1

Supporting Information for Prediction of Rate

Constants of Important Chemical Reactions in

Water Radiation Chemistry in Sub- and

Supercritical Water – Non-Equilibrium

Reactions

Guangdong Liua, Cody Landryb, Khashayar Ghandia,b*

aDepartment of Physics, Mount Allison University, Sackville, NB E4L 1E2, CanadabDepartment of Chemistry and Biochemistry, Mount Allison University, Sackville, NB E4L 1E2, Canada

*Corresponding author: Khashayar Ghandi, kghandi@mta.ca, kghandi@triumf.ca

1. Methodology

For non-ionic interactions, we use Noyes equation to predict the rate constant:

1k pre

= 1kdiff

+ 1kreact

[S1]

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where kpre is the predicted rate constant, kreact is the chemical reaction rate constant,

and kdiff is the diffusion rate constant. In Noyes equation, kdiff represents how fast

reactants in a solvent can diffuse. kreact represents the rate at which a reaction can occur

if the reactants diffuse into the same solvent cage. When kreact is larger than kdiff, it means

the reactants are not diffusing fast enough to reach each other for the reaction to occur

at kreact rate constant. The reaction rate of this type of reaction is controlled by the

diffusion rate of the reactants, thus is called the diffusion-controlled reaction. On the

other hand, an activation-controlled reaction is a reaction that is bounded by the

chemical reaction rate (kdiff > kreact). In this case, although the reactants can diffuse fast

enough, the reaction cannot occur at the rate of diffusion due to a large energy barrier

(or low probability of a reactive collision). We used the Smoluchowski equation to

calculate the diffusion rate constant:

k diff=4000πC (D1+D2)Reff N A [S2]

where Reff is the reaction distance between reactants that can be approximated as the

sum of the hydrodynamic radii, C is a statistical factor that accounts for the case of

identical reactants and that of reacting doublets (for reactants with one unpaired

electron), and NA is Avogadro’s constant. D1 and D2 for most reactants are calculated

using Stokes-Einstein equation [S3]:

D=kbT

nπηRₒ [S3]

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where kb is the Boltzmann’s constant, T is temperature, η is solvent viscosity and Rₒ is

the hydrodynamic radius. The variable n is a constant that depends on the size and the

shape of the reactant. In our study, hydrodynamic radius, n and C are assumed to be

temperature independent.S1 If we combine all the temperature independent terms in a

single constant, [S2] becomes:

k diff=B (r ) x Tη [S4]

where B(r) is used as a fitting parameter.

kreact usually has an Arrhenius temperature dependence [S5]:

k react=Ae−E a

RT [S5]

Here A is the pre-exponential factor, Ea is the activation energy, and R is the gas

constant. The pre-exponential factor A is a constant that is proportional to the

concentration of the reactants and the rate collisions occur; it is also known as the

frequency factor. The activation energy Ea is the minimum kinetic energy that is required

for a collision to result in a reaction.

In this work, kreact is modified to account for the cage effect through the inclusion of an

additional factor: fR.S1,2 This modification is shown below [S6]:

k react= f R Ae−E aRT [S6]

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fR represents an efficiency factor of collisions per encounter, and has the form [S7]:

f R=pR k gas×( η

T)

kdiff+ pRk gas×( ηT

) [S7]

In [S7], pRkgas is the rate of potentially reactive collisions at room temperature and kdiff

is the rate of encounter from [S4].S2–4 The rate of potentially reactive collisions are

proportional to viscosity and inversely proportional to temperature.S2 At room

temperature, the rate of potentially reactive collisions pRkgas X ηT is a large number,

therefore fR is close to 1. As temperature increases, hydrogen bonds become weaker

and species can diffuse out of the water cage faster. As a result, the rate of potentially

reactive collision decreases, while rate of encounter increases. Thus, at high enough

temperature, fR is equal to the rate of potentially reactive collision divided by rate of

encounter, and become a number much smaller than 1.S1,2 At high enough temperature,

viscosity increases linearly with temperature in a given pressure, thus the value of fR

become approximately a constant. From a physical perspective, this is expected, since

there is at least one collision per encounter in SCW. The pre-exponential factor A,

activation energy Ea, pRkgas and B(r) are temperature independent fitting parameters in

this work.

For ionic reactions (such as R2 and R10 in this work), we have to account for the

effect of a dielectric constant. [S1] has to be modified to [S8]:

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1k pre

= 1FD×kdiff

+ 1kreact

er c

Reff [S8]

where kdiff is multiplied by the Debye factor. The Debye factor has the form [S9]:

FD=( r c

Reff) 1

e( rc

Reff)−1

,where rc=za zbe

2

4 π ε o ε kBT [S9]

where za and zb are the charges of the reactants, e is the charge on the electron, Reff is

the reaction distance, ε0 is permittivity of the free space, ε is the relative permittivity

(dielectric constant) of the medium.S5–7

We know that the diffusion rate of hydrated electrons has a larger temperature

dependence than other species.S8,9 In our work on equilibrium reactions, we have shown

that Stoke-Einstein model underestimate diffusion rate constants above the critical

point.S1 Thus, we used a modified diffusion coefficient from the work of Kallikragas et

al.S10(since it predicts the diffusion coefficients better at high temperaturesS1), which is

based on diffusion coefficient of water from molecular dynamic simulation, to model the

reactions that are diffusion-controlled above the critical point.S1 In this work, however, all

the reactions studied are activation-controlled above the critical point except R3. The

method to model R3 will be described in the main article. An adjustment of diffusion rate

constants based on Stokes-Einstein vs Kallikragas model will not make a difference in

the predicted rate constant of the reactions that are activation-controlled.S1 Therefore, in

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this work, we used the Stokes-Einstein-Smoluchowski equation to model the diffusion

rate constant for all reactions except R3.

Table S1 shows almost all reactions involved in the radiolysis of water. Table S2

shows all the fitting parameters used in this paper.

2. Discussion of Individual Reactions

2.1 Addition / Non-dissociative attachment

R9:

eaq−¿+O2→O2

−¿¿ ¿

The experimental information for the reaction between a hydrated electron and oxygen

is taken from Stuart et al.S11 and Cline et al.S12 Cline et al.S12 studied this reaction at a

pressure of 250 bar up to slightly above the critical temperature. This reaction was done

under alkaline conditions with a saturated SF6 scavenger. This to our knowledge is the

only reaction, other than muonium reactions,S2,3,13–15 that has been studied up to such a

high temperature. Stuart et al. studied this reaction from 20 to 200°C with a pressure

less than 10.3 MPa and found an activation energy of 11.9 kJ mol-1.S11 The AECL report

found that an Arrhenius fit was appropriate for the data up to 350°C using an A = 2.52 x

1012 dm3 mol-1 s-1 and an Ea = 11.6 kJ mol-1. Our fitted activation energy was 8.8 kJ mol-1

for this reaction.

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While the temperature dependence of this reaction is consistent with that of a

diffusion-controlled reaction at room temperature, it does not appear to be diffusion-

controlled past 100 °C.S7 Our fit drew on more information from Cline et al. than the

AECL report and these points can be seen in Figure S1. Cline et al.S12 reported that this

reaction must be diffusion-controlled up to at least 100°C. R9 is certainly not diffusion-

controlled near the critical point. Both this reaction and R6 are diffusion-controlled at

room temperature, the diffusion rate constants for these two reactions are very similar.

Figure S1 The plot of experimental data from Stuart et al.S11 and Cline et al.S12, along

with our fit of kpre to the experimental data and its extrapolation to high temperatures for

R9: eaq- + O2 → O2

-. A pressure of 250 bar is used to fit in the figure.

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R11:

eaq−¿+HO 2→H O2

−¿¿ ¿

There is no existing data for the reaction between hydrated electron and hydroperoxyl

radical. R6: eaq- + ·OH → OH- and R9: eaq

- + O2 → O2- both involve hydrated electrons

reacting with another reactant and are both similar to this reaction. The rate constants

for R6 and R9 are very close; R6 is a little faster than R9 (at the maximum difference

above the critical point, R6 has a rate constant about twice that of R9). We chose to use

a pragmatic approach and assumed the rate constant of R11 is the average of R6 and

R9.

R13:

H·+O2→H O2

The reaction between a hydrogen atom and oxygen was studied by Janik et al.S16 and

Elliot et al.S17,18 Janik et al.S16 studied this reaction up to 350°C using pulse radiolysis in

near neutral pH water at 250 bar. They reported non-Arrhenius behavior for R13 below

the critical point and obtained values of 7.75 kJ mol-1 and 5.71 x 1011 dm3 mol-1 s-1 for Ea

and A respectively from their fit.S16 Elliot studied this reaction using an optical method,

and found an activation energy of 6.25 kJ mol-1.S18The data obtained by Janik et al.S16

agrees with data obtained by Elliot et al.S17,18 Our fitted activation energy for this reaction

was 10.9 kJ mol-1.

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The experimental study in the gas phase for this reaction shows there is no barrier to

the O-H bond formation when H· approaches at an angle of about 45-degrees with

respect to the O-O bond.S16 At room temperature, the rate constant shows that the

reaction rate is controlled by the diffusion rate of the two species.S16 At a higher

temperature, however, the reaction switches to an activation-controlled reaction.S16 This

reaction is a very good demonstration of the solvent effect of water. At room

temperature, the hydrogen bonds are stronger and as such the cage effect is greater,

consequently the probability of H· radical to find the right orientation to react with O2

before escaping the cage is high. Therefore, the reaction is diffusion-controlled. At a

higher temperature, the hydrogen bonds become weaker and the diffusion rate of

species between cages increases dramatically. As such, at high enough temperatures

when the encounter time decreases, H· is not able to find the right orientation to react

with O2 before leaving the water cage. Therefore, the reaction is not diffusion controlled

any more.S16 The data obtained by Janik et al. shows different Arrhenius parameters

before and after 100°C, which can be explained by the change from near diffusion to

activation control near 100°C as shown in Figure S2. This reaction is diffusion-

controlled at low temperatures. The diffusion rate constant is larger than that of R3. This

is likely due to the larger reaction radius of O2 than of the H· atom S18.

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Figure S2 The experimental data from Elliot,S17 Elliot et al.,S18 Janik et al.S16 and kpre

and its extrapolation to a high temperature for R13: H· + O2 → HO2. A pressure of 250

bar was used to produce the figure.

R14:

R14: H·+H O2→H 2O2

The reaction between a hydrogen atom and hydroperoxyl radical has been studied by

Lundstrom et al.S19 and Janik et al.S16 Lundstrom et al.S19 studied the overall reaction rate

constant of H· + HO2 to 150°C at 100 bar by measuring the amount of perhydroxyl

radical immediately after a one microsecond radiolysis pulse in pH ~1 solution. An

overall Ea of 17.5 kJ mol-1 for the reaction between H· + HO2 below 200°C was found.

This activation energy is similar to what we have found (12.7 kJ mol-1). Janik et al.S16

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studied this reaction up to 350°C at 250 bar in neutral pH. Our fit to this data, shown in

Figure S3, assumed a pressure of 250 bar. This reaction is diffusion-controlled at room

temperature; however, the kdiff is very small compared to other diffusion-controlled

reactions. This is likely because the diffusion rate or reaction radius is small for HO2

compared to those of the H· atom. The kdiff for R14a is similar.

Figure S3 The experimental data from Janik et al.,S16 Lundstrom et al.S19, along with

our fit of kpre to the experimental data for R14: H· + HO2 → H2O2. A pressure of 250 bar

was used to produce the figure.

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2.2 Hydrogen abstraction reactions

R10:

eaq−¿+O2

−¿ (+H 2O )→ H 2O2+2O H−¿¿¿ ¿

The reaction between a hydrated electron and superoxide was been studied by

Gruenbein et al.,S20 and a reaction rate of 1.3 x 1010 L mol-1 s-1 was been found at room

temperature. Since there is no additional information on the reaction, we performed

quantum calculations on this reaction to find the activation energy and pre-exponential

factor. The method and base set has been described for R15. The mechanism for this

reaction is similar to R2. It involves two hydrogen donor water molecules (3,4,5 and

6,7,8 in Figure S4) donating two hydrogen atoms (5 and 8 in Figure S4) to the center of

O2-, and followed by hydrogen transfer from the outside water molecules (12,13,14 and

9,10,11 in Figure S4) to the two hydroxide residues (3, 4 and 6,7 in Figure S4). From

the gas phase calculation, we obtained an activation energy of around 9 kJ/mol, and a

pre-exponential factor of around 3 x 1014 dm3 mol-1 s-1. For this reaction, we also

performed quantum calculation with MP2 level of theory S21 using the same basis set,

and found an activation energy of around 10 kJ/mol and a pre-exponential factor of

around 8 x 1014 dm3 mol-1 s-1. The more realistic value would potentially be somewhere

between the DFT and MP2 results. We fit the B(r) and pRkgas to the data point from

Gruenbein et al.S20 Our prediction for this reaction is shown in Figure S5. Since this

reaction involves species with the same charge, the Debye correction factor significantly

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influences the rate constant of this reaction, like R2. We expect this reaction to be

insignificant in the supercritical phase of water.

Figure S4 Reactant state (1), product state (2), and the calculated transition state (3)

of reaction R10: eaq- + O2

- (+H2O) → H2O2 + 2OH-. The calculation is done with the QST2

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method using the density function theory (DFT) with the B3LYP functional and a base

set of 6-311 ++ G(d,p). The mechanism of this reaction is described in the text.

Figure S5 Our fit of kpre along with the single data point for R10 that was been reported

by Gruenbein et al.S20 A pressure of 250 bar is used in the figure.

R16:

·OH+H2O2→HO2+H 2O

The reaction between a hydroxyl radical and hydrogen peroxide has been studied by

two groups.S6,22 Both studied this reaction by pulse radiolysis, and by measuring the

growth of O2- in N2O saturated solution containing hydrogen peroxide, as HO2 is formed

first and then decompose to O2- and H+. Christensen et al.S22 studied this reaction in the

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temperature range of 14 to 160°C at a pH of 7.8 with a pressure of 50 bar. They

reported an activation energy of 14 kJ mol-1,S22 while our value is 18.5 kJ mol-1. A rate

constant of 2.7 x 107 dm3 mol-1 s-1 at 20°C was reported by Christensen et al.S22 The study

of this reaction is limited by the stability of hydrogen peroxide at high temperatures. The

fit for this reaction is shown in . kpre is visually overlapping kreact, and kdiff is far above

these two curves and, therefore, not shown on the graph; this reaction is definitely an

activation-controlled reaction at all temperatures. The diffusion rate constant is not

shown on the graph.

Figure S6 The experimental data from Christensen et al.S22 and ElliotS6 along with kpre

for R16: ·OH + H2O2 → HO2 + H2O. A pressure of 250 bar is used to fit in the figure.

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R19:

R19: H O2+H O2→H 2O2+O2

The bimolecular decay rate constant of HO2 (R19) has been studied by Christensen

and SehestedS23 in acid solutions. They report an activation energy of 20.6 kJ mol-1 for

R19 at pH ≤2.S23 Our fit leads to a higher activation energy of 27.7 kJ mol-1. At a pH

above 2, Christensen proposes that the decay of HO2 is mainly caused by R20 (this

suggests R20 will be more important than R19 for SCWR studies).S23 In the experiment,

they used a pressure of 140 to 150 bar.S23 Our fit for R19 is shown in Figure S7.

Figure S7 The experimental data from Christensen and SehestedS23, along with kpre for

R19: HO2 + HO2 → H2O2 + O2 at a pressure of 250 bar. This reaction is activation-

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controlled through all temperatures in our fit, kpre is visually overlapping kreact, and kdiff is

far above these two curves and, therefore, is not shown on the graph.

R20, R21:

Christensen and Sehested,S23 suggested that the rate constant is of second-order for

reaction of HO2/O2- in buffer of different pH. The rate constants have been shown in

Figure S8. The rate constant displays Arrhenius behavior, with an activation energy of

7.6 kJ mol-1 below 100°C. Above 100°C, the rate constant increase dramatically,

indicating another reaction became dominant. Similar behavior has been seen in heavy

water.S7 Christensen and Sehested suggest that the reaction mainly goes through the

channel R20 at below 100°C.

R20: O2−¿+HO 2→HO 2

−¿+O 2¿ ¿

At a higher temperature of around 200 to 320°C, the rate constant increases

dramatically. Christensen and Sehested suggest the following reaction becomes

dominant.S23

R21: O2−¿+O2

−¿+¿¿ ¿

R21 is not a hydrogen abstraction reaction but since this reaction was used to explain

the unusual behavior of the measured second-order decay of HO2/O2-,S23 it is more

appropriate to introduce it with R20. The rate constant of R21 was found to be less than

0.3 L mol-1 s-1 at room temperature.S24 However, Christensen and SehestedS23 suggest

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that the rate constant of R21 increases significantly as temperature increases. The rate

constant of this reaction decreases linearly with the H+ concentration, and with different

buffer concentrations (10-3 − 10-1 mol dm-3 phosphate); at pH ~7, the same O2- decay rate

is observed, which indicates an acid-base equilibrium for this reaction.S23 Based on

these findings, Christensen and Sehested suggest three other possible reaction

channels to describe the mechanism of this reaction:

2O2−¿⇌O 4

2−¿ ¿¿

O42−¿+H +¿⇌HO 4

−¿¿¿ ¿

HO4−¿→HO2

−¿+O2 ¿¿

This proposed mechanism, however, does not consider the charge on the reactants.

Like R2, with the Debye factor correction, the rate constant of reactions with reactants of

the same charge should decrease dramatically as temperature increases. Because of

this, the proposed mechanism of R21 should not be responsible for the dramatic

increase in the rate constant. We suggest that the rate constant shown in Figure S8 is

entirely due to the reaction of R20. Reaction of R20 should have a high barrier (52 kJ

mol-1 from our fit). At a low-temperature range, the reaction should be controlled by

quantum tunneling. As such, we only fit the data of the high-temperature part to our

model, as shown in Figure S9.

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Figure S8 The rate constant of second-order decay of HO2/O2- in buffer of different pH

from Christensen and Sehested.S23

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Figure S9 The experimental data from Christensen and SehestedS23, along with kpre for

R20: O2- + HO2 (+H2O) → H2O2 + O2 + OH- at a pressure of 250 bar. Note that kreact and

kpre are visually represented by the same line.

2.3 Addition dissociation / Dissociative attachment

R8:

eaq−¿+H2O 2→·OH+OH−¿¿¿

As previously mentioned, all the reactants and products in the reaction between a

hydrated electron and hydrogen peroxide are of high importance in the control of

corrosion and solution pH. This reaction has been studied in two laboratories:

Christensen et al.S25, and Elliot et al.S11,26. This reaction is difficult to study because

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hydrogen peroxide is thermally decomposed at high temperatures. Christensen et al.S25

studied this reaction in a temperature range of 5 to 150°C by determining the decay of

hydrated electrons as measured at 650 nm with a pressure of 90 to 140 bar with an

unbuffered Ar-saturated alkaline solution with a pH of 9.5 to 10. They found an activation

energy of 15.6 kJ mol-1 from their fit. Elliot et al.S11,26 studied this reaction in a

temperature range of 20 to 125°C and found an activation energy of 16 kJ mol-1.

Although Elliot studied this reaction using heavy water, the activation energies found in

both studies are similar, and not very far from the activation energy that we found from

our fit, which is 20 kJ mol-1. Our fit for this reaction is shown in Figure S10. Our fitting

parameters (Ea = 20.2 kJ mol-1, A = 7.0 x 1013 dm3 mol-1 s-1) are different from the

parameters used in the AECL report (Ea = 15.7 kJ mol-1, A = 1.0 x 1013 dm3 mol-1 s-1)

which is consistent with the cage effect.

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Figure S10 The plot of experimental data from Elliot et al.S11,26 and Christensen et

al.S25, along with our fit of kpre to the experimental data and its extrapolation to high

temperatures for R8: eaq- + H2O2 → ·OH + OH- at a pressure of 250 bar.

R12:

H·+H 2O2→·OH +H 2O

Our model for the reaction between a hydrogen atom and hydrogen peroxide uses

data from three different laboratories: Lundstrom et al. (60 bar)S27, ElliotS17, and Mezyk

and Bartels.S28 Lundstrom et al.S27 and ElliotS17 used an optical detection pulse radiolysis

method that used Cl- as a scavenger and measured the growth of Cl2- optical absorption.

Mezyk and BartelsS28 used a pulse radiolysis method where they followed the electron

paramagnetic resonance (EPR) free induction decay signal of the hydrogen atom.

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Mezyk and BartelsS28 measured a rate constant at 22.7°C and pH of 2.0 of 3.48 x 107

dm3 mol-1s-1 and an activation energy of 21.1 kJ mol-1 over temperatures between 7.6 to

84.6°C. The AECL report used an Arrhenius fit to model the reaction up to 350°C with

an A = 1.79 x 1011 dm3 mol-1s-1 and an Ea = 21.1 kJ mol-1.S7 Lundstrom et al. studied this

reaction from 10 to 120°C, at a pH of 1. At 25°C the rate constant was found to be 5.1 x

107 dm3 mol-1s-1 and the activation energy was found to be 10.7 kJ mol-1.S27 Our

activation energy was closer to the value reported by Mezyk et al. and was 18.5 kJ mol-1

for this reaction.

Lundstrom et al.S27 made a correction for the O2 present in the sample. They report

that at high temperatures (above 90°C), H2O2 can decompose to form O2. This O2 can

then react with H· to form HO2 (R14). This reaction is 200 times faster than the reaction

between H· and H2O2,S7; therefore ignoring this effect can predict a higher reaction rate

than anticipated at high temperatures for R12. Elliot, who used a similar setup as

Lundstrom, did not account for this effect and therefore likely predicted a higher

activation energy.S27 Lundstrom also questioned the EPR signal in Mezyk’s study to be

an H· reacting with H2O2 only and suggested it should be corrected with the reaction

between H· and O2.S27 Only Lundstrom's study reached 120°C; the other two groups

studied up to 90°C. In our study, we decided to fit all data below 60°C and use data only

from Lundstrom above 60°C shown in Figure S11. This reaction is definitely an

activation-controlled reaction at all temperatures. The diffusion rate constant is not

shown on the graph.

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Figure S11 The experimental data from Elliot,S17 Lundstrom et al.,S27 and Mezyk and

BartelsS28, along with our fit of kpre to the experimental data for R12: H· + H2O2 → ·OH +

H2O. This reaction is activation-controlled through all temperatures in our fit; kpre is

visually overlapping on kreact, and kdiff is far above these two curves and therefore is not

shown on the graph. A pressure of 250 bar was used to produce the figure.

R14a:

R14a: H·+H O2→2 ·OH

H· + HO2 reactions at room temperature mostly yield the products shown in reaction

R14a (90%) as compared to R14.S16 Janik et al.16 found an Ea = 16.3 kJ mol-1 and A = 6.6

x 1012 dm3 mol-1 s-1 for this reaction. We obtained a higher A of 5.0 x 1013 dm3 mol-1 s-1 but

a similar Ea (18 kJ mol-1) from our fit. LundstromS19 suggests that reaction R14 (R14a) is

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mainly in competition with reaction R18: ·OH + HO2 → (H2O3) → O2 + H2O. To minimize

this competition, Lundstrom applied a high H2 pressure, using the reaction H2 + ·OH ⇌

H· + H2O (R32f) to scavenge ·OH radicals. Data and fit for R14a are shown in Figure

S12.

Figure S12 The experimental data from Janik et al.S16 and Lundstrom et al.S19, along

with our fit of kpre to the experimental data for R14a: H· + HO2 → 2 ·OH. A pressure of

250 bar was used to produce the figure.

R17:

·OH+O2−¿→¿ ¿

Two sources have measured the temperature dependence of the rate constants for

the dissociative addition reaction between hydroxyl radical and superoxide: Elliot and

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BuxtonS29 and Christensen et al.S30 The data from Elliot et al. is significantly different with

that of Christensen et al. because Elliot et al. assigned HO3- as an absorbing product.

For our work, however, we only use the experimental data of Buxton and Elliot (due to

the potential problems with the extinction coefficients used in Christensen’s workS4),

which is included in Figure S13. Buxton and Elliot determined the rate constants by

fitting the time dependence of the optical absorption at 240, 250 and 260 nm wavelength

in pH 7.9 O2-saturated water.S29 The AECL report suggested A of 8.77 x 1011 dm3 mol-1 s-1

and an Ea of 10.9 kJ mol-1.7 Our fit lead to A = 5.1 x 1012 dm3 mol-1 s-1 and Ea = 12.9 kJ

mol-1.

Figure S13 The plot of experimental data from Elliot and BuxtonS29 along with our fit of

kpre to the experimental data and its extrapolation to a high temperature for R17: ·OH +

O2- → (HO3

-) → O2 + OH- at a pressure of 250 bar.

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R18:

·OH+H O2→ (H2O3 )→O2+H2O

The temperature dependence of the reaction of a hydroxyl radical with the perhydroxyl

radical has been measured by two groups: Elliot et al.S29 and Lundstrom et al.S19 Elliot et

al. studied this reaction up to 200°C using pulse radiolysis of O2- saturated solution at a

pH of 2.S29 Lundstrom used pulsed radiolysis to study this reaction at a temperature

range of 20 to 296°C with a pressure of 60 bar and a pH of 2.S19

Elliot et al. showed that both R17 and R18 are diffusion-controlled at low temperatures

and become activation-controlled reactions at high temperatures.S29 This is similar to our

prediction for R17. Our predictions have shown R18 is activation-controlled over the

whole range, as shown in Figure S14. Our fitted Ea is 13.7 kJ mol-1 for this reaction. The

rate constants for R17 and R18 are very closed at below 300°C, where our fit shows that

R17 can be three times faster than R18 above the critical point. We also show our fitted

curve for R17 on Figure S14 for comparison.

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Figure S14 The experimental data from LundstromS19 and Elliot and BuxtonS29, along

with our fit of kpre to the experimental data and its extrapolation to a higher temperature

for R18: ·OH + HO2 → (H2O3) → O2 + H2O at a pressure of 250 bar. We also show fitted

R17 on this graph as a comparison.

2.4 Dissociation

R22, R22a:

R22: H 2O 2→12O2+H 2O

The thermal decomposition of hydrogen peroxide cannot be modeled with the cage

effect as it is catalyzed by contact with the side of the pipe where the reaction is taking

place. Information from various sources show that the reaction rate is dependent not

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only on temperature but also on tube diameter and the type of tubing used.S31,32 Crioset

et al.S32 who studied this reaction in the supercritical phase of water used two separate

Arrhenius equations to fit their data below 350°C and above 380°C. The two different

slopes on their Arrhenius fit can be explained due to the critical fluctuation.S13 Since this

reaction does not involve collisions of reactants in an encounter pair, we use a simple

Arrhenius fit with an Ea of 60 kJ mol-1 for this reaction as shown in Figure S15.

Figure S15 The experimental data from different sources: Lin et al.,S31 Crioset et al.,S32

for R22: H2O2 → 1/2 O2 + H2O. We used a simple Arrhenius fit for this reaction.

If the two slopes are indeed due to the critical fluctuation, the small rate constants of

this reaction suggest R22 is not significant in modeling chemistry for SCWRs. However,

if it is, as suggested by Crioset et al.S32, that the activation energy of this reaction

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changes from 49 kJ/mol to 180 kJ/mol from sub into supercritical water, then this

reaction may have a rate constant of around 3 x 103 s-1 at 650°C. This reaction mainly

occurs on the wall of the tubing and produces corrosive oxygen. This indicates the

reaction is very important for the corrosion control of the SCWR. More study of the

surface effect of this reaction and critical fluctuation is required.

R22a: H 2O2→2·OH

We draw our data for R22a from Lin’s work.S31 It seems the rate constants of this

reaction are similar to R22. We did not attempt a fit because the rate of reaction is so

low. We suggest the use of parameters from R22 for R22a and a simple Arrhenius fit.

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3. List of Tables:

Number

Reactions

R2 eaq- + eaq

- + (2 H2O) → H2 + 2 OH-

R3 H· + H· → H2

R4 ·OH + ·OH → H2O2

R5 eaq- + H· (+ H2O) → H2 + OH-

R6 eaq- + ·OH → OH-

R7 H· + ·OH → H2OR8 eaq

- + H2O2 → ·OH + OH-

R9 eaq- + O2 → O2

-

R10 eaq- + O2

- (+ H2O) → H2O2 + 2 OH-

R11 eaq- + HO2 → HO2

-

R12 H· + H2O2 → ·OH + H2OR13 H· + O2 → HO2

R14 H· + HO2 → H2O2

R14a H· + HO2 → 2 OHR15 H· + O2

- → HO2-

R16 ·OH + H2O2 → HO2 + H2OR17 ·OH + O2

- → (HO3-) → O2 + OH-

R18 ·OH + HO2 → (H2O3) → O2 + H2OR19 HO2 + HO2 → H2O2 + O2

R20 O2- + HO2 → HO2

- + O2

R21 O2- + O2

- + (H+) → HO2- + O2

R22 H2O2 → 1/2 O2 + H2OR22a H2O2 → 2·OHR23 H+ + OH- ⇌ H2OR24 H+ + HO2

- ⇌ H2O2

R25 H2O2 + OH- ⇌ HO2- + H2O

R26 H+ + O- ⇌ ·OHR27 ·OH + OH- ⇌ O- + H2OR28 H+ + O2

- ⇌ HO2

R29 HO2 + OH- ⇌ O2- + H2O

R30 H+ + eaq- ⇌ H·

R31 H· + OH- ⇌ eaq- + H2O

R32 H2 + ·OH ⇌ H· + H2O

Table S1 All the reactions studied in this series is presented.

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A Ea pRkgas B (r)Unit dm3 mol-1 s-1 kJ mol-1 dm3mol-1s-1 dm3Pa mol-1 K-1

R2 2.2(1.0) x1013 1 (1) 7.4(3.0) x1014 3.5 (0.4) x104

R3 N/A N/A N/A 1.5 (0.4) x104

R4 7.7(2.0) x1011 12 (1) 2.6(1.0) x1017 3.1 (1.6) x104

R5 2.7(4.0) x1013 5 (3) 8.0(5.0) x1017 7.5 (3.0) x104

R6 1.0(0.6) x1013 4 (4) 1.6(1.1) x1018 7.4 (1.5) x104

R7 4.0(1.0) x1013 11 (1) 1.0(0.3) x1018 3.6 (0.7) x105

R8 7.0(1.0) x1013 20 (1) 7.0(2.3) x1017 1.4 (0.8) x105

R9 8.5(4.0) x1013 8.8 (4.0) 2.2(1.2) x1017 6.0 (2.0) x104

R10 3.0(0.3) x1014 10 (3) 1.0(0.3) x1017 7.5 (1.5) x104

R12 8.0(1.5) x1010 18.5 (0.5) 9.5(3.0) x1017 2.5 (1.0) x105

R13 2.7(1.5) x1012 10.9 (1.0) 6.0(2.0) x1017 5.3 (3.0) x104

R14 1.0(0.3) x1013 12.7 (2.0) 2.9(1.0) x1017 5.2 (1.0) x104

R14a 5.0(1.5) x1013 18.0 (1.5) 1.6(1.0) x1018 5.3 (1.0) x104

R15 6.3(0.7) x1011 42 (16) 2.2(0.7) x1017 4.2 (1.3) x104

R16 4.5(1.5) x1010 18.5 (1.0) 3.0(1.0) x1017 5.2 (2.0) x104

R17 5.1(1.5) x1012 12.9 (1.0) 3.3(1.5) x1017 4.4 (1.0) x104

R18 2.5(0.7) x1012 13.7 (0.7) 3.3(0.5) x1017 6.3 (3.0) x104

R19 5.3(1.5) x1010 27.7 (1.0) 1.3(0.5) x1018 1.5 (1.0) x105

R20 9.0(2.5) x1014 52 (2) 9.0(4.0) x1017 5.7 (3.0) x104

R22 1.0 (0.5) x105 60 (2) N/A N/AR22a 1.0(0.5) x105 60 (2) N/A N/A

Table S2 Fitting parameters for equilibrium reactions are presented.

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400°C 450°C 500°C 550°C 600°CRate constant 250 bar (units L mol-1 s-1for 2rd order s-1 for 1st order)R2 2.4x104 7.0x102 3.0x102 2.6x102 3.1x102

R3 5.0x1011 7.9x1011 1.0x1012 1.3x1012 1.5x1012

R3* 2.9x1011 4.1x1011 5.3x1011 6.4x1011 7.6x1011

R4 1.4x109 1.4x109 1.5x109 1.7x109 1.9x109

R5 1.9x1011 1.8x1011 1.8x1011 1.9x1011 2.0x1011

R6 1.7x1011 1.6x1011 1.6x1011 1.7x1011 1.7x1011

R7 2.9x1010 2.8x1010 3.1x1010 3.5x1010 3.8x1010

R8 1.8x1010 1.9x1010 2.3x1010 2.8x1010 3.3x1010

R9 1.1x1011 1.1x1011 1.1x1011 1.2x1011 1.3x1011

R10 3.6x106 1.2x105 5.8x104 5.5x104 7.1x104

R11 1.4x1011 1.3x1011 1.4x1011 1.4x1011 1.5x1011

R12 2.1x107 2.2x107 2.7x107 3.2x107 3.7x107

R13 7.9x109 7.8x109 8.5x109 9.4x109 1.0x1010

R14 1.1x1010 1.1x1010 1.2x1010 1.4x1010 1.5x1010

R14a 9.8x1010 1.1x1011 1.2x1011 1.4x1011 1.6x1011

R15 3.5x106 5.0x106 7.7x106 1.1x107 1.6x107

R16 1.8x107 1.9x107 2.3x107 2.7x107 3.1x107

R17 7.1x109 7.1x109 8.0x109 9.0x109 1.0x1010

R18 2.1x109 2.2x109 2.5x109 2.8x109 3.1x109

R19 5.9x106 7.0x106 9.3x106 1.2x107 1.5x107

R20 2.4x109 3.9x109 6.7x109 1.1x1010 1.7x1010

R22 2.2x100 4.6x100 8.8x100 1.6x101 2.6x101

R22a 2.2x100 4.6x100 8.8x100 1.6x101 2.6x101

Table S3 Predicted rate constant for none-equilibrium reaction R2-R22a in the

temperature range 400-600 °C with a pressure of 250 bar.

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650 °C 700 °C 750 °C 800 °CRate constant 250 bar (units L mol-1 s-1for 2rd order s-1 for 1st order)R2 4.2x102 6.2x102 9.4x102 1.4x103

R3 1.7x1012 2.0x1012 2.2x1012 2.5x1012

R3* 8.8x1011 1.0x1012 1.1x1012 1.3x1012

R4 2.1x109 2.2x109 2.4x109 2.5x109

R5 2.0x1011 2.1x1011 2.1x1011 2.2x1011

R6 1.8x1011 1.8x1011 1.8x1011 1.8x1011

R7 4.1x1010 4.4x1010 4.6x1010 4.9x1010

R8 3.9x1010 4.4x1010 4.9x1010 5.5x1010

R9 1.4x1011 1.4x1011 1.5x1011 1.6x1011

R10 1.0x105 1.6x105 2.6x105 4.2x105

R11 1.6x1011 1.6x1011 1.7x1011 1.7x1011

R12 4.2x107 4.8x107 5.3x107 5.8x107

R13 1.1x1010 1.2x1010 1.3x1010 1.3x1010

R14 1.7x1010 1.8x1010 1.9x1010 2.0x1010

R14a 1.8x1011 2.0x1011 2.2x1011 2.4x1011

R15 2.2x107 2.9x107 3.7x107 4.6x107

R16 3.6x107 4.1x107 4.5x107 5.0x107

R17 1.1x1010 1.2x1010 1.3x1010 1.4x1010

R18 3.5x109 3.8x109 4.1x109 4.4x109

R19 1.9x107 2.2x107 2.6x107 3.0x107

R20 2.4x1010 3.4x1010 4.6x1010 6.1x1010

R22 4.0x101 6.0x101 8.6x101 1.2x102

R22a 4.0x101 6.0x101 8.6x101 1.2x102

Table S4 Predicted rate constant for none-equilibrium reaction R2−R22a in the

temperature range 650−800 °C with a pressure of 250 bar.

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