Unit 4 Assessment Research

ARTICLE

“Acid spike” formation in the fast neutron radiolysis of supercritical water at 400 °C studied by Monte Carlo track chemistry simulations Md Mohsin Patwary, Sunuchakan Sanguanmith, Jintana Meesungnoen, and Jean-Paul Jay-Gerin

Abstract: A reliable understanding of radiolysis processes in supercritical water (SCW) cooled reactors is required to ensure optimal water chemistry control. In this perspective, Monte Carlo track chemistry simulations of the radiolysis of pure, deaerated SCW at 400 °C by 2 MeV mono-energetic neutrons were carried out as a function of water density between 0.15 and 0.6 g/cm3. The yields of hydronium ions (H3O+) formed at early time were obtained based on the G values calculated for the first three generated recoil protons. Combining our calculated G(H3O+) values with a cylindrical track model allowed us to estimate the concentrations of H3O+ and the corresponding pH values. An abrupt, transient, and highly acidic pH response (“acid spikes”) was observed at early times around the “native” fast neutron and recoil proton trajectories. This intra-track acidity was found to be strongest at times of less than a few tens to a hundred of picoseconds, depending on the value of the density considered (pH � 1). At longer times, the pH gradually increased for all densities, finally reaching a constant value corresponding to the non-radiolytic, pre-irradiation concentration of H3O+, due to the autoprotolysis of water. Interestingly, the lower the density of the water, the longer the time required to reach this constant value. Because many in-core processes in nuclear reactors critically depend on the pH, the present work raises the question whether such highly acidic pH fluctuations, though local and transitory, could promote or contribute to corrosion and degradation of materials under proposed SCW-cooled reactor operating conditions.

Key words: supercritical water (SCW), fast neutron and recoil protons, radiolysis, acid spike, Monte Carlo track chemistry simulations, generation IV SCW-cooled reactor.

Résumé : Il importe d’avoir une compréhension fiable des processus de radiolyse qui ont cours dans les réacteurs refroidis à l’eau supercritique afin d’assurer un contrôle optimal de la chimie de l’eau. Dans cette optique, nous avons effectué des simulations Monte Carlo de la trajectoire des particules pour décrire la radiolyse à 400 °C de l’eau supercritique pure, désaérée, par des neutrons monoénergétiques de 2 MeV en fonction de la densité de l’eau dont les valeurs sont comprises entre 0,15 et 0,6 g/cm3. Les rendements d’ions hydronium (H3O+) formés dans les premiers instants ont été obtenus à l’aide des valeurs G calculées pour les trois premiers protons de recul générés. En intégrant nos valeurs calculées de G(H3O+) à un modèle de trajectoires cylin- driques, nous avons été en mesure d’estimer les concentrations de H3O+ et les valeurs de pH correspondantes. Nous avons observé une réponse caractérisée par une variation brève et abrupte du pH vers des valeurs très basses (« pics d’acidité ») aux premiers instants de la trajectoire des neutrons rapides/protons de recul. Cette acidité intratrajectorielle s’est révélée être la plus forte à des instants correspondant à moins de quelques dizaines à une centaine de picosecondes, selon la valeur de densité considérée (pH � 1). À des temps plus longs, le pH augmentait graduellement à toutes les valeurs de densité, pour finalement atteindre une valeur constante correspondant à la concentration de H3O+ non radiolytique prévalant avant l’irradiation, en raison de l’autoprotolyse de l’eau. Fait intéressant, plus la densité de l’eau est faible, plus le temps nécessaire pour atteindre cette valeur constante est long. Comme de nombreux processus au cœur des réacteurs nucléaires dépendent dans une large mesure du pH, les présents travaux soulèvent la question à savoir si de telles fluctuations de pH fortement acide, bien qu’elles soient localisées et transitoires, pourraient favoriser la corrosion et la dégradation des matériaux dans les conditions proposées de fonctionnement d’un réacteur refroidi à l’eau supercritique. [Traduit par la Rédaction]

Mots-clés : eau supercritique, radiolyse par neutrons rapides/protons de recul, pic d’acidité, simulations Monte Carlo de la trajectoire des particules, réacteur de 4e génération refroidi à l’eau supercritique.

Introduction Supercritical water (SCW) (i.e., water at temperatures and pres-

sures above its thermodynamic critical point in the P–V–T diagram; for light water, H2O: Tc = 373.95 °C, Pc = 22.06 MPa, and �c = 0.322 g/cm3) has been a subject of growing interest in recent decades. Besides its importance for fundamental scientific research, SCW has at- tracted attention for its important role in a variety of innovative technological and industrial applications.1−5 Most of this attention

is driven by the nature of SCW whose density can be varied contin- uously at constant temperature over a wide range from liquid-like to gas-like values with only small changes in applied pressure. This tunability of SCW densities with pressure provides access to a wide range of density-dependent water properties while avoiding the oth- erwise perturbing gas-to-liquid phase transition.

Among the most attractive applications in this area is the pro- posed next generation (Gen IV) SCW-cooled reactor (SCWR) con-

Received 27 November 2018. Accepted 10 January 2019.

Md M. Patwary, S. Sanguanmith, J. Meesungnoen, and J.-P. Jay-Gerin. Département de Médecine Nucléaire et de Radiobiologie, Faculté de Médecine et des Sciences de la Santé, Université de Sherbrooke, 3001, 12e Avenue Nord, Sherbrooke, QC J1H 5N4, Canada. Corresponding author: Jean-Paul Jay-Gerin (email: [email protected]). Copyright remains with the author(s) or their institution(s). Permission for reuse (free in most cases) can be obtained from RightsLink.

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Can. J. Chem. 97: 366–372 (2019) dx.doi.org/10.1139/cjc-2018-0505 Published at www.nrcresearchpress.com/cjc on 23 January 2019.

cept to meet future global demand for electricity, hydrogen, and other products.6−8 The future Gen IV SCWR is a promising ad- vanced nuclear reactor system5,9 with �45% increased efficiency compared with �28%–32% for current conventional pressurized water reactors. The homogeneous supercritical phase also allows for more simple plant design and operation.

Before such technologies as the SCWR can be fully utilized, however, a thorough understanding of the SCW chemistry is re- quired. In particular, one of the most significant challenges for water chemistry in SCWR designs is to predict and, if possible, mitigate the effects of water radiolysis on material performance and corrosion, as the reactors under consideration operate at core inlet and outlet temperatures of �350 and 625 °C, respectively, at a pressure of 25 MPa.5 Under such “extreme” irradiation condi- tions of high temperatures and pressures, the effect of an intense, mixed fast neutron and �-radiation field passing through the re- actor core results in the radiolytic formation of oxidizing species at high concentrations such as •OH, H2O2, O2 (produced by decom- position of H2O2), and O2•− (or HO2•, depending on the pH).10,11

These species are highly reactive and can significantly increase the corrosion and degradation of structural materials both in the core and in the associated piping components of the reactor. Proper control of water chemistry, e.g., adding a small concentration of excess H2 to the reactor coolant, as with current pressurized high temperature water reactors, may be the key to maintaining the integrity of the reactors, although it is still unclear whether this strategy to suppress water radiolysis would also be effective under SCWR conditions.5,11,12

Direct measurements at very high temperatures and pressures, especially beyond the critical point of water, are difficult to per- form. Moreover, as Gen IV SCWRs are currently at the conceptual design stage, studies on water radiolysis in a SCWR have been laboratory based rather than reactor based. Consequently, exper- imental data on radiation chemistry and reaction kinetics of tran- sients under the proposed SCWR operating conditions are very limited and significant gaps still exist.5,13,14 Under these condi- tions, theoretical modeling and computer simulations are an important route of investigation for predicting the detailed radi- ation chemistry in a SCWR and the consequences for materials. Although a large body of data relevant to the radiolysis of water by �-rays or high-energy (�1 MeV) electrons is readily available in the literature, the fast neutron induced water chemistry remains largely unknown for the proposed SCWR operating conditions.

Recently, Monte Carlo track chemistry simulations were used to calculate the yields (or G values) of hydronium ions (H3O+) at ambient and elevated temperatures, which formed in spurs or tracks of the low or high linear energy transfer (LET) radiolysis of pure, deaerated water during and shortly after irradiation.15−17

Using simple, LET-dependent, spatiotemporal models of a spur or track, we found that the in situ, highly nonhomogeneous radio- lytic formation of H3O+ temporarily renders the “native” spur or track regions more acidic than the surrounding medium. At 25 °C, an abrupt transient acidic pH effect (which we termed an “acid spike”) was observed to be greatest for times shorter than �1 ns in an isolated “spherical” spur (characteristic of low-LET radiation, such as 60Co � and fast electron irradiation, LET � 0.3 keV/�m). In this time range, the pH remained almost constant at �3.3. For an axially homogeneous “cylindrical” track (characteristic of high- LET radiation), the acid-spike response to ionizing radiation was much more intense than that for the spherical spur geometry. For example, for a 2.4 MeV incident helium ion (LET � 150 keV/�m), the pH was found to be about 0.5 on a time scale of �100 ps. At longer times, the pH gradually increased for both low- and high- LET radiation types, ultimately reaching a constant value of seven (neutral pH at 25 °C) at �1 �s for the spur model and �0.1 ms for the track model.15

Interestingly, this early generation of a transient acid pH re- sponse around charged particle tracks was first highlighted in the

late 1940s.18,19 Although several authors have shown evidence for this intra-track acidity experimentally,20 these acid-spike effects have been largely ignored in water or in aqueous environments so far.21 From a chemical point of view, this may be somewhat sur- prising in view of the potential implications of a local, albeit temporary increase in acidity on damage induction and corrosion in water-cooled reactors.

In this work, we extend our previous calculations to determine the yields of H3O+ resulting from the radiolysis of pure, deaerated SCW (H2O) by mono-energetic 2 MeV incident neutrons at 400 °C as a function of water density (pressure) over the range of 0.15–0.6 g/cm3 (�24–56 MPa). Our goal is to investigate whether these early acid-spike effects persist under SCW irradiation con- ditions and then to determine their magnitude and time depen- dence. The 2 MeV energy of neutrons was considered to be representative of the average initial energy of a fast neutron flux in a reactor.22 The chosen density range mimics the coolant con- ditions in the heat transport system of the SCWR. SCW acts like a “dense fluid” whose density can vary continuously with tempera- ture and (or) pressure from �0.1 to 0.2 g/cm3 (low-density or “gas- like” regime at the reactor core outlet temperature) to higher values (�0.6–0.7 g/cm3) similar to those of liquid water below the critical point (high-density or “liquid-like” regime near the reac- tor core inlet).5

Fast neutron interaction with water “Fast” neutrons (i.e., those with kinetic energies ranging from

�0.5 to 10 MeV), which concern us in this work, deposit their energy in the water through ion recoils; in H2O, proton recoils absorb �88% of the neutron energy and the remainder is absorbed by oxygen ions.23 In this work, only the proton recoil component will be considered, as oxygen ion recoils are of minor importance for the fast neutron radiolysis of water due to their low average energies.24,25 Moreover, these proton recoils have maximum ranges (i.e., penetration depths) that are much smaller than the average distance between two successive neutron interactions. For exam- ple, the mean free path of a 2 MeV incident neutron in water at 25 °C is about 4 cm, whereas the maximum range of the proton recoil at this energy is �75 �m.24,26 Therefore, they can be con- sidered as behaving independently of each other, and under nor- mal irradiation conditions, their energy is deposited locally in isolated, dense tracks in the water, near the incident neutron collision sites (i.e., the generation points of the recoils).

For the estimation of the radiation chemical yields due to 2 MeV neutrons, only the contributions of the first three recoil protons was considered in the present calculations, because further recoil protons generated by the neutron as it is further moderated do not contribute significantly to radiolysis due to their low average energies.25,27,28 The initial proton energies (Epi, i = 1–3) are 1.264, 0.465, and 0.171 MeV.25 The fast neutron yields were then calcu- lated by summing the G values associated with each recoil proton considered (as determined by our Monte Carlo simulations; see below), weighted by its fraction of total neutron energy deposited:22,24,25

(1) G(X) � � i�1

3

G(X)piEpi

ET

where G�X�pi is the yield of species X associated with the recoil proton pi and

(2) ET � � i�1

3

Epi

is the sum of all recoil proton energies.

Patwary et al. 367

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Monte Carlo track chemistry simulations The entire sequence of events generated in the radiolysis of

SCW at 400 °C by incident protons of various initial energies was modeled using an extended version24,25,29 of our Monte Carlo track chemistry simulation code called IONLYS-IRT.30 In short, the IONLYS step-by-step program is used to cover all the events of the early physical and physicochemical stages of radiation action up to �1 ps in the track development in a three-dimensional geomet- rical environment. The complex, highly nonhomogeneous spatial distribution of the reactants formed at the end of the physico- chemical stage [eaq

� (hydrated electron), H+ (or H3O+), OH−, H•, H2, •OH, H2O2, O2•− (or HO2•), •O•, O•−, etc.]20,30,31 is then used directly as the starting point for the subsequent nonhomogeneous chem- ical stage. This third stage, in which the various radiolytic species diffuse randomly (at rates determined by their diffusion coeffi- cients) and react with each other (or competitively with any dis- solved solutes present in sufficient concentrations) until all spur or track processes are complete, is covered by our independent reac- tion times (IRT) program.32 This program uses the IRT method,32,33

a computationally efficient stochastic simulation technique that is used to simulate reaction times without having to follow the trajectories of the diffusing species. Its implementation has been reported previously32 and its ability to provide accurate time- dependent chemical yields under different irradiation conditions has been well validated by comparison with complete random flights Monte Carlo simulations, which follow the reactant trajec- tories in detail.34 In addition, this IRT program can be used to efficiently describe the reactions that occur in the bulk solution during the homogeneous chemical stage, i.e., in the time domain typically beyond some microseconds after the first ionization event.35

The current version of IONLYS-IRT has made various updates and modifications in the description of certain key parameters involved in the physicochemical and chemical stages of radiolysis. These changes are summarized as follows:

(i) We assumed that at 400 °C the thermalization distance (rth) of “subexcitation-energy electrons” (esub

� ) (those with ki- netic energies lower than �7.3 eV, the first-electronic ex- citation threshold in liquid water) is only affected by changes in the water density (�) and we scaled it according to a (1/�)1/3 law,36 namely

(3) rth(400 °C, �) � rth(400 °C, 0.6 g/cm 3)�0.6 g/cm3

� �1/3

with rth (400 °C, 0.6 g/cm3) ≈ 3.2 nm.37 This means that decreasing density further separates the water molecules but does not change their ability to interact with the energetic esub

� , resulting in an increase of rth. The density dependence of rth used in this work is shown in Fig. 1.

(ii) We included in the simulations a prompt geminate electron– cation (H2O•+) recombination (i.e., prior to thermalization of the esub

� ) that decreased in irradiated SCW at 400 °C as the water density decreased from �0.6 to 0.15 g/cm3.38

(iii) We used the rate constants recently predicted by Liu et al.,39,40 based on their so-called cage effect model that accounts for the non-Arrhenius temperature dependence of many reac- tions in water, for a number of reactions involved in the radiolysis of SCW at 400 °C. Given the lack of experimental data, this new database is important in providing us with recommendations for the best rate constant values to use at this time in modeling the radiolysis of SCW near and above the critical point. In some cases, we also used the chemical kinetic data compiled by Elliot and Bartels,22 sim- ply extrapolated above their experimentally measured temperature ranges (mostly 20–350 °C), as well as the re-

cent pulse radiolysis measurements by Muroya et al.41 for the rate constant of the radiation-induced reaction:

(4) H • � H2O ¡ H2 � •OH

that is a key reaction in high-temperature water radiolysis. In the absence of any other information, we chose to neglect any dependence of the reaction rate constants on water density for the 400 °C isotherm of interest. In the 0.15–0.6 g/cm3 range studied here, this approximation does not appear to have a large impact, considering the relatively slowly varying k values for the few reactions whose rates have been measured as a function of SCW density.42−44

(iv) We have taken into account that due to their limited ranges, all the recoil protons are completely stopped in the water. The chemistry measured under these conditions is an average over the proton energies from the initial proton energy to zero. To avoid complexity arising from the result- ing variations in the energy of the moving protons, simula- tions were performed with the simplifying approximation that the energies of the three considered recoil protons remained constant when passing through the water me- dium. These constant track average energy values Ēpi (i = 1–3) were obtained according to a procedure described previ- ously by Islam et al.17 using the SRIM software45 and our own Monte Carlo track structure simulations. They were found to be �0.6, 0.3, and 0.17 MeV, respectively. Interest- ingly, these values varied only slightly (at most �5%) as a function of water density over the studied range of 0.15– 0.6 g/cm3 and were therefore kept constant in all our chem- ical yield calculations.

The density dependences of the viscosity, static dielectric con- stant, and molar concentration of SCW at 400 °C used in this work were taken from the NIST Chemistry WebBook.46 The values for the ionic product of water (Kw) were obtained from Bandura and Lvov.47 From a microscopic perspective, we ignored the heteroge- neous character of the molecular structure of SCW,48 which is due to the presence of density fluctuations (or water “clustering”) as- sociated with criticality. In this study, we assumed that the overall

Fig. 1. Variation of the thermalization distance rth (in Å) of subexcitation electrons in pure, deaerated SCW at 400 °C as a function of water density in the range of �0.1–0.7 g/cm3 used in this work.

0.1 0.2 0.3 0.4 0.5 0.6 30

32

34

36

38

40

42

44)Å( ecnatsid

noitazila mreht

nortcel E

Water density (g/cm3)

SCW, 400 oC

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instantaneous picture of SCW at 400 °C could simply be viewed as a continuum medium with a mean density equal to the density of bulk water (�).

All our calculations were performed by simulating short (typi- cally, �15–150 �m) proton track segments, over which the energy and LET of the recoil protons are well defined and remain nearly constant. Such model calculations thus gave “track segment” yields for a well-defined LET as a function of time. For the three recoil protons under consideration, whose track average energies are �0.6, 0.3, and 0.17 MeV, respectively, the corresponding mean LET values increase from �5.5, 8.2, and 10.4 keV/�m to �22, 33, and 42 keV/�m, respectively, when the SCW density is increased from 0.15 to 0.6 g/cm3. With this LET range, the proton’s track can be modeled as a cylinder, characteristic of high-LET radiation15,17 (see below). The number of individual proton “histories” (usually �10–150, depending on the proton energy) was chosen to ensure only small statistical fluctuations in the computed averages of chemical yields, while meeting acceptable computer time limits.

Throughout this paper, G values are quoted in units of molecules formed or consumed per 100 eV of radiation energy absorbed. For conversion into SI units, 1 molecule/100 eV ≈ 0.10364 �mol/J.

Results and discussion Figure 2 shows the variations of G(H3O+) and G(OH−) calculated

from our simulations of the radiolysis of pure, deaerated SCW (H2O) at 400 °C by 2 MeV incident neutrons as a function of time from �1 ps to 10 �s, for different water densities in the range of 0.15–0.6 g/cm3. Obviously, the hydroxide ion OH−, which is formed largely by the reaction:

(5) eaq � � •OH ¡ OH�

during the track stage of the radiolysis, contributes to an alkaline track and consequently counteracts the acid-spike effect discussed in this work. However, as can be seen from Fig. 2, G(OH−) remains

much smaller than G(H3O+) over the time range of interest, inde- pendent of the considered density. As a result, its effect modifies the quantitative features of the pH only slightly and can be ig- nored to a good approximation. To our knowledge, there are no experimental data in the literature at 400 °C with which to com- pare these temporal variations of G(H3O+) or G(OH−) shown in Fig. 2.

The in situ formation of H3O+ by the generated recoil protons renders the “native” track regions acidic. A qualitative physical image, based on the spatial distribution of the various initial prod- ucts formed across an ionizing track,17−19 can be offered to explain the origin of this local and transitory acidity. Interestingly, there is indeed a charge separation that develops quickly between the more concentrated positive-ion (mainly H3O+ and •OH) core of the track and the negative ions (mainly OH− and H•) in the surround- ing medium, which are somewhat removed from the track. This charge separation is due to the faster motion and long penetration (or thermalization) range of the ejected secondary electrons,37

which, once hydrated, are captured by the slowly moving •OH and H3O+ to form OH− and H•. As a result, it is easy to see that this charge separation, and its associated local acidity will last until the diffusion of •OH and H3O+ has brought these species to the remote positions then occupied by the eaq

� . As discussed previously,15 the observed decrease of G(H3O+) is

predominantly due to H3O+ reacting with eaq � and with OH−, ac-

cording to

(6) H3O � � eaq

� ¡ H • � H2O

and

(7) H3O � � OH� ¡ 2H2O

Other reactions such as H3O+ + O•− ¡ •OH + H2O and H3O+ + HO2− ¡ H2O2 + H2O also contribute to the decay of G(H3O+) but only very weakly. This can be seen clearly in Figs. 3a and 3b, in which we show the time dependence of the cumulative yield variations �G(H3O+) for each of the reactions that contribute to the decay of G(H3O+), calculated from our Monte Carlo simulations at 400 °C, for � = 0.15 and 0.6 g/cm3, respectively, in the interval �1 ps–10 �s.

The effect of density (pressure) on the yield of H3O+ shown in Fig. 2 can be understood as follows. As we lower the density in SCW, there are fewer water molecules to present a “barrier” or, in other words, a solvent cage effect.49 This results in the in- creased cage escape of the various species originating from water dissociation, including H3O+, as the proximity condition that would allow them to combine or recombine is not favored. In con- trast, these density effects work in the opposite direction in the high-density liquid-like region, where a large barrier of solvent is present. In this case, the caged radiolytic products are forced to remain as colliding neighbors within the proton track where they are formed, thus increasing the likelihood of combination– recombination reactions38 and hence leading to a fast decrease of G(H3O+). This is in agreement with what we see in Fig. 2 (see also Fig. 3).

To calculate the pH values prevailing in the fast neutron and recoil proton track regions, we estimated the radiolytically gener- ated concentrations of H3O+ in these regions as a function of time using a cylindrical track model, characteristic of high-LET radia- tion.15 For each of the three considered recoil protons, we assumed the proton’s track as an axially homogeneous cylinder, with a length L = 1 �m and initial radius rc equal to the radius of the physical track “core” (corresponding to the tiny radial region within the first few nanometers around the impacting proton path, at �10−13 s).15,17,50,51 In this case, for the generated recoil

Fig. 2. Temporal evolution of the yields (in molecule per 100 eV) of radiolytically produced H3O+ (solid lines) and OH− (dashed lines) ions obtained from our Monte Carlo simulations of the radiolysis of pure, deaerated SCW by 2 MeV incident neutrons in the interval of �1 ps to 10 �s, for six different water densities: 0.15 (black), 0.2 (orange), 0.3 (olive), 0.4 (blue), 0.5 (green), and 0.6 (red) g/cm3 at 400 °C. Calculations are based on the radiation effects in 0.6, 0.3, and 0.17 MeV recoil proton tracks (see text).

10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 0

1

2

3

4

5

6

7 G(H3O

+) SCW, 400 oC

Y ie

ld (m

ol ec

ul e/

10 0

eV )

Time (s)

G(OH-)

= 0.15 g/cm3

0.2

0.3 0.40.50.6 g/cm3

ρ

Patwary et al. 369

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proton pi (i = 1–3), the track concentration of radiolytically gener- ated H3O+ can be derived from15,30

(8) �H3O��pi,radiolytic(t) � G(H3O �)pi(t)�(LET)pi r(t)2 �

where

(9) r(t)2 � rc 2 � 4D(H3O

+)t

is the change with time of rc due to the two-dimensional diffusive expansion of the track. Here, t is time, D is the diffusion coeffi- cient for H3O+ in water, and rc was estimated directly from our simulations. We assumed rc = 2 nm for all recoil protons and all considered densities. For D(H3O+), which is essentially unknown

at 400 °C, we first extrapolated the data reported by Elliot and Bartels22 over the 20–350 °C temperature range and then assumed that its dependence on density equaled that of the self-diffusion coefficient of compressed SCW at 400 °C.52 The variation of D(H3O+) in SCW at 400 °C as a function of density used in this work is shown in Fig. 4.

Finally, the total concentration of H3O+ is the sum of [H3O+]radiolytic, which simply results from the average of �H3O

��pi,radiolytic for the three generated recoil protons, and the non-radiolytic, pre-irradiation concentration [H3O+]autoprotolysis that results from the autopro- tolysis of water:16,17,47

(10) �H3O��total(t) � �H3O��radiolytic(t) � �H3O��autoprotolysis

The pH in the corresponding track regions is then given by the negative logarithm (to the base 10) of [H3O+]total:

(11) pH(t) � �log �H3O��total(t)

The temporal evolution of the pH values calculated from eqs. 8–11 for 2-MeV irradiating neutrons in pure, deaerated SCW (H2O) at 400 °C is shown in Fig. 5 for different water densities ranging from 0.15 to 0.6 g/cm3. As shown, for all densities considered, there is an abrupt, temporary, and highly acidic pH effect at the beginning of the chemical stage. This “acid-spike” effect is stron- gest at times of less than a few tens to a hundred of picoseconds, depending on the value of the density considered. In this time range, the pH remains nearly constant, around unity. Over �100 ps, the pH gradually increases over time. Ultimately, it reaches a constant value (pH of the body of the solution) equal to –log([H3O+]autoprotolysis), which depends on the density.47 As can be seen from Fig. 5, the lower the density of the water, the longer the time required to reach this constant value, ranging from �0.1 �s at 0.6 g/cm3 (pH � 5.6) to more than 100 �s at 0.15 g/cm3 (pH � 8.6).

Most interestingly, regardless of the SCW density considered, we see from Fig. 5 that the early acid pH conditions surrounding the “native” fast neutron and recoil proton trajectories persist for a period of more than six orders of magnitude. Rather surpris- ingly, the generation of such an early acid response around charged particle tracks has largely gone unnoticed in water or in

Fig. 3. Time dependence of the extents �G(H3O+) (in molecule per 100 eV) of the different reactions that are involved in the decay of H3O+, obtained from our Monte Carlo simulations of the radiolysis of pure, deaerated SCW by 2 MeV incident neutrons in the interval of �1 ps to 10 �s, for � = 0.15 (panel a) and � = 0.6 (panel b) g/cm3 at 400 °C.

Fig. 4. Variation of the diffusion coefficient (in m2/s) for the hydronium ion, D(H3O+), in SCW at 400 °C as a function of water density in the range of �0.1–0.7 g/cm3 used in this work (see text).

0.1 0.2 0.3 0.4 0.5 0.6 0.7 10-8

10-7

10-6

Hfotneiciffeoc noisuffi

D 3O

+ (m

2 / s)

Water density (g/cm3)

SCW, 400 oC

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aqueous environments subject to high-LET radiation, either at ambient or at elevated temperatures. Because many in-core pro- cesses in nuclear reactors, and in particular in proposed SCWRs, critically depend on the pH, a key water chemistry parameter,5

the present work raises the question whether such abrupt, highly acidic pH variations, which extend spatially about tens of nano- meters, could promote or contribute to material corrosion and damage. Because corrosion is a surface phenomenon, this can easily be envisioned, for example, when fast neutron and recoil proton tracks are formed in the immediate vicinity of a metal– water interface. The presence of H3O+ in contact with structural materials may readily induce spontaneous electrochemical reac- tions, which may release positive metal ions at the metal surface, thus creating a corrosive environment.5,53,54 The continuous re- lease of these ions from a certain location may actually cause a “stress corrosion cracking” (SCC) site after years.55 Perhaps more importantly, once the crack is developed, radiolysis in the crack and the resulting “acid spikes” could greatly speed up the SCC process.

In this regard, this work should stimulate novel predictive mod- eling of corrosion driven by these local, density-dependent acid- spike effects, which can then be tested with new measurements under SCWR conditions.

Summary and conclusion In this work, Monte Carlo track chemistry simulations were

used to calculate the yields of H3O+ formed early in the radiolysis of pure, deaerated SCW by 2 MeV incident neutrons at 400 °C for different water densities in the range of 0.15–0.6 g/cm3, chosen to mimic the coolant conditions in the heat transport system of proposed SCWRs. The fast neutron G(H3O+) values were obtained by assuming that the most significant contribution to radiolysis

comes from the first three recoil protons generated by the pas- sage of the irradiating neutron. The concentrations of H3O+ and the corresponding pH values for these three recoil protons were then obtained from our calculated G(H3O+) values using an ax- ially homogeneous cylindrical track model. An abrupt, tran- sient, highly acidic pH response was observed at early times around the “native” fast neutron and recoil proton trajectories. The magnitude and duration of this in situ “acid-spike” effect were found to be sensitive functions of the water density. At 400 °C and at times less than �10 ps, the pH for the highest (“liquid-like”) and lowest (“gas-like”) densities considered was around 0.8 and 1.3, re- spectively. At longer times, the pH gradually increased for all den- sities and finally reached a constant value corresponding to the non-radiolytic, pre-irradiation concentration of H3O+, due to the autoprotolysis of water at �0.1–100 �s following irradiation.

In conclusion, the question arises whether the strong intra-track acidity described here, although local and transitory, can trigger chemically aggressive conditions on metal surfaces, promoting the corrosion and degradation of materials in water-cooled nuclear re- actors, as well as in proposed SCWRs. As far as we know, the generation of such acidic pH spikes in water subject to the action of high-LET radiation, at both ambient and elevated temperatures including under SCW conditions, has never been mentioned before.

Acknowledgements Md M.P. is the recipient of a scholarship from the Faculty of

Medicine and Health Sciences of the Université de Sherbrooke. Thanks are due to Dr. David Guzonas and Dr. Craig R. Stuart (Canadian Nuclear Laboratories, Chalk River, Ontario) for stimu- lating correspondence and for their continued encouragement. J.-P.J.-G. is grateful to the Natural Sciences and Engineering Re- search Council of Canada (NSERC) for its financial support (Grant No. RGPIN-2015-06100).

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Fig. 5. Temporal evolution of the pH prevailing in the track regions of 2 MeV irradiating neutrons calculated for pure, deaerated SCW at 400 °C in the interval of �1 ps to 10 �s for the same six water densities as in Fig. 2 (see text). For the sake of comparison, the dashed lines show, for � = 0.15 (black) and 0.6 (red) g/cm3, the variation of pH with time in an isolated spherical “spur” (characteristic of low-LET radiation) (see Kanike et al.15,16) as calculated for irradiating 300 MeV protons (which mimic 60Co �/fast electron irradiation; LET � 0.3 keV/�m) using an initial spur radius (taken here as equal to rth; see Fig. 1) of 42.2 and 32 Å for the two water densities considered.

10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 0

1

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= 0.15 g/cm3 = 0.6 g/cm3p H

Time (s)

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