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Multi-Scale Modelling of the Gamma Radiolysis of Nitrate Solutions Gregory Peter Horne, Thomas Ashley Donoclift, Howard Sims, Robin Orr, and Simon M. Pimblott J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b06862 • Publication Date (Web): 25 Oct 2016 Downloaded from http://pubs.acs.org on October 26, 2016

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The Journal of Physical Chemistry

Multi-Scale Modelling of the Gamma Radiolysis of Nitrate Solutions Gregory P. Hornea,b,*, Thomas A. Donoclifta,b, Howard E. Simsa,c, Robin M. Orrd, and Simon M. Pimblotta,b,* a

The University of Manchester, Dalton Cumbrian Facility, Westlakes Science and Technology Park, Cumbria, CA24 3HA, UK.

b

The University of Manchester, School of Chemistry, Oxford Road, Manchester M13 9PL, UK.

c

National Nuclear Laboratory, Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB, UK.

d

National Nuclear Laboratory, Sellafield Central Laboratory, Sellafield, Seascale, Cumbria, CA20 1PG, UK. * Corresponding authors. ABSTRACT A multi-scale modelling approach has been developed for the extended timescale long-term radiolysis of aqueous systems. The approach uses a combination of stochastic track structure and track chemistry as well as deterministic homogeneous chemistry techniques and involves four key stages; radiation track structure simulation, the subsequent physicochemical processes, nonhomogeneous diffusion-reaction kinetic evolution, and homogeneous bulk chemistry modelling. The first three components model the physical and chemical evolution of an isolated radiation chemical track and provide radiolysis yields, within the extremely low dose isolated track paradigm, as the input parameters for a bulk deterministic chemistry model. This approach to radiation chemical modelling has been tested by comparison with the experimentally observed yield of nitrite from the gamma radiolysis of sodium nitrate solutions. This is a complex radiation chemical system which is strongly dependent on secondary reaction processes. The concentration of nitrite is not just dependent upon the evolution of radiation track chemistry and the scavenging of the hydrated electron and its precursors, but also on the subsequent reactions of the products of these scavenging reactions with other water radiolysis products. Without the inclusion of intra-track chemistry, the deterministic component of the multi-scale model is unable to correctly predict experimental data, highlighting the importance of intra-track radiation chemistry in the chemical evolution of the irradiated system. INTRODUCTION Traditionally, modelling the long-term radiolysis of aqueous systems has been performed using a deterministic treatment of the bulk homogeneous chemistry.1-3 A deterministic approach to modelling radiation chemistry involves the description of the radiolytic chemical kinetics as a set of coupled simultaneous differential equations and it requires the radiolytic yields of the primary radiolysis species as input parameters. These yields are used to calculate the homogeneous rate of production of the primary radiation chemical species. For aqueous solutions, the yields used are conventionally taken to be those of the species escaping from a radiation track in pure water and so

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depend on radiation quality, i.e. radiation type and energy, but not on the composition of the irradiated system.2,3 The passage of ionizing radiation through water results in the formation of a radiation chemical track, which is composed of a series of energy transfer events. Each energy transfer event results in the formation of a cluster of electronically excited or ionized reactive species, known as a spur. The subsequent evolution of the radiation chemical track involves a competition between intra- and interspur reactions (i.e. recombination processes) and diffusion (spur relaxation), leading to the formation of molecular species and ultimately the escape of both radical and molecular species into bulk solution. Because of the nonhomogeneous spatial distribution of the reactants in a radiation track, irradiated systems have characteristic short-time (of the order of microseconds) nonhomogeneous chemistry which depends on the radiation quality. In pure water, the species that diffuse out of the radiation track into bulk solution during its spatial relaxation are eaq−, Haq+, H•, OH•, H2, and H2O2 and will henceforth be referred to as the primary products of water radiolysis. Their yields at this point in time are referred to as escape yields, expressed as G-values (throughout this work G-values are quoted in the conventional radiation chemical unit of ions or molecules 100 eV−1, the corresponding S.I. unit is related by 1 ion or molecule (100 eV)−1 = 0.096 μmol J−1). These yields are truly only representative of pure water and very dilute aqueous solutions. They are not appropriate for aqueous solutions that contain significant amounts of chemical scavengers, i.e. bulk species that react with the primary products of water radiolysis; for instance the nitrate anion (NO3−) rapidly scavenges the hydrated electron (eaq−) and its precursor (epre−).4-6 The influence a chemical scavenger has upon an irradiated aqueous solution depends upon its scavenging capacity ( s), which is defined as the pseudo first-order rate constant for the scavenging reaction ( s

).

Increasing the concentration of a scavenger increases the extent to which the scavenger interferes with the chemical and spatial evolution of a radiation track. To accurately model the long-time radiation chemistry of complex aqueous solutions, it is necessary to develop a multi-scale model incorporating the radiation track chemistry, and its modification in the presence of chemical scavengers, within a description of the bulk homogeneous radiation chemistry. As the interaction of ionising radiation with an absorbing medium is a stochastic process that produces a spatially nonhomogeneous distribution of species, stochastic Brownian dynamics techniques offer the most effective method for modelling intra-track chemistry. These methods have been successfully used to simulate the radiation chemical kinetics of isolated tracks;7-10 however, extending these methods from this “infinitely low dose” limit to realistic complex chemical systems receiving significant dose is not straightforward.


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This article describes the development of a novel multi-scale modelling approach, using a combination of stochastic and deterministic models, for the radiation chemistry of complex, concentrated aqueous solutions, approaching the challenge in four key stages, each representing one of the four stages in the evolution of the radiation chemical system; track structure, physicochemical processes, nonhomogeneous diffusion-reaction kinetics, and homogeneous bulk chemistry. To test the modelling approach and demonstrate the importance of radiation track chemistry in determining the bulk radiation chemistry and observable radiolysis products, a comparison with experimental data for the gamma radiolysis of sodium nitrate (NaNO3) solutions is presented. The radiolytic yield of nitrite (G(NO2−)) from the radiolysis of aerated solutions of nitrate (NO3−) has been experimentally investigated by a number of research groups.11-15 The dependence of the observed nitrite yield on the concentration of NO3− is consistent in all of the studies, although there is scatter between the data of the different studies. Without exception the dose at which the yields are quoted is not specified. Furthermore, the measured yields of NO2− are considerably smaller than the yields measured for other scavengers of the hydrated electron and its precursors.5,6 A thorough experimental re-evaluation of the gamma radiolysis of aerated and deaerated aqueous NO3− solutions has recently been undertaken to resolve the radiation chemistry of NO2− formation and will be communicated in a follow up article.16 This study confirmed the experimental (concentration dependence and absolute yield) data in the literature, but revealed a significant non-linear dose dependence of the measured yields. This non-linear dose dependence and the significant difference between the G(NO2−) and the yields measured for other scavengers implies significant bulk phase secondary chemistry between the reactive products of NO3− reduction and other radiation induced species, making this an ideal system for study using a multi-scale modelling formalism for radiation chemistry incorporating the evolution of the radiation chemical track. In aerated solution, the radiolytic formation of NO2− in NO3− solution occurs by two different routes: (i)

the reduction of NO3− by the hydrated electron and its precursors (plus H•), and

(ii)

the direct interaction of radiation with NO3− leading to an excited state that decays to give NO2− and O. Formation of NO2− by the transfer of radiation energy to the electrons of NO3− proceeds by reactions (1) and (2) to direct chemical change. Consequently, the extent to which this route contributes to G(NO2−) depends upon the relative electron fraction of NO3− compared to the bulk solvent, water; high concentrations (≥1 mol dm-3) of NO3− are necessary for direct effects to influence G(NO2−).



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The principal formation mechanism is summarised by the reaction scheme in Table 1. In the former case, which is dominant in the experimental studies reported, reduction of NO3− leads to the formation of the reactive intermediate NO3•2− (and HNO3−). This intermediate is converted to NO2 and then ultimately to NO2− (or it is consumed by homogeneous bulk chemical processes). The extent to which this indirect chemical route contributes to G(NO2−) is dependent upon the concentration of NO3− and its scavenging of epre− and eaq− in competition with their intra-track reactions with other primary species, e.g. H2O+ or OH•, respectively, or with other scavengers, e.g. O2. As NO3− is a highly effective scavenger of epre− and eaq−, a relatively small concentration of NO3− is capable of having a significant effect upon the chemical evolution of a radiation track. Table 1. Simplified reaction scheme for the radiolytic formation of nitrite from the radiolysis of aqueous nitrate. number

chemical reaction

1

NO3− ⇝ NO3−* → NO2− + O

2 3 4 5 6 7

−

−

•

−

NO3 ⇝ NO3 * → NO3 + e −

−

NO3 + epre → NO3 −

−

NO3 + eaq → NO3 −

•

NO3

•2−

1.0

•

HNO3 → NO2 + OH NO2•

17

9.7

−

+ H2O → NO2 + 2OH

•

N/A 1

•2−

•

−

reference

N/A

•2−

NO3 + H → HNO3

rate constant (dm3 mol−1 s−1)

−

−

1.0 2.0

8

NO2 +

9

N2O4 + H2O → HNO2 + HNO3

18

10

HNO2 → NO2− + Haq+

3

→ N 2 O4

4.5

17 13

18

10

9

4

7

19

10 10

3

19,20

10

5

−1

10 (s ) 8

10

19,20 21 21

107 (s−1)

22

NO2− and its radiation chemical precursors NO3•2− and NO2 are reactive species which have extensive chemistry with the primary species resulting from water radiolysis. This bulk secondary chemistry has a significant effect on the measured yield of NO2−. Consequently, the radiolytic production of NO2− from NO3− is an interesting system to demonstrate the importance of using a multi-scale modelling approach to simulate the radiation chemistry of irradiated aqueous systems. The complete reaction scheme used in the calculations reported is included in the supplementary material along with the reaction rate constants.


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METHODLOGY

Multi-scale Modelling The multi-scale modelling methodology developed and deployed is outlined in Figure 1.

Figure 1. Schematic representation of the multi-scale modelling approach. It approaches the challenge of modelling the bulk radiolysis of an aqueous system by breaking the calculation down into four key stages, which correspond to different time (and distance) regimes: (i)

track structure formation (> (5), but, at the higher concentration, both of the scavenging reactions contribute although the reaction with eaq− is still dominant (4) > (6) > (5).

5x10-5

(4)

[NO2] / mol dm-3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(6) (3)

(5)

(2)

4x10-5

3x10-5

(1) -5

2x10

1x10-5

0 0

150

300

450

600

750

900

1050

Dose / Gy

Figure 3. Concentration of NO2− produced as a function of dose from the gamma irradiation of aerated 0.1 mol dm−3 NO3− solution: Experiment (); Radiation chemistry calculation using water radiolysis escape yields (1); incorporating the predictions of stochastic track chemistry (2); Predicted concentration of NO2− in the absence of secondary bulk reactions (3); Predicted concentration of NO3•2− formed from NO3− scavenging of electrons(4); Contribution from epre− (5) and eaq− (6), determined by stochastic calculations; experimental standard deviation ≤ (±) 2 10−6 mol dm−3. DISCUSSION Non-homogeneous Radiation Track Chemistry. For the systems investigated, the yields of water ionisation and excitation are independent of scavenger concentration, with G(ionization) = 4.18 ions (100 eV)−1, and G(excitation) = 2.43 molecules (100 eV)−1. Table 2 lists the radiolytic yields at 1 ps for eaq−, OH•, H•, H2, H2O2 and NO3•2− for pure water, and aerated 1

10−3 and 0.1 mol dm−3

NaNO3 solutions predicted by stochastic track chemistry simulations and their temporal evolution through to 1 μs is included in the supporting information. These simulations are the primary inputs for the bulk chemistry modelling calculations. Table 3 lists the calculated “initial radiolytic yields” at 1 μs for pure water, and aerated 1

10−3 and 0.1 mol dm−3 NaNO3 solutions as well as the accepted

escape yields for the gamma radiolysis of pure water taken from the compilation of Elliot and Bartels.1 Comparison of these yields shows that the true radiolysis products are strongly dependent



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upon intra-track processes and scavenger chemistry. Of particular importance is the change in initial yields of NO3•2− and NO2• with increasing NO3− concentration and their values relative to the escape yield of eaq− from pure water. Table 2. Calculated initial radiolytic yields at 1 ps for the gamma radiolysis of pure water and aerated aqueous 1 10−3 and 0.1 mol dm−3 NaNO3 solutions. picosecond radiolytic yield (species / 100 eV)

species pure water

1

10−3 mol dm-3 NO3−

0.1 mol dm−3 NO3−

eaq−

4.15

4.13

2.57

OH•

4.49

4.47

4.38

H•

0.34

0.33

0.29

H2

0.35

0.35

0.29

O(3P)

0.07

0.06

0.05

H2 O2

0.28

0.29

0.27

-

0.02

1.59

NO3•2−

In aerated NO3− solutions (1

10−3 to 6 mol dm−3), the electrons (epre− and eaq−) from water

radiolysis are scavenged by NO3− and O2, leading to the formation of NO3•2− and O2•−; by reactions (3), (4), and (11), respectively. eaq− + O2  O2•−

k11 = 1.9 x 1010 dm3 mol−1 s−1

(11)4

Similarly, H• is converted into HNO3− and O2•−; via reaction, (5) and (12), H• + O2  HO2•  Haq+ + O2•−

k12 = 2.1 x 1010 dm3 mol−1 s−1

(12)4

These scavenging reactions lead to a noticeable discrepancy between the sum of the escape yields of the reducing radicals; [G(eaq−) + G(H•)] = 3.20, for water radiolysis and the sums [G(NO3•2−) + G(NO2•) + G(O2−) + G(HO2•)] for 1

10-3 and 0.1 mol dm-3 NO3− solutions, which are 3.35 and

4.20, respectively. The latter sum is more than 30% higher than the corresponding [G(eaq−) + G(H•)] for water radiolysis.

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Table 3. Comparison of calculated (escape) yields at 1 μs for the gamma radiolysis of pure water and aerated aqueous 1 10−3 and 0.1 mol dm−3 NaNO3 solutions with the gamma radiolysis escape yields for water. stochastic calculation (species / 100 eV)

Species

10−3 mol dm-3 NO3−

1 eaq−

escape yields (species / 100 eV)1

0.1 mol dm−3 NO3−

pure water

pure water

-

-

2.63

2.64

+

2.92

3.76

2.65

2.64

•

2.74

3.11

2.65

2.53

H•

-

-

0.47

0.56

H2

0.43

0.30

0.47

0.42

H2 O2

0.69

0.78

0.63

0.75

•

0.34

0.15

0.01

-

1.01

0.07

-

-

1.90

3.76

-

-

0.10

0.22

-

-

Haq

OH

HO2 O2 −

NO3•2− NO2

•

The origins of this difference are clearly demonstrated in Figure 4 and Figure 5, which show the calculated decay kinetics of eaq− and the formation kinetics of NO3•2−, respectively, in pure water and in aerated 1

10−3 and 0.1 mol dm−3 NO3− solutions. The escaping yield of eaq− has in its very nature

to be smaller than the yield of electrons scavenged by NO3− and converted to NO3•2− at any NO3− concentration where scavenging competes with intra-track reaction and spatial relaxation, i.e. where ( s)

−1

< 1 s. As the concentration of NO3− increases, there is a progressive increase in the

scavenging capacity of NO3− for the hydrated electron and its precursors. This increase leads to fewer electrons being consumed by intra-track processes and to [G(NO3•2−) + G(NO2•) + G(O2−) + G(HO2•)] yields higher than the corresponding [G(eaq−) + G(H•)] for water radiolysis. This scavenging is highlighted by the decrease in the lifetime of the hydrated electron to 100 ps. The bulk homogeneous chemistry of NO2− is driven by NO3•2− and not the bulk homogeneous chemistry of eaq−, the latter of which is implicit when using water radiolysis escape yields as initial input parameters.



5.0

G(eaq) / ions 100 eV-1

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4.0

3.0

(1)

2.0

(3)

(2)

1.0

0.0 1

2

3

4

5

6

Log10(time / ps)

Figure 4. Decay kinetics of the eaq− in pure water and in aerated 1 10−3 and 0.1 mol dm−3 NO3− solutions. Experimental pulse radiolysis decay kinetics of eaq−: Fanning ()27; Buxton ()28; Jonah (▼)29; Bartels (dashed line)30. Escape yield of eaq− (→)1.Radiation chemistry calculation for the stochastic track chemistry of deaerated water (1); of aerated 1 10−3 NO3− solution (2); and of − −3 aerated 0.1 mol dm NO3 solution (3). At sufficiently high NO3− concentrations, NO3− is able to scavenge epre− in competition with the hydration process which occurs on a sub-picosecond timescale before diffusion limited reactions can occur. This scavenging prior to hydration leads to a potentially significant increase in G(NO3•2−) and a proportional decrease in the initial yield of eaq−, e.g. G(eaq−) at 1 ps is 2.57 for 0.1 mol dm−3 NO3−, compared to 4.16 for pure water. The use of water radiolysis escape yields places an artificial cap (G(eaq−) = 2.64) on the amount of electrons available for scavenging by NO3−, leading to greater under-estimation of NO2− yields with increasing NO3− concentration. A further consequence of the scavenging is that the remaining “sibling” primary water radiolysis species, i.e. OH•, H2, H2O2, and Haq+, show either an enhanced escape yield or undergo different intra-track chemistry. For instance G(OH•) increases from 2.65 to 2.75 to 3.11, in going from pure water to 1

10−3 mol dm−3 NO3− solution to 0.1 mol dm−3 NO3− solution. This increase in OH•

escape yield is also accompanied by an increase in H2O2 formation with G(H2O2) rising from 0.69 to 0.78 as NO3− concentration increases from 1

10−3 to 0.1 mol dm−3. According to the compilation

of Elliot and Bartels, G(H2O2) is 0.75 for the gamma radiolysis of pure water.1 This value is intermediate between the values predicted by track chemistry calculation for aerated solutions of


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NO3− and somewhat larger than that predicted by calculations (not reported) for pure water, 0.69; however, it should be noted that the value selected by Elliot and Bartels is somewhat higher than the usually accepted value of G(H2O2) = 0.68.31

5.0

G(NO32) / ions 100 eV-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(2) 4.0

3.0

(1)

2.0

1.0

0.0 0

1

2

3

4

5

6

Log10(time / ps)

Figure 5. Formation kinetics of NO3•2− in aerated 1 10−3 and 0.1 mol dm−3 NO3− solutions. Escape yield of eaq− from pure water (→)1. Radiation chemistry calculation for the stochastic track chemistry of aerated 1 10−3 NO3− solution (1); and of aerated 0.1 mol dm−3 NO3− solution (2). Overall, scavenging from within the radiation chemical track alters the proportions and speciation of the primary products of water radiolysis, which in turn has an effect upon bulk homogeneous chemistry. Without the inclusion of intra-track chemistry, the deterministic component of the multiscale model is unable to predict experimental data, highlighting the importance of intra-track radiation chemistry in the chemical evolution of the irradiated system. Homogeneous Bulk Chemistry. As demonstrated in Figure 2 and Figure 3, the potential concentration of NO2− is significantly higher than that measured experimentally. This is because the concentration of NO2− is not just dependent upon the evolution of radiation track chemistry and the scavenging of the hydrated electron and its precursors, but also on the subsequent reactions of the products of these scavenging reactions with other water radiolysis products.



(A) NO32 Reaction Kinetics 2.0x10-4

(B) NO2 Reaction Kinetics

(P,1)

(P) = Total Production (1) = NO3 + eaq/epre  NO32

6.0x10-4

(P) = Total Production (1) = NO2 + OH  NO2 + OH 



(2) = OONOO  NO2 + O2

(P)



(3) = NO32 + H2O  NO2 + 2OH -4

4.0x10

(4) = HOONOO  NO2 + HO2

(1)

-4

1.0x10

0.0

(2) (3) -1.0x10-4

(4)

Cumulative [NO2] / mol dm-3

Cumulative [NO32] / mol dm-3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(3) (4) 0.0

(6)

-4.0x10-4

-2.0x10

(4) = NO

0

150

 3

 2

(C)

+ O2  NO + O

300

450

600

750

(7) (C) = Total Consumption (5) = NO2 + HO2  HOONOO

(3) = NO32 + H2O  NO2 + 2OH 2 3

(5)

-2.0x10-4

(C) = Total Consumption (2) = NO32 + H2O2  NO3 + OH + OH -4

(2)

2.0x10-4

900 1050

-6.0x10-4 -150

(6) = net 2NO2  N2O4 (7) = NO2 + O2  OONOO

0

Dose / Gy

(C)

150 300 450 600 750 900 1050

Dose / Gy

Figure 6. Predominant reaction kinetics for NO3•2− (A) and NO2• (B) production and consumption from the gamma radiolysis of aerated 1 10−3 mol dm−3 NO3− solution. These so-called secondary radiation induced reactions are responsible for the attainment of the measured steady-state concentration of NO2−, through their consumption of NO2− and its precursors (i.e. NO3•2−, NO2, N2O4, and HNO2). The importance of these secondary reactions will be discussed in further detail by taking the 1

10−3 mol dm−3 NO3− system as our example. Figure 6 gives the

predominant reaction kinetics for the production and consumption of NO3•2− and NO2, and Figure 7 gives the predominant reaction kinetics for the production and consumption of N2O4 and NO2−.


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(B) NO2 Reaction Kinetics

(A) N2O4 Reaction Kinetics 6.0x10-5

(P) = Total Production (1) = 2NO2  N2O4

(P,1)

3.0x10-4

(P)

(P) = Total Production (SS) = Steady-State (1) = OONOO  NO2 + O2

(1)

(2) = HNO2  NO2 + H

4.0x10-5

2.0x10-4

Cumulative [NO2] / mol dm-3

Cumulative [N2O4] / mol dm-3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.0x10-5

0.0

-2.0x10-5

(2) (SS)

0.0

-1.0x10-4

-4.0x10-5

-6.0x10-5

1.0x10-4

-2.0x10-4

(C) = Total Consumption (2) = N2O4 + H2O  HNO2 + HNO3

0

200

400

600

-3.0x10-4

(C,2) 800

1000

(C) = Total Consumption (3) = NO2 + OH  NO2 + OH

0

150

Dose / Gy

300

450

600

(C,3) 750

900 1050

Dose / Gy

Figure 7. Predominant reaction kinetics for N2O4 (A) and NO2− (B) production and consumption from the gamma radiolysis of aerated 1 10−3 mol dm−3 NO3− solution. NO3•2− is formed within the radiation track at a rate of 2.05

10−7 mol J−1 s−1, from scavenging

electrons, allowing for the formation of >200 μmol dm−3 for an absorbed dose of 1 kGy. Once formed, NO3•2− is rapidly consumed resulting in a tiny steady-state concentration. The processes responsible for its consumption are reactions with H2O (40%), O2 (56%), and H2O2 (4%), reactions (6), (13), and (14), respectively. NO3•2− + O2  NO3− + O2•−

k13 = 2.4

108 dm3 mol−1 s−1

(13)11

NO3•2− + H2O2  NO3− + OH• + OH−

k14 = 1.6

108 dm3 mol−1 s−1

(14)32,*

Reaction with H2O results in the formation of NO2•, the subsequent precursor in the NO2− formation pathway, whereas reaction with O2 and H2O2 oxidises NO3•2− back to NO3−. Consequently, a substantial fraction of NO2− precursor is consumed by O2, although more than this is recovered via reaction of NO2• with O2•− (15), see Figure 6 and Figure 7 (B). *

Rate constant has been optimized using FACSIMILE’s fitting parameters, the literature rate constant from reference 33 is 1 108 dm3 mol−1 s−1.



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NO2• + O2•−  O2NOO−

k15 = 4.5

109 dm3 mol−1 s−1

Page 16 of 22

(15)19

The reaction of NO3•2− with H2O2 becomes progressively more important with time, due to the accumulation of H2O2 in the bulk solution. This reaction is primarily responsible for the non-linear dose dependency in NO2− concentration exhibited in Figure 2 and Figure 3.Although 40% of the total NO3•2− yield is converted into NO2•, this pathway amounts to only 15% of the cumulative yield of NO2•, the majority of which (49%) is formed by the reaction of NO2− with OH• (16), and the remainder by decomposition of peroxynitric acid species, HOONO2 (3%) and O2NOO− (33%), reactions (17) and (18), respectively. NO2− + OH•  NO2• + OH−

k16 = 1

HOONO2  NO2• + HO2•

k17 = 0.026 s−1

(17)20

O2NOO−  NO2• + O2•−

k18 = 1.05 s−1

(18)33

1010 dm3 mol−1 s−1

(16)4

Reaction (16) not only serves as the primary means through which to form NO2•, but acts as the predominant pathway through which NO2− itself is consumed (>99%), see Figure 7 (B). As with NO3•2−, NO2• also exhibits a tiny steady-state concentration, decaying through reaction with O2•− (72%), HO2• (8%), and with itself to yield N2O4 (20%). Reactions of NO2• with O2•− (15) and with HO2• (19) lead to the formation of peroxynitric acid species, which recycle nitrogen species ultimately contributing 80% of the cumulative yield of NO2−. NO2• + HO2•  HOONO2

k19 = 1.8

109 dm3 mol−1 s−1

(19)19

N2O4 is quantitatively converted into HNO2 through hydrolysis, which in turn deprotonates to yield NO2−, contributing the remaining 20%. Of the cumulative NO2− yield, 91% is consumed by OH•. It is evident that the bulk homogeneous chemistry of NO2− and its precursors is strongly influenced by dissolved O2 and a number of the products from water radiolysis (i.e. OH•, O2−, H2O2, and O−). The yield of the water radiolysis products are dependent upon the effects of scavenging on nonhomogeneous radiation track chemistry. Consequently, it is crucial that the initial radiolytic yields of these species are accurately determined. In summary, the measured radiolytic yields of NO2− are a result of the interplay between radiation track chemistry and the secondary homogeneous bulk chemistry of NO2− and its precursors.


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CONCLUSIONS The importance of radiation chemical track chemistry on bulk radiation chemistry has been shown by comparing the effects of stochastic escape yields with water radiolysis escape yields. The use of water radiolysis escape yields does not allow for changes in intra-track radiation chemistry, without the inclusion of which, the deterministic component of the multi-scale model is unable to predict experimental data. This is a consequence of the bulk homogeneous chemistry of NO2− and its precursors being strongly dependent upon the initial yields of the products of water radiolysis, which are in turn determined by the extent to which chemical scavengers drive non-homogeneous chemical evolution within the radiation track. The non-homogeneous fate of the electron (epre−/eaq−) is critical in determining the potential yield of NO2− and the initial yields of the oxidising products of water radiolysis, whereas the initial yields of the remaining sibling water radiolysis products are important in establishing the bulk homogeneous steady-state yield of NO2−. Predictions of the multi-scale model developed here using stochastic track chemistry calculations accurately predict the experimental data and the observed non-linear dose dependence in NO2− concentration. Complex radiation chemical systems require consideration for the chemistry occurring over a number of different time regimes to allow for correct chemical evolution of the irradiated system to be predicted. The presented multi-scale modelling approach has demonstrated that the evolution of radiation track chemistry has a significant influence upon the observed steady-state chemistry, and that understanding the radiation track chemistry of solutions containing chemical scavengers is crucial to being able to effectively model their radiation chemistry. AUTHOR INFORMATION Corresponding Authors: E-mail:

[email protected]. [email protected]

SUPPORTING INFORMATION AVAILABLE Title: Supporting Information for the Multi-Scale Modelling of the Gamma Radiolysis of Nitrate Solutions The supplementary information contains: (i) FACSIMILE bulk chemistry code chemical reaction sets used in the associated manuscript:



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Page 18 of 22

water radiolysis escape yields and direct effect nitrate and nitric acid yields; nitrate radiolysis reactions; water radiolysis reactions; water radiolysis equilibria; and acid-base equilibrium constants. Table S1. Water radiolysis escape yields and direct effect nitrate and nitric acid yields. Table S2. Nitrate radiolysis reaction set. Table S3. Water radiolysis reaction set. Table S4. Water radiolysis equilibria. Table S5. Acid-base equilibrium constants. •

•

(ii) Additional figures concerning the temporal evolution of key radiolytic species (OH , H ,

H2O2, H2, O2•−, HO2•, NO3•2−, and NO2•) within a spur from initial energy deposition (femtosecond timescale) to 10−6 s for pure water and aerated 1 and 100 mM NaNO3 solutions. Figure S1. Calculated radiation track yield of OH• as a function of time from the gamma radiolysis of pure water and aerated 1

10−3 and 0.1 mol dm−3 NaNO3.

Figure S2. Calculated radiation track yield of H• as a function of time from the gamma radiolysis of pure water and aerated 1


Figure S3. Calculated radiation track yield of H2O2 as a function of time from the gamma radiolysis of pure water and aerated 1


Figure S4. Calculated radiation track yield of H2 as a function of time from the gamma radiolysis of pure water and aerated 1


Figure S5. Calculated radiation track yield of O2•− as a function of time from the gamma radiolysis of pure water and aerated 1


Figure S6. Calculated radiation track yield of HO2• as a function of time from the gamma radiolysis of pure water and aerated 1


Figure S7. Calculated radiation track yield of NO3•2− as a function of time from the gamma radiolysis of pure water and aerated 1


Figure S8. Calculated radiation track yield of NO2• as a function of time from the gamma radiolysis of pure water and aerated 1



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ACKNOWLEDGEMENTS The authors thank Professor Jay A. LaVerne for informative discussions and for use of the University of Notre Dame Radiation Research Laboratory facilities. This research was funded by the Engineering and Physical Sciences Research Council (EPSRC), Sellafield Ltd, and the Dalton Cumbrian Facility project, a joint initiative of the Nuclear Decommissioning Authority (NDA) and The University of Manchester. G. P. Horne was supported by a PhD studentship from the EPSRC Nuclear FiRST Doctoral Training Centre at The University of Manchester. REFERENCES

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