Hatano Y., Katsumura Y., Mozumder A. (Eds.) Charged Particle and Photon Interactions with Matter - Recent Advances, Applications, and Interfaces

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410 Charged Particle and Photon Interactions with Matter

12PD, and −2.8 × 10

−3

eV/K in 13PD are determined. At lower temperature, Okazaki et al. reported

the values of −2.7 × 10

−3

and −3.0 × 10

−3

eV/K, for 12PD and 13PD, respectively (Okazaki et al.,

1984), but if we add their data to Figure 15.5, we note a good agreement with our results and deduce a

common temperature coefcient of −2.9 × 10

−3

eV/K in 12PD and −2.8 × 10

−3

eV/K in 13PD. Those

latter values are very close to each other, but are lower than the value in methanol (−3 × 10

−3

eV/K,

Herrmann

and Krebs, 1995) and in 1-propanol (−3.5 × 10

−3

eV/K) (Han et al., 2008).

The results show that even if the behavior of the solvated electron in these three polyols as a func-

tion of temperature is similar, a few differences exist. As the length of the aliphatic chain and the

number of hydroxyl groups are the same for both solvents, our observations emphasize the signicant

inuence of the distance between the two OH groups on the behavior of the trapped electron. At room

temperature, the energy of the absorption maximum is higher in 12PD than in 13PD and the absorption

band of the solvated electron is narrower in 12PD than in 13PD. These observations indicate that the

two neighboring OH groups create deeper electron traps and a narrower distribution of traps in 12PD

as compared to 13PD. These results are in agreement with those reported for 12ED at high temperature

and

for 12ED and 13PD glasses. However, the traps in 12PD appear less deep than in 12ED since the

energy of the absorption maximum of the solvated electron measured at a given temperature is lower

in 12PD than in 12ED. This shows an inuence of the additional methyl group on the solvent structure,

in particular on the created three-dimensional networks of hydrogen-bonded molecules. Moreover, an

increase in temperature affects electron trapping in 12PD more than in 13PD since the temperature

coefcient is more negative. The shape of the spectrum changes only in 12PD. Taking into account that

the decrease in viscosity versus temperature is also faster in 12PD, the different behavior of the two

solvents results from larger modications of the solvent structure and molecular interactions for 12PD.

15.4.2

•

oh radical

At room temperature the

•

OH radical has a broad absorption band with a maximum around 230nm

and a long-wavelength tail that extends beyond 320nm. The absorption band at deep UV (low intensity

of analyzing light) and the low absorption coefcient become an obstacle for precise measurements.

The use of a double monochromator is highly recommended due to the scattering of the longer wave-

length light. In their very rst paper on high-temperature pulse radiolysis, Christensen and Sehested

reported

•

OH spectrum changes from 20°C to 200°C (Christensen and Sehested, 1980). A decade later,

Buxton et al. reported the temperature-dependent absorption spectra of

•

OH and

•

OD and claimed no

signicant changes with temperature (Elliot and Buxton, 1992; Buxton et al., 1998). Recently, Janik

et al. reported their pulse radiolysis study of N

O-saturated water up to 350°C (Janik et al., 2007a,b).

The UV absorption spectra of

•

OH showed a decrease in the primary band at 230nm and growth of a

weak band at 310nm at elevated temperatures, with an isosbestic point near 305nm. They interpreted

the 230nm band as due to hydrogen-bonded

•

OH, and the 310nm band corresponding to “free”

•

OH.

A decrease in the absorption coefcient of

•

OH at elevated temperatures was also reported.

15.4.3 other tranSient SpecieS

Table 15.2 lists the spectral shifts of some of the intermediate radicals at room temperature and elevated

temperatures (in most cases, above t

), respectively. Generally, the anion or cation radicals show a red-

shift while the neutral radical of aromatic compounds show a blueshift, except that CO

•−

(Wu et al.,

2002b) and MV

•+

(Lin et al., 2004) exhibit no change with increasing temperature. This is probably

due to their fairly good symmetric molecular structure and the delocalization of the electric charge.

In general, the optical absorption spectral shift is in fact a problem of solute–solvent interaction. The

direction of shift should be largely related to the nature of the intermediate radical. The spectrum

shift reects a change in the energy difference between the ground state and the excited state with

the changes of solvent environment. These energies reect the differences in solvation where the

solvent responds to a solute by means of lowering the energy of the system. Recently, Wu et al. have

Radiation Chemistry of High Temperature and Supercritical Water and Alcohols 411

qualitatively interpreted the redshift of the benzophenone anion and the blueshift of the neutral

ketyl radical in terms of electrostatic forces and the hydrogen bonding of water (Wu et al., 2002a,b).

Boutin et al. have quantitatively explained the redshifts of Ag° and Ag

using QCMD simulations

(Boutin et al., 2005). Nevertheless, a more general and precise model remains to be developed, taking

into account the hydrogen bonding network, the dielectric constant, the electrostatic forces and polarity

of solute, the clustering effects of water molecules under supercritical conditions, etc.

15.5 radiolytiC yields oF water deComposition produCts

The estimation of G-values of water decomposition products can be done by pulse radiolysis techniques

or steady state radiolysis with product analysis methods. For pulse radiolysis, a direct measurement of the

transient species is desirable. This is difcult for nanosecond pulse radiolysis because of the rapidity of

spur reactions and the limitation of detection techniques (e.g., the absorption of the OH radical is in the

far UV region with a rather small absorption coefcient). One is forced to adopt the scavenging method,

that is, to use a chemical additive to react with the transient species that forms another easy-to-detect, rel-

atively stable product. In this section, we introduce the estimation of the G-values of water decomposition

products by pulse radiolysis, with the support of steady state γ-radiolysis of some aromatic compounds.

15.5.1 G(e

−

)

One suitable scavenging system involves the use of 0.5mM methyl viologen (MV

) in the presence

of tert-butanol as an OH radical scavenger, under neutral pH conditions (Lin et al., 2004). Another

involves the use of 0.5mM 4,4′-bipyridyl (4,4′-bpy) together with tert-butanol in alkaline solution

(pH > 11) (Lin et al., 2005). In both cases, ideally only e

−

reacts with MV

or 4,4′-bpy to form a

radical cation MV

•+

or radical anion 4,4′-bpy

•−

, with fairly strong absorption at 605 and ∼540nm,

respectively. The temperature-dependent G(e

−

) from 25°C to 500°C at a xed pressure of 25MPa

is shown in Figure 15.6a. G(e

−

) increases with temperature up to 300°C, which agrees well with

the previous reports. It decreases to a minimum near t

before jumping to a rather high value at

400°C, and then it decreases again with increasing temperature up to 500°C. An independent mea-

surement

of G(e

sol

−

) in methanol shows a similar trend (Figure 15.6b).

The big change in G(e

sol

−

) at constant pressure is due to density effects. As displayed in the 3D

plots of Figure 15.7, under supercritical conditions at a xed density, G(e

sol

−

) decreases with increas-

ing temperature while at a xed temperature, G(e

sol

−

) decreases with increasing water density. Around

, the density effect is the most signicant, but it becomes less important as temperature increases.

table 15.2

spectral

hifts

of v

arious

ntermediate

adicals

Chemical radical Form λ

max

at rt λ

max

in sCw

reference

Benzophenone

•

COH

545nm 525 nm (400°C) Wu et al. (2002a,b)

•

−

610nm 650 nm (300°C) Wu et al. (2002a,b)

Thiocynate (SCN)

•−

470nm 510 nm (400°C) Wu et al. (2001a,b)

Carbonate CO

•−

600nm 600 nm (400°C) Wu et al. (2002a,b)

Methyl viologen MV

•+

605nm 605 nm (400°C) Lin et al. (2004)

Silver Ag° 355nm 370 nm (200°C) Mostafavi et al. (2002)

310nm 380 nm (380°C) Mostafavi et al. (2002)

4,4′-bipyridyl

44BpyH

•

540nm 525 nm (400°C) Lin et al. (2005)

Formate CO

•−

235nm 275 nm (380°C) Lin et al. (2008)

max

is density dependent in SCW; here we choose a typical value.

412 Charged Particle and Photon Interactions with Matter

From the viewpoint of the W-value and the initial yield of the hydrated electron (recent values are

4.0–4.2 molecules/100eV (Bartels et al., 2000; Muroya et al., 2002), G(e

−

) in low-density SCW (e.g.,

at 400°C/25MPa, G(e

−

) is about 5.8 molecules/100eV) seems to be overestimated. This could be

due to the use of an extrapolated absorption coefcient for MV

•+

or incomplete scavenging of the H

atom by tert-butanol (Lin et al., 2004). However, an increase in G(e

−

) due to water structure changes

near t

, such as the formation of monomers, dimers, and small clusters should not be excluded.

In a recent report, Sims (2006) reanalyzed the data reported by W.G. Burns and W.R. Marsh

(Burns and Marsh, 1981) and gave a value of G(e

−

) for 400°C at a water density of 0.45 g/cm

as 0.8

molecules/100 eV. This is only about one third of the value reported by Lin et al. In their β/γ radioly-

sis of water combined with gas product analysis by mass spectrometry (Janik et al., 2007a,b), Janik

et al. reported that their measured G(e

−

) at 380°C and 400°C agreed with that of Lin et al. (2004),

G (e

–

)

0 100 200 300 400 500

T (°C)(a)

25 MPa

0 50 100 150 200

250 300

G (e

sol

–

)

T (°C)(b)

Figure 15.6 (a) G(e

−

) as a function of temperature at 25MPa. (b) G(e

sol

−

) of methanol as a function of

temperature

at 9.0

MPa.

360

380

400

25 MPa

420

440

460

480

500

0.6

0.5

0.4

0.3

0.2

0.1

T (°C)

ρ (g/cm

)

G (e

–

)

Figure 15.7 3D plots of G(e

−

)as a function of temperature and water density. The black curve shows the

values

at a xed pressure of 25

MPa.

Radiation Chemistry of High Temperature and Supercritical Water and Alcohols 413

but there was a big discrepancy in low-density water and the density effect on G(e

−

) was not very

signicant. Although they claimed that the ratio of G(

•

H)/G(e

−

) agreed with their previous work

(Cline et al., 2002), there was an apparent discrepancy with the kinetic measurements of density

effect on the yield (relative intensity of absorption signals at 1200nm by 4ns pulse radiolysis) of e

−

at 380°C in the same report. In fact, the trend of their “direct” measurements of the decay of e

−

in better agreement with Lin et al. (2004). A direct measurement with higher time resolution, that is,

picosecond or sub-picosecond pulse radiolysis, might eventually resolve the discrepancy.

15.5.2 {G(e

−

) + G(oh) + G(h)}

Two scavenging systems have been used to evaluate {G(e

−

) + G(H) + G(OH)} (denoted as G

sum

hereafter). One is 0.5mM MV

with 0.2M ethanol, another is 0.5mM 4,4′-bpy in the presence of

10mM HCOONa (Lin et al., 2004). The solutions are deaerated with Ar gas. Ethanol MV

and

HCOO

−

are used to convert

•

OH radical and

•

H atom to ethanol radical and COO

•−

, which will subse-

quently reduce MV

and 4,4′-bpy to form MV

•+

and 4,4′-bpyH, the same products produced by e

−

Therefore, the total yields of MV

•+

or 4,4′-bpyH should be equal to the total yield G

sum

. Figure 15.8a

0 100 200 300 400 500

{

–

G(H)+G(OH)}

T (°C)(a)

25 MPa

380

400

420

T (°C)

440

460

0.6(b)

ρ (g/cm

)

0.4

0.2

{

–

G (H)+G (OH)}

Figure 15.8 (a) {G(e

−

) + G(H) + G(OH)} as a function of temperature at 25MPa. (b) 3D plots of {G(e

−

) +

G(H)

+ G(OH)} as a function of temperature and water density.

414 Charged Particle and Photon Interactions with Matter

shows the temperature dependence of G

sum

at 25MPa from room temperature to 500°C and Figure

15.8b displays the 3D plots of G

sum

as a function of temperature and water density. Their trends are

very similar to that of G(e

−

). An estimation of the yield of COO

•−

up to 400°C by pulse radiolysis of

10mM sodium formate in N

O-saturated solution supported these results (Lin et al., 2008).

Figure 15.9 shows the experimental results of γ-radiolysis of benzophenone from room tem-

perature to 400°C, in deaerated solutions or N

O-saturated solutions (Miyazaki et al., 2006a).

Apparently, the tendency of temperature dependence and density effects (inset gure) on the yields

of benzophenone decomposition and product formation is similar to that of G(e

−

) and G

sum

. The

studies of other aromatic compounds such as phenol and benzene gave similar results. All these

strongly imply that the decomposition of the aromatic compounds is related to the yields of water

decomposition under irradiation. However, it should be pointed out that the reactions during steady

state radiolysis are much more complicated. Some reverse reactions even give back the reactant.

Thus the yields of solute decomposition are generally much lower than those of water decomposi-

tion

products (Miyazaki et al., 2006a,b).

15.5.3 G(oh)

The estimation of G(OH) has been carried out using an aerated solution of 100 mM NaHCO

or a deaerated solution of 100 mM NaHCO

in the presence of 1 mM NaNO

. In these systems,

hydrated electrons are scavenged by O

or NO

−

while the reaction between H atoms and HCO

−

rather slow. Consequently, the yield of CO

•

would correspond to G(OH). Figure 15.10 shows

G(OH) as a function of temperature. From room temperature to 380°C, the pressure is 25 MPa

0 100 200 300 400

G (molecules/100 eV)

t (°C)

0.1 0.2 0.3 0.4 0.5

G (molecules/100 eV)

ρ (g/cm

)

Figure 15.9 G-Values of benzophenone (BP) consumption and phenol formation at various temperatures

and pressures by γ-radiolysis of BP in aqueous solutions. (

◯

) Ar, 25MPa, BP consumption; (▲) Ar, 25 MPa,

phenol formation; (⚫) Ar, 35MPa, BP consumption; (⬜) 35MPa, phenol formation; (△) N

O, 25 MPa, BP

consumption; (

◇

) N

O, 25MPa, phenol formation; (◆) N

O, 35MPa, BP consumption; and (▼) N

O, 35MPa,

phenol formation. Inset: Density dependence at 400°C of total G-values of BP consumption and products

formation. (

◯

) Ar, BP consumption; (△) Ar, phenol formation; (⬜) Ar, 9-uorenone formation; (⚫) N

O, BP

consumption;

(

▲) N

O, phenol formation; and (■) N

O, 9-uorenone formation.

Radiation Chemistry of High Temperature and Supercritical Water and Alcohols 415

while at 400°C it is 35 MPa because the solubility of NaHCO

at 400°C/25 MPa is too small

to perform the measurements.

15.5.4 G(h)

G(H) has not been measured directly by pulse radiolysis, but it can be calculated by a subtraction

of G(e

−

) and G(OH) from G

sum

. The trend is that it slightly increases as temperature increases

up to 200°C and drops to a minimum around t

, and then increases sharply. At 400°C/25 MPa

(ρ = 0.167g/cm

), it reaches a value of 7.5 molecules/100eV. If this value is divided by G(e

−

then we have a ratio of G(H)/G(e

−

) ≈ 1.3. Considering that G(e

−

) might be overestimated, the

ratio G(H)/G(e

−

) could be higher than 1.3. As is known, at room temperature, G(H)/G(e

−

) is

about 0.16. This qualitatively agrees with the result reported by Cline et al., who derived the ratio

G(H)/G(e

−

) from the tting of the decay kinetics of hydrated electrons scavenged by SF

under

alkaline conditions (Cline et al., 2002). They found that at 380°C, the ratio is greater than unity and

becomes larger as density decreases. In low-density supercritical water, the initial yield of H atoms

seems to be roughly ve to six times the yield of hydrated electrons. Considering the uncertainty of

the

ttings, these two results seem to be consistent.

The

yield of molecular products, especially G(H

) and G(H

), is difcult to evaluate by pulse

radiolysis techniques. This must be claried by experiments, although H

might be thermally

unstable under supercritical conditions. At least one of these two molecular products should be mea-

sured by product analysis, the other component could be calculated by the material balance equation:

G G G G G G( ) ( ) ( ) ( ) ( ) ( )− = + + = +

−

H O e H 2 H OH 2 H O

2 aq 2 2 2

15.6 rate Constants

In this section, we do not attempt to describe in detail all the reactions that have been studied.

Instead we focus on the common features of the radiation induced reactions with the two most

important

species of water radiolysis—the hydrated electron and hydroxyl radical.

0 100 200

T (°C)

Elliot (1994)

G(OH)

300 400

Figure 15.10 G(OH) as a function of temperature at 25 MPa (35MPa at 400°C). The line is based on the

equation

given by Elliot (1994).

416 Charged Particle and Photon Interactions with Matter

15.6.1 reactionS with e

−

15.6.1.1 ionic reactants

The temperature-dependent reaction rates of e

−

with H

, NO

−

, and NO

−

have been reported (Cline

et al., 2002; Takahashi et al., 2002; Wu et al., 2002a,b). As mentioned above, the dielectric constant

of water is similar to nonpolar organic solvents, and the dissociation constants of inorganic salts are

extremely small around the supercritical point. It is thought that these properties affect those ionic

reactions that are coulombic-force-inuenced. As shown in Figure 15.11, for the e

−

reaction with

, the rate strongly increases between 250°C and 350°C (Cline et al., 2002; Wu et al., 2002a,b).

For NO

−

, the rate constant increases as the temperature increases, reaches a maximum around

125°C–200°C,

and then decreases (Takahashi et al., 2002).

The

rate constants for diffusion-controlled reactions can be described by the Debye–

Smoluchowski

equation as follows:

diff D

4 ,= πRDF

r R

exp 1

( / ) −

where

is the Debye factor

is the reaction distance

≡ e

/εk

T (e, electronic charge; ε, dielectric constant; k

, Boltzmann constant) represents the

critical distance at which the electron-positive-ion potential energy is numerically equal to k

Because the dielectric constant of water decreases as temperature increases, the coulomb poten-

tial between reactants will change signicantly. Thus the rate of the proton–electron reaction is

350

1.5 2 2.5

1000/T (K

–1

)

T (°C)

k (M

–1

/s)

3 3.5

200 100 25

Figure 15.11 Temperature-dependent rate constants for the reactions of e

−

with nitrate ion (

◇

, 25.7 MPa,

Takahashi

et al., 2002) and proton (

○

, 25.7MPa, Takahashi et al., 2002;

□

, 25MPa, Wu et al., 2002a,b).

Radiation Chemistry of High Temperature and Supercritical Water and Alcohols 417

accelerated further by attraction, while the nitrate–electron reaction is retarded due to repulsion

between

the two anions.

For a non-diffusion-controlled reaction, the Noyes equation is applied as follows:

1 1

k k

r R

obs diff act

exp

= +

( / )

where k

act

is the activated rate constant. There are two limiting cases, when k

act

» k

diff

, the reaction

will occur on every encounter, so that k

obs

≈ k

diff

; when k

act

« k

diff

, the reaction rate will be given by

obs

≈ k

act

15.6.1.2 hydrophobic

or n

eutral

pecies

Reaction rates of e

−

with O

, SF

, N

O, nitrobenzene, and 4,4′-Bpy have been investigated

(Cline et al., 2002; Marin et al., 2002; Takahashi et al., 2004; Lin et al., 2005). For temperatures

<300°C, the rate constants for scavenging by O

or SF

follow Arrhenius behavior but become

increasingly dependent on water density (pressure) at higher temperatures. At xed tempera-

tures of 360°C, 370°C, 380°C, and 400°C, the rate constants for these reactions reach a distinct

minimum near 0.45g/cm

(Figure 15.12). This behavior has been interpreted in terms of the

potential of mean force separating an ion (OH

−

or e

−

) from a hydrophobic species (H, O

, or

) in the compressible uid (Cline et al., 2002; Marin et al., 2002). As is well known, around

the supercritical point, the inhomogeneity of water density or the clustering effect of water mol-

ecules

becomes a very important feature, which would affect the distribution of the hydrophobic

reactant and hydrated electron. For example, the hydrophobic molecules such as O

would exist

in the lower density region with higher probability. This kind of inhomogeneous distribution will

hinder the encounter of hydrophobic molecules with hydrated electrons, thus the reaction rates

decrease dramatically.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

–

(×10

ρ (g/cm

)

0.4 0.45 0.5 0.55 0.6 0.65

Bpy+e

–

(×10

ρ (g/cm

)

Figure 15.12 Density effect on the rate constant of the reaction of e

−

with O

at (△) 360°C, (

◇

) 370°C,

(□) 380°C, and (

○

) 400°C (Cline et al., 2002). Inset: density effect on the rate constant of the reactions of e

−

with

4,4′-Bpy at 380°C (Lin et al., 2005).

418 Charged Particle and Photon Interactions with Matter

15.6.2 reactionS with

•

oh radical

The

•

OH radical is probably the most important oxidizing species related to the corrosion of struc-

tural materials in nuclear reactors. The studies of the reactions of

•

OH radical at elevated tem-

peratures or in supercritical water are thus essential. Most such studies have been carried out with

aromatic compounds, or simple molecules such as CO

2−

or HCO

−

, partly due to their excellent

thermal stability (Ferry and Fox, 1998, 1999; Feng et al., 2002; Marin et al., 2002; Wu et al.,

2002a,b; Ghandi and Percival, 2003). Figure 15.13 shows a typical example of the temperature-

dependent behavior for the reactions of

•

OH radical with aromatic compounds. The measured

bimolecular rate constant of

•

OH radical with nitrobenzene shows distinctly non-Arrhenius behav-

ior below 300°C and an increase in the subcritical and supercritical region. Feng et al. (2002)

succeeded in modeling these data with a three-step reaction mechanism originally proposed by

Ashton et al. (1995), while Ghandi and Percival (2003) claimed to have developed a so-called

multiple collisions model to predict the rates for the reactions of the

•

OH radical in subcritical and

supercritical water.

It is worth mentioning that the rate constant for the reaction of

•

OH radical with H

, which is one

of the most important reactions in water chemistry, has also been studied up to 350°C by competi-

tion kinetics using nitrobenzene as an

•

OH scavenger (Marin et al., 2003). At higher temperatures,

the value of the rate constant is lower than the extrapolation of the Arrhenius plot and actually

decreases in value above 275°C. At 350°C, the measured rate constant is more than a factor of 5 below

the Arrhenius extrapolation. This implies that the amount of hydrogen injection calculated by the

current

model of water radiolysis in a nuclear reactor might need reconsideration.

a recent study by Janik et al., the rate constant for the self-recombination of

•

OH in aqueous

solution giving H

was measured from 150°C to 350°C by direct measurement of the OH radi-

cal transient optical absorption at 250nm (Janik et al., 2007b). The values of the rate constant are

smaller than predicted previously in the 200°C–350°C range and show no apparent change in this

regime. In combining their measurements with previous results, the non-Arrhenius behavior can be

well described in terms of the Noyes equation k

obs

−1

= k

act

−1

+ k

diff

−1

, using the diffusion-limited rate

constant k

diff

estimated from the Smoluchowski equation and an activated barrier rate k

act

nearly

equal

to the gas-phase high-pressure limiting rate constant for this reaction.

9.5

10.5

1.5 2 2.5 3 3.5

Log (k)

1000/T (K

–1

)

Figure 15.13 The bimolecular rate constant of

•

OH with nitrobenzene shows non-Arrhenius behavior

below 300°C and an increase in the subcritical and supercritical region. (○) Ashton et al. (1995); (

□

) Feng et al.

(2002);

and (

△) Marin et al. (2002).

Radiation Chemistry of High Temperature and Supercritical Water and Alcohols 419

15.7 monte Carlo and moleCular dynamiCs simulations

15.7.1 Solvation dynaMicS of e

−

in Scw

Boero et al. performed a rst principles study of the hydrated electron in water at ordinary and

supercritical conditions (Boero et al., 2003). According to their study, for normal water, the hydro-

gen bond (H-bond) network needs about 1.6ps to accommodate the additional e

−

. Subsequently,

the

delocalized state becomes localized, the H bonds of the system rearrange, and water molecules

reorient in such a way that a cavity forms in the system. Six water molecules reorient in such a way

that all of them point at least one H toward the electronic cloud, thus forming a solvation shell and

the electron distribution is assumed to be ellipsoidal. Those cavities survive for a period ranging

from ∼50fs to a maximum of about 90fs. In contrast, under supercritical conditions the H-bond

network is not continuous and the electron localizes in preexisting cavities in a more isotropic way.

Four

water molecules form the solvation shell and the localization time shortens signicantly.

15.7.2 Spectral Shift of Solvated electron

Boutin et al. have performed quantum-classical molecular-dynamics (QCMD) simulations to study

the temperature and density dependence of the absorption spectra of the hydrated electron at ele-

vated temperatures and supercritical conditions (Nicolas et al., 2003; Boutin et al., 2005). Their

simulation quantitatively explains the experimental data to some extent. When extending these

simulations to very low densities corresponding to supercritical conditions, the results display a

progressive and continuous “desolvation” of the hydrated electron. It was also suggested that the

observed shift could be a density rather than a temperature effect. However, these expectations are

in marked contrast to experimental results that exhibit only weak density dependence in a wide

density interval of SCW, from ∼0.1 to 0.6g/cm

(Jortner and Gaathon, 1977; Bartels et al., 2005;

Jay-Gerin

et al., 2008).

15.7.3 teMporal behaviorS of the hydrated electron

The radiolytic yield is time dependent and at any given time G(e

−

) is the result of the competition

between diffusion into the bulk medium and intra-spur reactions. Both diffusion and reaction are

known to be temperature dependent, but which process dominates at high temperatures is unknown.

Since these processes occur at the beginning, a few tens of seconds after the formation of e

−

, such

a short temporal domain is not easily accessible experimentally. Thus computer simulations are

very

helpful.

Two

approaches have been reported. One is the deterministic diffusion-kinetic modeling

approach and the other is the stochastic Monte Carlo simulations approach. For the deterministic

approach, the spur diffusion model is based on the concept of an average spur with a deposited

energy of 62.5eV. This produces an initial yield of electrons and ionized and excited water mol-

ecules that undergo thermalization through random collisions. The Monte Carlo simulations are

more complex, and start from the “physical stage”—consisting of the period prior to 10

−14

s, during

which energy is deposited by the primary radiation particles and by all of the secondary (tertiary,

and so forth) electrons that result from the ionization of the water molecules. The subsequent non-

homogeneous chemical evolution of the reactive species formed in the spurs (or tracks) was simu-

lated by using the independent reaction times approximation. Both methods have been reported to

give satisfactory results when compared to existing experimental data for the radiolytic yields of

water decomposition products up to 300°C. However, there is some difference in the temperature-

dependent temporal behaviors of e

−

, especially in the rst few nanoseconds. There is also a con-

tradictory opinion about the temperature dependence on the thermalization distances of electrons.

By Monte Carlo simulations, du Penhoat et al. (2000) demonstrated that the best agreement with

experimental results occurs when the distances of electron thermalization decrease with increasing