Sequential radiation chemical reactions in aqueous bromide solutions: pulse radiolysis experiment and spur model simulation

Abstract

Pulse radiolysis experiments were carried out to observe transient absorptions of reaction intermediates produced in N₂O- and Ar-saturated aqueous solutions containing 0.9–900 mM NaBr. The most important species among the reaction intermediates are BrOH˙⁻ and Br₂˙⁻, which commonly have absorption peaks around 360 nm. The experimental results were compared with the results of simulation based on a spur diffusion model. Each of several complicated sequential radiation-induced chemical reactions was carefully considered, optimizing its rate constant within a range of reported values, including experimental uncertainty. All the experimental results, covering a wide variety of conditions, were able to be universally reproduced by the simulation, assuming a reaction not yet reported, 2BrOH˙⁻ → Br₂ + 2OH⁻, with a rate constant of 3.8 × 10⁹ M⁻¹ s⁻¹, which is significant only within 10 μs for rather high bromide concentrations (>10 mM). Primary G values, which are yields after sufficient diffusion from the spur to the perimeter region during 100 ns, of major water decomposition products, as well as of the reaction intermediates, were calculated for N₂O- and Ar-saturated conditions as a function of NaBr concentration. Such comprehensive information on primary G values allows one to predict radiation-induced chemical change by considering only homogeneous chemical kinetics.

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Introduction

Water radiolysis has been studied since the discovery of ionizing radiations at the end of the 19th century.^1–3 Ionizing radiations transfer their energies and induce ionization and excitation of water molecules. Such ionization leads to the production of a highly oxidizing species, water radical cation (H₂O˙⁺),^4,5 and a recoiled electron. H₂O˙⁺ becomes a hydroxyl radical (˙OH) by giving a proton (H⁺) to one of the neighboring water molecules, leading to the production of a hydronium cation (H₃O⁺). On the other hand, the recoiled electron is thermalized and solvated to become a hydrated electron (e_aq⁻). In brief, the water decomposition products after physical and physicochemical stages within 1 ps are mostly ˙OH and e_aq⁻. These radicals are localized in narrow regions called “spurs”. Due to such localization as well as their high reactivity, they react with each other in parallel with their diffusion to perimeter regions. Such reactions are called intra-spur reactions and are very different from homogeneous chemistry after complete diffusion. As a result of intra-spur reactions, some ˙OH and e_aq⁻ are consumed, while hydrogen peroxide (H₂O₂), molecular hydrogen (H₂) and OH⁻ are produced. Most of the features of radiation-induced chemical reactions are strongly related to spur structure and the intra-spur dynamics of radical species.

Pulse radiolysis is a powerful tool for directly observing radiolytic species.^6,7 The species most widely investigated by this technique is, without any doubt, e_aq⁻, because it exhibits a strong absorption band in the visible and near-infrared regions with a peak around 720 nm. As is noted above, ˙OH is as important as e_aq⁻ in water radiolysis; however, few pulse radiolysis studies have been conducted to observe it directly. This is because ˙OH exhibits a very weak absorption band in the ultraviolet region with a peak around 240 nm. Note that the maximum molar absorption coefficient of e_aq⁻ is 19 000 M⁻¹ cm⁻¹,⁸ while that of ˙OH is about 700 M⁻¹ cm⁻¹.⁹ Also, the reaction mechanisms and rate constants of ˙OH have been investigated by utilizing many different scavengers which produce rather stable and easily detectable intermediates.

Halide anions, such as chloride and bromide anions (Cl⁻ and Br⁻), are some of the most often used ˙OH scavengers, and their radiation chemistry has been intensively discussed.^10–15 Scavenging reactions of halide anions lead to the production of rather stable intermediates with strong absorption bands in the near-ultraviolet or visible regions. However, the production mechanisms of the intermediates are very complicated and some intermediates exhibit similar absorption bands overlapping with each other. There are several reports on the molar absorption coefficients of BrOH˙⁻, Br₂˙⁻, and Br₃⁻.^16–20

Sworski measured the yield of production of H₂O₂ from aqueous bromide solution with varying Br⁻ concentration, as well as saturating gas.²¹ The measured yields were discussed stoichiometrically but detailed reaction dynamics could not be considered. Zehavi and Rabani pointed out the absorption observed in the UV domain in aqueous bromide solutions would be attributed to Br₃⁻.¹³ Ershov et al. observed the formation of Br₃⁻ in the radiation-chemical oxidation of Br⁻ in an aqueous solution by pulse radiolysis, exhibiting optical characteristics of Br₃⁻ and its equilibrium, Br₂ + Br⁻ ↔ Br₃⁻.²² It is worth noting that the optical absorption bands and equilibrium constants of trihalide anions such as Br₃⁻, Br₂Cl⁻, BrCl₂⁻, and Cl₃⁻ were well investigated without any ionizing radiation by Wang et al.²³ LaVerne et al. investigated the production of H₂ in the radiolysis of aqueous bromide solutions.²⁴ They concluded that oxidizing species containing bromine atoms are recycled by reaction with reducing species such as e_aq⁻, H˙, and HO₂˙, although detailed mechanisms, including rate constants, were not well clarified. Lin et al. scrutinized the spectral change of Br⁻, Br₂˙⁻, and Br₃⁻ as a function of temperature and pressure from ambient to supercritical conditions by a nanosecond pulse radiolysis technique, although the detailed mechanism of sequential radiation-induced chemical reactions in bromide solution was not well clarified.²⁵ Thus, most discussions in past reports are based on yields of final products after irradiation.

It is clear that sequential radiation-induced chemical reactions in aqueous bromide solutions begin from a scavenging reaction toward ˙OH, leading to production of a stable product, Br₃⁻. Due to the high stability of Br₃⁻, it was proposed to utilize Br₃⁻ production in concentrated bromide solutions in chemical dosimetry.²⁶ The direct effect of the solute, Br⁻, becomes non-negligible with its increasing concentration and was evaluated by the picosecond pulse radiolysis technique and final product analysis after ⁶⁰Co γ-irradiation.^14,27,28 An increase in bromide concentration not only makes its direct effect non-negligible but also affects competition among the sequential radiation-induced chemical reactions. In order to precisely predict the change in competition, it is necessary to strictly separate the contributions of each reaction forming the sequence. The bromide anion has been widely used not only as a probe for ˙OH but also as an inhibitor of H₂O₂ production via the reaction between two ˙OH radicals, as well as of H₂ destruction via the reaction between H₂ and ˙OH.^29–34 Furthermore, Br⁻ has been used in radiation chemistry, not only of low LET (linear energy transfer) radiations, such as fast electrons and γ-rays, but also of high LET radiations, such as ion beams. Ion beam pulse radiolysis studies with aqueous bromide solutions were performed to investigate the yield and behavior of ˙OH in heavy-ion tracks.^35,36 The primary yields of ˙OH for several therapeutic high-energy heavy ions were estimated from the difference in H₂O₂ production from aerated aqueous solutions containing Br⁻ and formate anions (HCOO⁻).^37,38 Thus, the influence of Br⁻ on the sequential reactions in water radiolysis is of crucial importance. In this study, it was proposed to resolve the contribution of each reaction by electron pulse radiolysis experiments, as well as by spur diffusion model simulations. Based on the simulations, which were validated by reproducing all the experimental results, variations in the primary G values of major water decomposition products, as well as major reaction intermediates involving Br atoms, were reported. Note that the primary G value is the yield after sufficient diffusion during 100 ns, which allows one to predict the radiation-induced chemical effect by considering only homogeneous chemical kinetics.

Pulse radiolysis experiment

Pulse radiolysis experiments were carried out with an electron beam provided from a linear accelerator (LINAC), at the Nuclear Professional School, University of Tokyo. The energy and pulse width of the beam were 35 MeV and 10 ns, respectively. Other details of the system are described elsewhere.³⁹ Each sample solution was gradually flowed through a quartz cell with a 20 mm optical path to avoid interference by accumulated stable products. Dosimetry was performed with a thiocyanate dosimeter,⁴⁰ which is an N₂O-saturated aqueous solution of 10 mM KSCN. The highest dose per single pulse was 47.0 Gy. An aluminum plate of a few millimeters thickness was located at the end of the accelerator to reduce the dose given to the sample to 14.3 Gy.

All sample preparations were carried out with ultrapure water (>18.3 MΩ cm) from a Milli-Q system (Merck KGaA). Sodium bromide (NaBr, >99.9%), sodium perchlorate (NaClO₄, >98%), sodium hydroxide (NaOH, >95.0%), and potassium thiocyanate (KSCN, >99.5%) were purchased from Wako Pure Chemical Industries, Ltd. and used without any further purification. The concentrations of the aqueous bromide solutions were 0.9, 9, 90 and 900 mM, which were bubbled with N₂O or Ar gas for 30 minutes or longer just before irradiation. It is worth noting that e_aq⁻ is converted into ˙OH by N₂O gas as follows:^13,41

e_aq⁻ + N₂O → O˙⁻ + N₂, 9.1 × 10⁹ M⁻¹ s⁻¹

O˙⁻ + H₂O → ˙OH + OH⁻, 9.4 × 10⁷ M⁻¹ s⁻¹

The reaction time scales of the first and second steps are 4.4 and 0.19 ns, respectively, because of the concentration of water itself, 55.6 M, and the solubility of N₂O in water, 25 mM.

Spur diffusion model simulation

Radiolysis products, such as ˙OH and e_aq⁻, are initially localized in the spur. To mimic spur processes, it is necessary to take into account not only chemical reactions but also diffusion due to concentration gradients. The spur diffusion model is a simple deterministic model, but a powerful tool to explain the intra-spur behavior of water radiolysis products.^42,43 Generally, the initial distributions of water decomposition products at the beginning of the simulation, i.e. 1 ps after irradiation, are given by 3D symmetric Gaussian distributions. The model requires solving simultaneous differential equations of multiple variables. FACSIMILE for Windows version 4.2 (MCPA Software Ltd.) is software for numerical calculations and was used to solve the differential equations. Details of the precise methodology are summarized in our previous report.⁴⁴ The input parameters for the simulation were slightly modified to reproduce the latest report on the fast behavior of water decomposition radicals within a few nanoseconds.^45,46 The standard deviations of the Gaussian distributions for e_aq⁻ and for the other species were modified to 3.20 and 1.15 nm, respectively. A reaction set for radiolysis of pure water was taken from a 2009 AECL report.⁴⁷ Other reactions related to bromide ions were taken from a report of Kelm and Bohnert.¹⁵ The diffusion coefficients used for Br⁻, Br˙, Br₂˙⁻, BrOH˙⁻, Br₃⁻ and Br₂ were 2.1, 2.1, 1.2, 1.1, 1.1, and 1.1 × 10⁻⁵ cm² s⁻¹, respectively, which are the same as those used in the literature.³⁴

It is well known that the dose rate can affect the behavior of radiolytic species. Such a dose rate effect is explained by overlapping of neighboring spurs.⁴⁸ In the present simulations, a spherical space was considered, with a boundary condition that no chemical species can leave the sphere or enter from the outside. In short, the size of the sphere corresponds to half the average distance between neighboring spurs. Assuming that all spurs appear simultaneously and their intervals are all equal to twice the radius of the sphere, r₀ (m), there must be the following relationship:

where ρ is the density of the aqueous solution (∼0.001 kg m⁻³), E is the average energy necessary to produce a single spur (10⁻¹⁷ J (=62.5 eV)), and X is the dose per pulse in Gray units (J kg⁻¹). Specifically, the radii (r₀) corresponding to doses of 47.0 and 14.3 Gy are 37.0 and 55.1 nm, respectively.

High concentrations of a salt can affect the solubility of a gas in solution, which is called “salting out/in”. The solubility of N₂O gas in water is interfered with by high concentrations of NaBr. Schumpe proposed a universal function,⁴⁹ from which the following relationship is derived in the case of pH 7:

[N₂O] = [N₂O]₀ exp(−0.1308C_NaBr − 7.56 × 10⁻⁹) ≈ 0.8774^C_NaBr[N₂O]₀

where [N₂O]₀ is the concentration without any salt (25 mM) and C_NaBr is the dissolved concentration of NaBr in molar units. Based on this function, the concentrations of dissolved N₂O in aqueous solutions of 0.9, 9, 90 and 900 mM NaBr are estimated to be 25, 25, 24 and 20 mM, respectively.

The rate constants of reactions between charged species are affected by ionic strength. In short, increasing ionic strength accelerates reactions between charged species of the same sign and slows those between charged species of opposite signs. The ionic strength effect was taken into account by following established models.^50,51

Results and discussion

Absorption spectra of BrOH˙⁻ and Br₂˙⁻

Fig. 1 shows normalized absorption spectra observed with an N₂O-saturated 0.9 mM NaBr aqueous solution. Both spectra have peaks in common around 360 nm; however, their shapes are slightly different and the spectra become narrower with time. The experimentally observed spectra at 100 and 500 ns agree very well with reported spectra of BrOH˙⁻ and Br₂˙⁻,¹⁸ respectively, shown as solid lines. Thus, BrOH˙⁻ appears as a reaction intermediate within 100 ns and then is gradually converted into Br₂˙⁻ during the time range from 100 to 500 ns.

Fig. 1 Normalized absorption spectra of BrOH˙⁻ and Br₂˙⁻. (+, × ): normalized absorption spectra experimentally observed with an N₂O-saturated aqueous solution of 0.9 mM NaBr at 100 and 500 ns after the pulse, respectively, (solid lines): reported spectra of BrOH˙⁻ and Br₂˙⁻.¹⁸

Fig. 2 shows a scheme of sequential radiation-induced chemical reactions expected to occur in aqueous bromide solutions. As a first step, ˙OH is scavenged by Br⁻ to give BrOH˙⁻.

˙OH + Br⁻ ↔ BrOH˙⁻, 1.1 × 10¹⁰ M⁻¹ s⁻¹ (forward) (R1)

3.0 × 10⁷ s⁻¹ (backward)

Fig. 2 Scheme of sequential radiation-induced chemical reactions in aqueous bromide solutions.

There are the following two pathways for BrOH˙⁻ to become Br₂˙⁻, depending on the Br⁻ concentration. In the case of a rather high Br⁻ concentration, (R2) is predominant and BrOH˙⁻ reacts directly with Br⁻ to give Br₂˙⁻.

BrOH˙⁻ + Br⁻ → Br₂˙⁻ + OH⁻, 1.9 × 10⁸ M⁻¹ s⁻¹ (R2)

On the other hand, in the case of a rather low Br⁻ concentration, the forward reaction of (R3) is faster than (R2). Thus, BrOH˙⁻ dissociates into OH⁻ and Br˙, which immediately reacts with Br⁻ to give Br₂˙⁻ (R4).

BrOH˙⁻ ↔ Br˙ + OH⁻, 4.2 × 10⁶ s⁻¹ (forward) (R3)

1.3 × 10¹⁰ M⁻¹ s⁻¹ (backward)

Br˙ + Br⁻ ↔ Br₂˙⁻, 1.0 × 10¹⁰ M⁻¹ s⁻¹ (forward) (R4)

2.5 × 10⁴ s⁻¹ (backward)

The branching ratio between the two pathways is fifty–fifty at a bromide concentration of about 20 mM.

After that, Br₂˙⁻ decays via a disproportionation reaction to produce Br₃⁻.

2Br₂˙⁻ → Br₃⁻ + Br⁻, 3.4 × 10⁹ M⁻¹ s⁻¹ (R5)

One of the products, Br₃⁻, is in an equilibrium, Br₂ + Br⁻ ↔ Br₃⁻, of which the equilibrium constant is 17.4 M⁻¹.²² In this paper, this equilibrium was not taken into account because we mostly focused on experimental data obtained at 360 nm, where only BrOH˙⁻ and Br₂˙⁻ exhibit strong absorptions. Note that the rate constants of the reactions (R1)–(R5) were taken from a report⁸ and are slightly different from the values optimized in this work (see Table 1).

Table 1 Important reactions in aqueous bromide solutions

Index	Reaction	Rate constant/10^10 M^−1 s^−1
a Unit for first-order reactions such as k1b, k3f and k4b is s^−1.b The subscripts indicate the directions of the reactions (f: forward, b: backward).c The rate constants in this table are the values re-estimated in this work and some of them are slightly different from the values reported by Kelm and Bohnert,^15 which are written in parentheses.
R1	˙OH + Br^− ↔ BrOH˙^−	k1f^b	0.87 (1.1)^c
		k1b^a^,^b	0.003
R2	BrOH˙^− + Br^− → Br2˙^− + OH^−	k2	0.019
R3	BrOH˙^− ↔ Br˙ + OH^−	k3f^a^,^b	4.5 × 10^−4 (4.2 × 10^−4)^c
		k3b^b	1.3
R4	Br˙ + Br^− ↔ Br2˙^−	k4f^b	1.0
		k4b^a^,^b	2.5 × 10^−6
R5	Br2˙^− + Br2˙^− → Br3^− + Br^−	k5	0.14 (0.34)^c
R6	BrOH˙^− + BrOH˙^− → Products	k6	0.38 (0)^c

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Molar absorption coefficient and decay kinetics of Br₂˙⁻

The bottom panel of Fig. 3 shows temporal behaviors of absorbance at 360 nm observed with N₂O-saturated aqueous bromide solutions of 0.9, 9, and 900 mM. The peak value of the absorbance increased with the Br⁻ concentration, showing that ˙OH scavenging by Br⁻ (R1) becomes predominant in competition with ˙OH consumption in spur reactions. The build-up behavior within 5 μs or less depends on the Br⁻ concentration, which is reasonable because the reaction rates of (R2) and (R4) are proportional to the Br⁻ concentration.

Fig. 3 Build-up and decay kinetics experimentally observed at 360 nm. (+, ×, ■): N₂O-saturated aqueous solutions of 0.9, 9 and 900 mM, respectively. Note that the upper panel shows reciprocal plots of the data in the lower panel.

In the upper panel of the figure, reciprocal plots of the temporal behaviors are shown. These are all straight lines except for build-up within 5 μs or less, implying that the decays are due to the disproportionation reaction of Br₂˙⁻ (R5). The slope of the straight line gives 2k_app/ε[small script l] for each situation, where ε, [small script l], and k_app are the molar absorption coefficient of Br₂˙⁻ at 360 nm, optical path (2 cm), and apparent rate constant of (R5) at a given ionic strength. The value of ε is necessary when estimating the value of k_app from the slope. Several values have been reported for ε, as follows: 9600 ± 800 (ref. 17), 7800 ± 2000 (ref. 19), 8200 (ref. 20), and 9900 ± 600 M⁻¹ cm⁻¹.⁵² One of the reasons for this variation is the difficulty in separating the absorption of Br₂˙⁻ from that of BrOH˙⁻, because the two species exhibit very similar absorption bands. Recently, Lampre et al. carefully separated the bands of the two species by a pulse radiolysis system combined with a streak camera, as well as by Bayesian data analysis.¹⁸ They concluded the molar absorption coefficients of Br₂˙⁻ and BrOH˙⁻ are 9600 ± 300 and 7800 ± 300 M⁻¹ cm⁻¹ at their peak positions of 354 and 352 nm, respectively. In the present study, molar absorption coefficients at 360 nm were estimated from the ratio of absorbance at 360 nm to that at the peak wavelength (9500 for Br₂˙⁻ and 7700 M⁻¹ cm⁻¹ for BrOH˙⁻). Employing 9500 M⁻¹ cm⁻¹ as ε, the values of k_app for Br⁻ concentrations of 0.9, 9, 90, and 900 mM were determined as 1.48, 1.74, 2.04 and 2.53 × 10⁹ M⁻¹ s⁻¹, respectively. The dependence of the apparent rate constant on ionic strength agrees well with the established models,^50,51 which allowed one to re-evaluate the rate constant at the limit of zero ionic strength, k_5f, as 1.4 × 10⁹ M⁻¹ s⁻¹. This re-evaluated value is smaller than the reported value¹⁵ by a factor of 2.4, although this difference would be due to lack of correction for the ionic strength effect in the past work.

Optimization of rate constants

Spur diffusion model simulations were conducted with the re-evaluated rate constant, k_5f. Fig. 4 shows the time profile of absorbance experimentally observed at 360 nm in an N₂O-saturated 0.9 mM NaBr aqueous solution in comparison with simulation results. The experimental results, shown as open circles, comprise a fast build-up within 100 ns and a rather slow build-up after that. The sequential reactions proceed in the order (R1), (R3) and (R4) (see Fig. 2) at this Br⁻ concentration, so the inflexion point at 100 ns is due to conversion from BrOH˙⁻ to Br₂˙⁻ via Br˙. The dotted line in the figure shows a simulation result with the rate constants of reactions (R1)–(R4) reported by Kelm and Bohnert¹⁵ (see Table 1). The simulation result clearly overestimates the experimental result. It was attempted to vary the molar absorption coefficients of BrOH˙⁻ and Br₂˙⁻ within the range of the latest report;¹⁸ however, the difference could not be resolved. Thus, it was necessary to carefully re-examine the rate constants in the simulation.

Fig. 4 Time-dependent absorbance observed with an N₂O-saturated aqueous solution containing 0.9 mM sodium bromide in comparison with simulations. (○): experimental result observed at 360 nm, (dotted and solid lines): simulation results before and after modification of the rate constants (k_1f and k_3f), respectively, (dashed lines): contributions of BrOH˙⁻ and Br₂˙⁻ in the simulation after consideration of (R6). For simulation results, see the vertical axis on the right.

Among the four reactions (R1)–(R4), the rate constant of (R4) has been reported by several groups and the values agree with each other, i.e. k_4f = (1.0 ± 0.3) × 10¹⁰ M⁻¹ s⁻¹. On the other hand, the rate constants of reactions (R1)–(R3) have been reported in only one publication⁶ and might be less reliable, so these rate constants were optimized to reproduce the experimental result. More specifically, k_1f and k_3f were modified from 1.1 to 0.87 × 10¹⁰ M⁻¹ s⁻¹ and from 4.2 to 4.5 × 10⁶ s⁻¹, respectively. The contributions of BrOH˙⁻ and Br₂˙⁻ after optimization are shown as dashed lines and their summation is shown as a solid line, which agrees well with the experimental result.

Disproportionation reaction of BrOH˙⁻

The same experiments were performed for other conditions, Br⁻ concentrations of 0.9, 9, 90 and 900 mM, as well as Ar saturation. The obtained experimental results at 360 nm are shown in Fig. 5 in the form of Gε, which was calculated from the observed absorbance and dose by the following relation:
where N_A is Avogadro's number (6.022 × 10²³ mol⁻¹) and Abs. is the absorbance. Spur diffusion model simulations conducted with the optimized rate constants could not well reproduce the experimental results at high concentrations, i.e. 90 and 900 mM (data are not shown). The Gε values at 1 μs and later obtained by the simulations increased with increasing Br⁻ concentration, while those in the experiments did not differ much in the Br⁻ concentration range from 9 to 900 mM. Such a discrepancy was consistently seen in both N₂O- and Ar-saturated conditions. An increasing scavenger concentration corresponds to an acceleration in the scavenging time scale. In the present study, increasing the Br⁻ concentration from 9 to 900 mM corresponds to an acceleration in the scavenging time scale for ˙OH from 10 to 0.1 ns. It is known that ˙OH decays from 5.2 (100 eV)⁻¹ at 1 ps to 2.8 (100 eV)⁻¹ at 100 ns in pure water due to intra-spur reactions as follows:

˙OH + ˙OH → H₂O₂, 4.8 × 10⁹ M⁻¹ s⁻¹

˙OH + e_aq⁻ → OH⁻, 3.5 × 10¹⁰ M⁻¹ s⁻¹

Fig. 5 Comparison between experiments and simulations with the revised rate constants. The left and right panels show data for N₂O- and Ar-saturated conditions, respectively. (○, △, ◊, □): experimental results for aqueous solutions of 0.9, 9, 90 and 900 mM NaBr, respectively, (solid lines): simulation results for corresponding conditions. Note that the contribution of direct effects was taken into account in all the simulation results shown in this figure.

Thus, the scavenged amounts of ˙OH in 9 and 900 mM bromide solutions must be different, although the produced amounts of Br₂˙⁻ are comparable for these Br⁻ concentrations. One possibility that can account for this discrepancy is that there is a reaction not yet reported, through which some scavenged ˙OH is lost before production of Br₂˙⁻

As is explained above, ˙OH and e_aq⁻ are initially localized in the spur and their distributions become homogeneous after diffusion and intra-spur reactions during 100 ns. Insofar as the scavenging reaction occurs within 100 ns, reaction intermediates such as BrOH˙⁻, Br˙, and Br₂˙⁻ appear inside the spur. The average diffusion distance of ˙OH, x (m), at a time t (s) is given by the following equation:

where D is the diffusion coefficient of ˙OH (2.3 × 10⁹ m² s⁻¹). The average diffusion distance of ˙OH before the scavenging reaction (R1) decreases from 37 to 1.2 nm with an increase in Br⁻ concentration from 0.9 to 900 mM. Therefore, the time and space where BrOH˙⁻ and Br₂˙⁻ appear become shorter and smaller, respectively, with an increase in Br⁻ concentration. Due to the localization of the intermediates, the reactions among ˙OH, BrOH˙⁻, Br˙, and Br₂˙⁻ would be non-negligible, especially for high Br⁻ concentration conditions. Among these reactions, there are reports on the rate constants of 2˙OH → H₂O₂ and Br₂˙⁻ + Br₂˙ ↔ Br₂˙⁻ + Br₂˙⁻, which were already incorporated in the simulations. In addition, Br˙ hardly exists in high Br⁻ concentration conditions. Thus, the following four reactions might be candidates for “a reaction not yet reported”.

BrOH˙⁻ + BrOH˙⁻ → Br₂ + 2OH⁻ (R6)

BrOH˙⁻ + Br₂˙⁻ → products

BrOH˙⁻ + ˙OH → products

Br₂˙⁻ + ˙OH → Br₂ + OH⁻

Among these candidates, only the reaction of 2BrOH˙⁻ (R6) was effective and non-negligible. Spur diffusion model simulations were reconducted taking into consideration the (R6) rate constant, which was optimized as 3.8 × 10⁹ M⁻¹ s⁻¹. It is worth noting that a reaction similar to (R6), COO˙⁻ + ˙OH → products, has been reported in a study using aqueous solutions containing concentrated formate.⁵³ Results of the simulations are shown as solid lines in Fig. 5. Note that the contribution of direct effects was taken into account for all the simulation results shown in the figure. In short, simulation results without consideration of direct effects were multiplied by a factor of the ratio of the number of electrons in the whole solution to that in the solvent, which is 1.0001, 1.0007, 1.0075 and 1.0745 for 0.9, 9, 90 and 900 mM NaBr aqueous solutions, respectively. More specifically, the direct effects in the system are ionizations of Br⁻ and Na⁺, giving Br˙, Na²⁺ and e_aq⁻. Na²⁺ might be able to be produced, but it would soon remove one electron from neighboring water molecules, giving H₂O˙⁺ or ˙OH. In addition, Br˙ soon reacts with Br⁻ to give Br₂˙⁻ in high concentrations of Br⁻, the reaction time scale of which is 0.1 ns for 1 M Br⁻. It is clearly seen that the simulations agree very well with the experimental results for a wide variety of conditions such as saturating gas and Br⁻ concentration. Reactions of e_aq⁻ are important in Ar-saturated conditions.

The decay seen in Ar-saturated conditions was not only due to the disproportionation reaction of Br₂˙⁻ (R5) but also to the following reaction:⁵¹

e_aq⁻ + Br₂˙⁻ → 2Br⁻, 1.1 × 10¹⁰ M⁻¹ s⁻¹

In addition, e_aq⁻ is not converted into ˙OH in Ar-saturated conditions, so the contribution of e_aq⁻ was taken into account with a molar absorption coefficient of 1535 M⁻¹ cm⁻¹, which is obtained by extrapolating a function reported by Bartels et al.⁸ An increasing concentration of a metal cation leads to a blue shift of the absorption band of e_aq⁻ due to a so-called contact pair structure.^14,54,55 The molar absorption coefficient of e_aq⁻ at 360 nm might be slightly higher than the value used in the present work due to the blue shift. Based on the fact that the absorption band width does not change with the blue shift,^56,57 the molar absorption coefficient of e_aq⁻ at 360 nm in 1 M NaBr aqueous solution would be the same as that at 361–364 nm in neat water, which is 1550–1590 M⁻¹ cm⁻¹. Thus the possible increase in the contribution of e_aq⁻ in this study is at most 1–4%.

Direct observation of the reaction (R6) was attempted; however, this was quite difficult due to the following two reasons. Firstly, as is claimed above, the absorption band of BrOH˙⁻ mostly overlaps with that of Br₂˙⁻. Secondly, the experimental conditions keeping BrOH˙⁻ in being for a sufficiently long duration are very limited, because it tends to be converted into Br˙ or Br₂˙⁻. As seen in Fig. 2, BrOH˙⁻ dissociates into Br˙ with a reaction time scale of 200 ns (forward reaction of (R3)) or reacts with Br⁻ to give Br₂˙⁻ with a reaction time scale between 6 ns and 6 μs (R2), depending on the Br⁻ concentration. Of course, there is also a backward reaction of (R3) and its reaction time scale depends on the pH: ca. 1 ms at pH 7 and ca. 100 ns at pH 11. Thus, the conditions are limited to Br⁻ concentrations lower than 30 mM, as well as a pH higher than 11, in order to observe BrOH˙⁻ for 100 ns. In addition, dissociation of ˙OH into O˙⁻ at a high pH also restricts the experimental conditions. Possible products in the reaction (R6) would be Br₂ and OH⁻ or H₂O₂ and Br⁻. It was confirmed that there is no obvious increase in H₂O₂ with an increasing Br⁻ concentration, implying that the most probable products are Br₂ and OH⁻. Due to the equilibrium between Br₂ and Br₃⁻, the yield of Br₃⁻ after sufficient time is stoichiometrically not affected by (R6) in conditions of high Br⁻ concentration. Note that all simulations with (R6) were conducted assuming these products.

Primary yields of reaction intermediates

Temporal behaviors of water decomposition radicals and reaction intermediates within the sequential reactions are shown in Fig. 6. The solid and dotted lines are simulation results with and without consideration of (R6), respectively. It is clear that (R6) is effective in the cases where the Br⁻ concentration is 90 and 900 mM; however, the production yield of Br₃⁻ at the end of the simulation, 1 ms, is not affected by (R6). This is because Br₂ is assumed to be a product of (R6) which immediately becomes Br₃⁻ via reaction with Br⁻ at high Br⁻ concentrations. The decay of ˙OH, as well as the build-up of BrOH˙⁻, corresponds to the progress of (R1). Note that Br₃⁻ production via (R6) occurs within 1 μs, while it is much slower than that via the other pathways. The decay of BrOH˙⁻, as well as the build-up of Br₂˙⁻, corresponds to the progress of (R2) except in the case of the lowest Br⁻ concentrations. Br˙ appears only at the lowest concentration (0.9 mM), because (R3) followed by (R4) is predominant in the conversion of BrOH˙⁻ into Br₂˙⁻, while (R2) is predominant in the other cases. Note that an increase in ˙OH yield from 1 to 100 ns for 0.9 mM Br⁻ is due to conversion from e_aq⁻.

Fig. 6 Simulated temporal behaviors of major products in N₂O-saturated aqueous bromide solutions. (Dotted and solid lines): G values of transient species with and without consideration of (R6), respectively. Note that all data shown in the figure are without correction for the contribution of direct effects.

Balcerzyk et al. measured the yield of a final product, Br₃⁻, in various conditions.²⁷ For example, the yield of Br₃⁻ in an N₂O-saturated 2 M NaBr aqueous solution is reported as 4.13 (100 eV)⁻¹. Similarly to the present work, they conducted spur diffusion model simulations, showing that they could reproduce the Br₃⁻ yield, which was also able to be reproduced by our simulations. The largest difference between the simulations in the two studies is seen in the decay of Br₂˙⁻ and the build-up of Br₃⁻. They intensively worked on picosecond pulse radiolysis as well;^14,28 however, behaviors of reaction intermediates on a medium time scale were not observed in their experiments.

Primary G values, which are yields after sufficient diffusion for a hundred nanoseconds, are of crucial importance because such information allows one to predict radiation-induced chemical effects by considering only homogeneous chemical kinetics. Fig. 7 shows primary G values of important reaction intermediates as a function of Br⁻ concentration. An increase in Br⁻ concentration accelerates the forward reaction of (R1), leading to a decrease in the primary G value of ˙OH. Corresponding to the trend, the primary G value of BrOH˙⁻ increases, but begins to decrease at a Br⁻ concentration of approximately 10 mM. Beyond this concentration, the primary G value of Br₂˙⁻ increases, which is due to acceleration of (R2). In addition, the primary G value of Br₃⁻ becomes non-negligible for higher Br⁻ concentrations, resulting from the faster rate constant of (R5) due to the ionic strength effect, as well as from a larger primary yield of Br₂˙⁻. The primary yield of H₂O₂ decreases with increasing Br⁻ concentration. This is because ˙OH is converted into BrOH˙⁻ or Br₂˙⁻ before the reaction 2˙OH → H₂O₂ proceeds. It is worth noting that such a trend in H₂O₂ yield as a function of Br⁻ concentration was recently carefully discussed by Mustaree et al.³⁴

Fig. 7 Primary G values of transient species appearing in aqueous bromide solutions as a function of bromide concentration. All data in the figure are simulation results and not corrected for direct effects. The left and right panels are for N₂O- and Ar-saturated conditions, respectively. In order to avoid too much complexity, products with rather low and high primary yields are separately shown in the upper and bottom panels, respectively. Note that results for concentrations of 1 M and higher are shown as dashed lines, because direct effects are non-negligible in this bromide concentration range. Dotted lines show results without consideration of (R6).

It is seen that the primary G values of H˙ and Br₂˙⁻ slightly increase for Br⁻ concentrations higher than 1 M. This tendency is explained as follows. In the models of Czapski and Schwarz⁵⁰ and D'Angelantonio et al.,⁵¹ the ionic strength effect is reduced, as opposed to the trend below 1 M. As a result, the reaction e_aq⁻ + H⁺ → H˙ is accelerated and the reaction, 2Br₂˙⁻ → Br₃⁻ + Br⁻ (R5) is slowed. Note that direct effects were not taken into account here. Of course, direct effects become more and more significant in concentrated solutions. In addition, a strongly oxidizing species produced by ionization of water molecules, H₂O˙⁺,^4,5 can react with Br⁻ to give H₂O and Br˙, followed by (R4), leading to instant production of Br₂˙⁻. This pathway becomes non-negligible in concentrated solutions^14,27,28 and should be taken into account in further accurate discussions of higher Br⁻ concentrations.

Conclusions

Electron pulse radiolysis experiments with a time resolution of 10 ns and spur diffusion model simulations were performed to resolve the contributions of each reaction in aqueous bromide solutions under a wide variety of conditions. The reaction rate constant of the disproportionation reaction of Br₂˙⁻, 2Br₂˙⁻ → Br₃⁻ + Br⁻, at the limit of zero ionic strength was evaluated as 1.4 × 10⁹ M⁻¹ s⁻¹, which is slightly smaller than the reported values (1.6–3.4 × 10⁹ M⁻¹ s⁻¹). A reaction not yet reported, 2BrOH˙⁻ → Br₂ + 2OH⁻, needed to be introduced into the simulation with a rate constant of 3.8 × 10⁹ M⁻¹ s⁻¹ in order to universally reproduce the experimental results.

The primary G values of major water decomposition products, as well as major reaction intermediates involving Br atoms, were reported as a function of bromide concentration from 0.1 mM to 7 M. Such information is inevitably important when predicting radiation chemistry by considering only homogeneous chemical reactions. The contribution of the introduced reaction was derived from the simulations, showing that this reaction can be significant for Br⁻ concentrations higher than approximately 10 mM. The yield of a final product, Br₃⁻, after a sufficient duration (>1 ms), is not much affected by the reaction. However, its production via this reaction occurs within 1 μs while it is much slower via the other pathways. Apparently, this reaction need not exist as far as only the initial and final states of the sequential reactions are focused on. However, a product of the reaction, Br₂, is rather stable and a reaction between BrOH˙⁻ and a certain additive would not be as effective as expected without the disproportionation reaction of BrOH˙⁻. This point is important in a detailed discussion of seawater radiolysis because it contains not only chloride (0.56 M) but also bromide (0.82 mM) and some other components.⁵⁸ Oxidizing species in bromide solutions tend to exist in the form of BrOH˙⁻ in the equilibrium Br⁻ + ˙OH ↔ BrOH˙⁻. However, those in chloride solutions tend to be free ˙OH in a similar equilibrium, Cl⁻ + ˙OH ↔ ClOH˙⁻. Such a difference leads to a difference in H₂ production in bromide and chloride solutions. H₂ production in Ar-saturated 1 mM Br⁻ solution increases linearly, at least up to 100 kGy, while there is almost no H₂ production in 1 mM Cl⁻ solution.²⁴ Even with a small amount of Br⁻ compared to Cl⁻, the former is predominant in the production of H₂O₂, which is one of the oxidizing species most responsible for oxidative corrosion.^59,60 Another notable point is that ˙OH is produced in ion tracks with very high local concentrations, which would lead to high local concentrations of BrOH˙⁻ as well. In that case, the disproportionation reaction of BrOH˙⁻ would be non-negligible, even if the bromide concentration was not so high.

Acknowledgements

We are grateful to Mr. T. Ueda and Prof. M. Uesaka (Univ. Tokyo) for their technical assistance and encouragement in pulse radiolysis experiments.

Notes and references

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