and the catholyte by applying a negative bias of ∼3 kV using a high-voltage power supply (Glassman EH Series). A 220 kΩ ballast resistor was used to limit the current and prevent the transition of the plasma to an arc. Because the cathode and anode are in separate compartments, the oxidation products at the anode, mainly oxygen, did not interfere with the plasma chemistry. Similarly, neither ClCH₂CO₂⁻ nor Fe(CN)₆³⁻ were oxidized at the anode. Experiments were run for 10 minutes at a constant current of 10 mA, with a distance between the capillary and the liquid surface of ∼1 mm that lead to a current density that varied less than 5% from experiment to experiment. Unless otherwise specified, the solutions were not stirred during experiments. To determine the effect of forced convection on the faradaic efficiency, some experiments were run with a stirred solution using a magnetic stirrer and 1 cm stir bar revolving at a rate of 300 rpm.

Glycerol (≥99.5%, Sigma Aldrich) and methanol (for HPLC, ≥99.9%, Sigma Aldrich), were used as •OH scavengers in some experiments to analyze the effect of •OH radicals on the liquid-phase chemical reduction. Glycerol was chosen as an •OH scavenger because it reacts with •OH with a reaction rate constant of k = 1.9 × 10⁹ M⁻¹s⁻¹,²⁰ but it does not react with e⁻_aq.²⁴ In a similar manner, methanol readily reacts with •OH (k = 9.7 × 10⁸ M⁻¹s⁻¹),²⁰ but not e⁻_aq and was used to confirm the glycerol results. Both were mixed in the catholyte only, glycerol at a concentration of 500 mM and methanol at 200 mM. Due to higher reduction efficiency in the presence of the alcohols, •OH scavenger experiments with Fe(CN)₆³⁻ were run for 3 minutes instead of 10 minutes to prevent bulk concentration depletion.

A chloride-selective electrode (double junction, Cole-Parmer) was used to measure the chloride concentration produced by the reaction of e⁻_aq with ClCH₂CO₂⁻ via

A calibration curve was built prior to each measurement because the voltage response of the electrode tended to slowly drift from day to day. Solutions of sodium chloride (NaCl), adjusted for ionic strength with NaClO₄, were used to relate known concentrations of chloride (Cl⁻) to voltage measurements obtained by the chloride-selective electrode connected to a multimeter (Agilent 34401A 6 ½ Digit Multimeter). More details of the calibration can be found in Section S.1 of the Supplementary Material. Additionally, given that recent publications have made a case for the importance of the hydrogen radical (H•) as a reducing species both in RF-driven plasmas,²⁵ where H• may be introduced into the liquid by convection, as well as in plasma cathodes,²⁶ where H• can be formed in the liquid phase, the use of ClCH₂CO₂⁻ as a model system made it simple to distinguish the reduction by e⁻_aq as opposed to H•, which reacts with ClCH₂CO₂⁻ via

That is, by measuring only the Cl⁻ yield, we were able to distinguish only the dissociative attachment of e⁻_aq, Reaction 3, for accurate calculation of the faradaic efficiency, as discussed below.

For the ferri/ferrocyanide experiments, an UV-Vis-ES spectrometer (Ocean Optics USB2000+) was used to measure the absorbance of Fe(CN)₆³⁻ at ∼ 420 nm in a quartz cuvette (3.5 mL, 10 mm, Vernier). Fe(CN)₆³⁻ reacts with e⁻_aq via

producing ferrocyanide (Fe(CN)₆⁴⁻). Because Fe(CN)₆⁴⁻ does not absorb light at 420 nm,²⁷ the absorbance measurements were then used to obtain the amount of Fe(CN)₆³⁻ reacted after each plasma treatment. A calibration curve was built and used to measure the Fe(CN)₆³⁻ concentration after plasma experiments (see Section S.2 in the Supplementary Material).

Additionally, because reactions between ions are inevitably affected by electrostatic interactions with the solvent and thus depend on the ionic strength of the solution, the reaction rate constants between e⁻_aq and ClCH₂CO₂⁻, and e⁻_aq and Fe(CN)₆³⁻, were obtained as a function of ionic strength. A Titan-Beta 8 MeV pulsed electron Linear Accelerator (LINAC) in the Radiation Laboratory at the University of Notre Dame was used to obtain the reaction rate constants via transient absorption spectroscopy of e⁻_aq with ClCH₂CO₂⁻ and Fe(CN)₆³⁻ dissolved in DI water, as well as in 82 and 163 mM NaClO₄ solutions. The reaction rate constant between e⁻_aq and ClCH₂CO₂⁻ at an ionic strength of ∼82 mM is 1.48 × 10⁹ M⁻¹s⁻¹, and the reaction rate constant between e⁻_aq and Fe(CN)₆³⁻ at an ionic strength of ∼82 mM is 1.16 × 10¹⁰ M⁻¹s⁻¹. The details of these experiments are explained in Section S.3 of the Supplementary Material.

The faradaic efficiency for the reaction of solvated electrons with the reactant (Reaction 1) is defined as the rate of reduction of the reactant by solvated electrons divided by the creation rate of solvated electrons. For a plasma cathode system, a steady state species rate balance for solvated electrons equates their generation from the current of the plasma and their consumption via Reaction 1 (for any reactant R) and Reaction 2 (second-order recombination). The resulting balance is

where j is the current density of the plasma, l is the interfacial penetration depth of the electrons, and F is Faraday's constant. At the extreme of an abundance of reactants, when k_r[R] ≫ 2k₂[e⁻_aq], there is no competition for solvated electrons and the faradaic efficiency, η, is equivalently 100% (i.e., all of the electron current is consumed through reduction of the reactant). However, in some practical conditions such as the reduction of dissolved gases,¹⁵ the reaction rate k_r[R][e⁻_aq] is much slower than the second order recombination, and the faradaic efficiency becomes

That is, there is a linear relationship between η and [R] when η is small.

Figure 2 shows both measured and theoretical (using Equation 7) faradaic efficiencies as a function of the reactant concentration [R] for both the ClCH₂CO₂⁻ (Figure 2a) and Fe(CN)₆³⁻ (Figure 2b) systems. The theoretical estimation is based on a second-order recombination reaction rate constant of 2k₂ = 1.1 × 10¹⁰ M⁻¹ s⁻¹, a current density of j = 15,600 A m⁻², and a penetration depth of l = 24 nm. The current density was estimated by dividing the current by the area of the plasma, as previously reported,²⁸ and the penetration depth was obtained from an analytical approximation,²⁹ which is on the order of previously reported penetration depths.^30,31 For both reactant systems, the measured faradaic efficiencies (closed circles) are far lower than what is predicted from the theory in Equation 7 (solid lines). One possible explanation is that competition with •OH, which is not accounted for in the analytical expression, reduces the measured faradaic efficiency.

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It is well-known that in plasma electrolysis, •OH are readily produced by the dissociation of water, and that these rapidly react with solvated electrons,

Consequently, a large presence of •OH should reduce the faradaic efficiency by pure competition with Reaction 1. In addition to lowering the e⁻_aq concentration, when the reactant has a reversible oxidation reaction, the presence of •OH has the potential to further decrease the reduction efficiency by oxidizing the product back into the reactant. Such is the case for Fe(CN)₆⁴⁻, which can be reduced back to Fe(CN)₆³⁻ by

The effects of Reaction 8 and Reaction 9 on the reduction efficiency can be quantified using an •OH scavenger, such as glycerol. When glycerol is present at high concentrations, the reaction of •OH with glycerol (k₁₀ = 1.8 × 10⁹ M⁻¹ s⁻¹),³²

dominates over Reaction 8 and Reaction 9, and minimizes the reduction of •OH by e⁻_aq and the oxidation of Fe(CN)₆⁴⁻ by •OH. The product glycerol radical, like any other carbon-centered alcohol radical, does not react with e⁻_aq.¹¹

The reduction efficiency in the presence of 500 mM of glycerol (open circles) is also shown in Figure 2 and can be compared to the measurements without glycerol (closed circles). The competition with •OH for solvated electrons (Reaction 8) seems to have little effect on the faradaic efficiency in the ClCH₂CO₂⁻ experiments in Figure 2a, where the measurements with and without glycerol overlap. However, in the Fe(CN)₆³⁻ experiment, the presence of •OH does affect the reduction efficiency significantly, as shown in Figure 2b. This observation can be reconciled with that of Figure 2a by realizing that the product glycerol radical is in fact a reducing species, capable of reducing Fe(CN)₆³⁻ to Fe(CN)₆^4-. This reduction reaction is known for other alcohol radicals with Fe(CN)₆³⁻,³³ and transient absorption experiments at the Notre Dame LINAC have confirmed this process in the case of glycerol, with a measured rate constant 2.2 × 10⁹ M⁻¹ s⁻¹ (Section S.4 of the Supplementary Material). As a point of comparison, very similar results to Figure 2b were obtained using methanol as an •OH scavenger (Section S.5 of the Supplementary Material). If we presume that the •OH flux is only a few percent relative to the e⁻_aq, the alcohol might have very little effect on the steady state concentration of e⁻_aq, in agreement with results of Figure 2a. However, the glycerol product radicals, though few in number, will be relatively long-lived species, and will eventually find and react with Fe(CN)₆³⁻. The absolute increase of faradaic efficiency shown in Figure 2b is at most 1.5%, even though the relative increase is a factor of two.

It seems safe to conclude that •OH radicals play a very minor role in the chemistry induced by the plasma cathode in this system. Critically, the measured faradaic efficiencies shown in Figure 2, both with and without an •OH scavenger, are much lower than the theoretical kinetics-based prediction of Equation 7. These results indicate that the measured low efficiencies cannot be explained solely by competing chemical reactions.

An alternative explanation for the measured low faradaic efficiencies is the depletion of the target reactant R at the plasma-liquid interface. Recent analytical models show that the penetration of both e⁻_aq and •OH will only be on the order of 10–100 nm due to recombination.²⁹ If the electron reactant is depleted within this small distance near the interface, then the faradaic efficiency will be inherently limited. Figure 3a shows this concept schematically, where the reaction and subsequent diffusion of reactant from the bulk cause a depletion profile similar to that described by Nernst.³⁴

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To approximate this, a one-dimensional, steady state reaction-diffusion equation can be derived for the electron reactant

where is the diffusion coefficient of R in the catholyte. While Equation 11 describes the diffusive transport of reactants from the bulk to the interface, it is also important to note that the e⁻_aq concentration also decreases with depth from the liquid surface as shown in Figure 3a.²⁹ This will limit the rate of reaction in Equation 11. We account for this reduction by defining an effective concentration [e⁻_aq]_eff as some fraction of the e⁻_aq concentration at the catholyte surface [e⁻_aq], that is, [e⁻_aq]_eff = β[e⁻_aq], where β takes some value less than 1. To simplify this further, the concentration gradient for R can be approximated as two different constant concentrations, one at the bulk and one at the interface as shown in Figure 3b. Equation 11 can hence be approximated by the difference between the reactant concentration in the bulk [R]_B and at the interface [R],

where l_r is the depletion length of the reactant from the bulk to the interface and is the characteristic time of diffusion. With this approximation, the concentration of the reactant at the interface can be written as

where τ is an effective time constant that has units of time and incorporates both the diffusion transport () and embeds any fraction of the e⁻_aq concentration as a result of depletion (β):

When this revised concentration (Equation 13) is plugged into the definition for the faradaic efficiency in Equation 7, a modified expression with transport-limited reactant depletion is derived,

This expression contains the derived constant τ, and it should be clear that if this value goes to zero (indicating infinitely fast transport of the reactant to the interface), then Equation 7 is recovered. Although in this model, this time constant stems from diffusion of the reactant, it can be modified to reflect the characteristic transport time for other transport processes such as ionic migration via drift or convection.

While the value of τ is unknown a priori, its order of magnitude can be estimated using the diffusion time scale l²_r/, where the diffusivities of ClCH₂CO₂⁻³⁵ or Fe(CN)₆³⁻³⁶ are known, and approximating the fractional electron depletion β using models for the electron transport.²⁹ Given the extremely high rates of Reactions 3 and 5 and the small interfacial length, the interfacial concentration profiles are expected to reach steady state on the order of microseconds. With this assumption, l_r is expected to be constant and can be estimated as

where the reactant flux from the bulk toward the interface, J_r, is obtained from the experimental rate of reaction. Given a reactant concentration of ∼1 mM, this would yield a length of l_r ∼ 300 nm. Additionally, the interfacial reactant concentration will overlap with approximately β ∼ 5–10% of the peak e⁻_aq concentration at the catholyte surface, due to the sharp decline in e⁻_aq concentration as a function of distance from the interface.²⁹ Taking all of these into account, the value of τ should be close to 10 μs. The corrected theoretical line is shown in Figure 4, where it can be seen that a τ of ∼10 μs provides a good fit to the experimental data for ClCH₂CO₂⁻ from Figure 2.

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These results show that a pure kinetics-based description of the faradaic efficiency in plasma cathode electrolytic systems is insufficient, even when accounting for competing reactions with oxidizing species. Rather, the faradaic efficiency is inherently limited by the transport of the reactant to the interface as well as the depletion of electrons from the liquid surface. It is also worth mentioning that Equation 15 is not meant as an accurate a priori prediction of the faradaic efficiency, but rather an approximate analytical model that is illustrative of how transport negatively affects the faradaic efficiency, with a very clear relationship between the efficiency and important system parameters.