Article pubs.acs.org/JPCA

Source of Molecular Hydrogen in High-Temperature Water Radiolysis Marcin Sterniczuk and David M. Bartels* Notre Dame Radiation Laboratory & Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, United States ABSTRACT: Molecular hydrogen is a primary product of the interaction of low-LET (γ, β) radiation with water, and previous measurements have shown that its initial yield increases at elevated temperature. This has been the subject of controversy because more atomic H and (e−)aq free radicals escape recombination at elevated temperature, and the corresponding production of H2 should decrease. Room temperature experiments have demonstrated that a large fraction of H2 also comes from early physicochemical processes (presumably electron− hole charge recombination and/or dissociative electron attachment), which can be suppressed by scavenging presolvated electrons. In the present work we extend these scavenging measurements up to 350 °C to investigate why the H2 yield increases. We find that most of the H2 yield increase is due to the “presolvation” processes. Relatively small changes in the scavenging efficiency vs LET, and a significant effect of temperature depending on the (positive or negative) charge of the scavenger, indicate that the presolvation H2 is dominated by electron−hole charge recombination rather than dissociative electron attachment at all temperatures. •

I. INTRODUCTION The fundamental understanding of water radiolysis by ionizing radiation1−3 is very important for a number of practical applications. One of these is nuclear power generation, where knowledge of the yields of the radicals and molecules (given as a G value, or number of species formed per unit of radiation energy2) is extremely important for cooling loop simulations and chemical models used for the prediction of corrosion.4−11 In pure water radiolysis, essentially three radical species ((e−)aq, • H, •OH) and two molecular products (H2, H2O2) are created:1−3 (1)

Initial chemistry involves recombination of the radicals created near each other in “spurs” and “tracks”, to form the molecular products.1,2 The competition between recombination and diffusive escape of the primary radical species depends on temperature.9 With increasing temperature diffusion “wins” and we observe an increase of radical escape yields and a corresponding decrease of the recombination product yield for H2O2. Curiously, the escape yield of H2 product increases with temperature. The escape yield value for molecular hydrogen Gesc(H2) (in molecules/100 eV) is close to 0.44 at 25 °C and increases to 0.76 at 350 °C.9 In the present work we investigate the source of this additional H2 yield. On the basis of the measured free radical reaction rates, it is expected that H2 is produced in spurs on the picosecond− microsecond time scale in the three following recombination reactions,3 with the first two dominating:

−

•

(e )aq + H( +H 2O) → H 2 + OH

−

© XXXX American Chemical Society

(4)

In the presence of sufficient added scavenger for the (e−)aq, it should be possible to completely prevent these recombination reactions. However, very early in the development of the theory of radiolysis, it was found that even for very high scavenging rates for the electrons (ks[S] ∼ 1 × 1010 s−1) the formation of H2 remains significant.12,13 Schwarz postulated there must be an “unscavengeable” yield of H2 (on the order of 0.15 molecules/100 eV by his estimate) formed in the earlier physicochemical stage of track evolution to account for the observation.14 Nearly 40 years later, Pastina et al.15 investigated the H2 formation in the presence of species (SeO42−, MoO42−, Cr2O72−, NO2−, NO3−, Cd2+, Cu2+, and H2O2), which are known16,17 to prevent the formation of hydrated electron by scavenging its “precursor” (for the most part, these are low energy electrons which have not yet solvated). They demonstrated that scavenging the hydrated electron precursor simultaneously reduced the yield of the “unscavengeable” molecular hydrogen. The very clear conclusion is that most of the H2 formed in the subpicosecond physicochemical stage of track evolution comes from some process(es) involving presolvated electrons. In this work, we measure the G(H2) yields at elevated temperatures (to 350 °C) in the presence of presolvated electron scavengers. The experiments with high concentrations of scavenger allow us to cleanly separate the yields of H2 generated in early time processes (which we denote by Go(H2)) from the spur recombination reactions. We demonstrate for the first time that an increase of Gesc(H2) in high temperature water radiolysis is directly correlated with processes occurring in the

H 2O ⇝ (e−)aq + (H+)aq + •H + •OH + H 2O2 + H 2

(e−)aq + (e−)aq ( +2H 2O) → H 2 + 2OH−

H + •H → H 2

(2)

Received: December 15, 2015 Revised: December 26, 2015

(3) A

DOI: 10.1021/acs.jpca.5b12281 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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reaction (e)aq + Cr2O72−. Far more importantly, CrO42− ions are also ∼2 times less effective in scavenging of the precursor of solvated electron. The C37 values17 that characterize the presolvation scavenging efficiency are 0.2 M for CrO42−and 0.12 M for Cr2O72−. The ca. 2× difference in scavenging efficiency of dimer and monomer means the equilibrium (6) should hardly influence the scavenging power of dichromate solution for (e−)aq or its precursor. Because of very strong oxidative (and acidic) character of Cr2O72−, causing corrosion and occlusion of our metal flow system, the experiments with this scavenger have been limited to 250 °C and below. Additional experiments were performed with positively charged Cd2+ and Cu2+ scavengers that are also efficient scavengers of the precursor to the solvated electron.16 The cadmium cation reacts with hydrated electron with rate constant 5.35 × 1010 M−1 s−1 at 25 °C, 5.17 × 1011 M−1 s−1 at 150 °C, and 1.92 × 1012 M−1 s−1 at 250 °C.21 Copper cations react with hydrated electron with rate constant 3.4 × 1010 M−1 s−1 at 25 °C, 1.3 × 1011 M−1 s−1 at 100 °C, and 2.2 × 1011 M−1 s−1 at 150 °C.21 Above 150 °C, copper metal precipitated to clog our flow system. Figure 1 shows the molecular hydrogen yields as a function of temperature in the presence of different concentrations of

physicochemical stage of track chemistry. In our Discussion, we demonstrate that the evidence strongly favors electron−hole charge recombination as the source of this subpicosecond H2.

II. EXPERIMENTAL SECTION In the radiolysis experiments we used the 3 MeV Van de Graff electron accelerator at the Notre Dame Radiation Laboratory. The experimental system is described in detail in ref 18. Argonsaturated water samples were pumped from two separate reservoirs by a pair of independent HPLC pumps with total flow of 6 mL/min. The reservoirs contain respectively 1 mM water solution of phenol, and 1 mM of phenol + 1 M of NaNO3 (or 0.5 M Na2Cr2O7 or 0.3 M Cd(ClO4)2 or 0.5 M Cu(ClO4)2). The phenol (>99%, Aldrich), sodium nitrate (≥99%, Baker) sodium dichromate (>99.5%, Aldrich), cadmium perchlorate (≥99%, Alfa Aesar), and copper perchlorate (≥99%, Alfa Aesar) were used without further purification. The two flows were combined in a “tee” and the pumping ratio determined the scavenger concentration. The water was heated in a preheater and then passed through a ca. 2 mm i.d. Hastelloy tube, where it was continuously irradiated by a 2.5 MeV electron beam. The water temperature was monitored by two thermocouples inserted into the flow before and after the irradiation zone. As a secondary dosimeter, we used a fiber optic placed in front of the irradiation tube. The intensity of Cerenkov light generated in the fiber was measured by a photodiode. After the light passed through the irradiation tube, the temperature and pressure of water was dropped (to room temperature (RT), 1 atm) in a capillary held in a water bath. Next, the samples were precisely collected in a glass vessel and then bubbled by ultrahigh purity argon to strip out dissolved hydrogen. The stream of gas was directed to a Varian CP-3800 gas chromatograph equipped with a thermal conductivity detector or sampled by a mass spectrometer (Prisma 200) detector set for mass 2. III. RESULTS Experiments. The first experiments were performed with use of NO3− ions, which are well-known to scavenge both hydrated electron and the precursor to the hydrated electron. Nitrate ion reacts with hydrated electron in the scheme: −

(e )aq +

NO3−

→ NO3

2−

9

k(25) = 9.7 × 10 M

Figure 1. Molecular hydrogen yields vs temperature of irradiation and change of NO3− concentrations: ■, 0.0016 M; ●, 0.025 M; ▲, 0.1 M; ☆, 0.25 M; +, 0.5 M; ◆, 0.75 M; ▼, 1.0 M; ···, total H2 yield (ref 9).

−1 −1

s

(5a)

NO32 − + H 2O → NO2 + 2OH−

k(25) ≈ 1 × 105 M−1 s−1 (5b)

NO3− ions. The lowest concentration, 0.0016 M, was chosen so that (at room temperature) the scavenging power is ca. 107 s−1 for hydrated electrons. To preserve the scavenging power for • OH radicals and •H atoms close to 106−107 s−1, the phenol concentration of 0.001 M was chosen.22 We anticipate this will not significantly perturb the part of the escape yield for H2 that results from spur recombination events. At 0.1 M [NO3−], the chemical lifetime of hydrated electrons should be only a nanosecond, and the great majority of recombination events giving H2 will be prevented. Nevertheless, Figure 1 shows a large fraction of the H2 yield persists at this nitrate concentration (yellow triangles). As the nitrate concentration is increased toward 1 M, the H2 yield further decreases. As Pastina et al. demonstrated,15 this is correlated with scavenging of electrons prior to their solvation. The analogous experiments were performed with use of dichromate, copper, and cadmium ions. In Table 1 we summarize the data for all four scavengers.

The rate constants for reaction 5a at elevated temperatures are respectively k(150) ≈ 3.8 × 1011 M−1 s−1, k(250) ≈ 4.0 × 1011 M−1 s−1, and k(350) ≈ 9.0 × 1010 M−1 s−1.19 The second scavenger used was Cr2O72−, which reacts with hydrated electron with rate constant 2.9 × 1010 M−1 s−1 at 25 °C. In water solution of chromium salts we can expect the equilibrium: Cr2O7 2 − + H 2O ↔ 2HCrO4 −

(6)

HCrO4 − ↔ CrO4 2 − + H+

(7)

It is important to remark that dissolution of one dimer always leads to formation of two monomer molecules (eq 6). The CrO42− reacts with hydrated electron with rate constant 1.6 × 1010 M−1 s−1 at 25 °C,20 which is ∼2 times smaller than for B

DOI: 10.1021/acs.jpca.5b12281 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Table 1. G(H2) at Various Temperatures and Scavenger Concentrations G(H2) [molecules/100 eV] vs temperature scavenger concn [M]

25 °C

100 °C

150 °C

200 °C

250 °C

300 °C

350 °C

NO3− 0.0016 0.025 0.1 0.25 0.5 0.75 1.0

0.438 0.347 0.281 0.218 0.167 0.131 0.107

± ± ± ± ± ± ±

0.026 0.021 0.017 0.013 0.011 0.009 0.007

0.0016 0.025 0.1 0.25 0.5 0.75 1.0

0.452 0.288 0.189 0.095 0.046 0.036 0.029

± ± ± ± ± ± ±

0.023 0.017 0.012 0.007 0.003 0.002 0.002

0.238 ± 0.012 0.183 ± 0.010 0.150 ± 0.009

0.473 0.384 0.310 0.269 0.210 0.177 0.152

± ± ± ± ± ± ±

0.487 0.323 0.194 0.121 0.067

± ± ± ± ±

0.024 0.019 0.016 0.013 0.304 ± 0.015 0.011 0.241 ± 0.013 0.010 0.211 ± 0.011 0.009 Cr2O72− 0.024 0.016 0.010 0.007 0.005

0.562 0.454 0.383 0.322 0.274 0.225 0.199

± ± ± ± ± ± ±

0.028 0.023 0.019 0.016 0.014 0.011 0.010

0.367 0.246 0.163 0.102

± ± ± ±

0.018 0.012 0.010 0.007

0.434 ± 0.022 0.358 ± 0.018 0.313 ± 0.018

0.732 0.612 0.535 0.495 0.427 0.379 0.341

± ± ± ± ± ± ±

0.037 0.031 0.027 0.025 0.021 0.019 0.017

Cu2+ 0.1 0.2 0.3 0.4 0.5 0.025 0.05 0.1 0.15 0.2 0.3 0.0 0.1 0.2 0.3

0.287 0.275 0.261 0.249 0.230

± ± ± ± ±

0.014 0.014 0.013 0.012 0.011

0.300 ± 0.015 0.268 ± 0.014 0.242 ± 0.012 0.332 0.287 0.261 0.245

± ± ± ±

0.017 0.014 0.013 0.012

0.284 0.264 0.253 0.233 0.228

± ± ± ± ±

0.014 0.013 0.013 0.012 0.011

0.269 ± 0.013

0.227 ± 0.011 Cd2+ 0.355 ± 0.018 0.338 ± 0.017 0.318 ± 0.016 0.283 ± 0.014 0.275 ± 0.014 Cd2+ + 0.1 M NO2− 0.409 ± 0.020 0.305 ± 0.015 0.284 ± 0.014 0.260 ± 0.013

0.450 ± 0.032 0.398 ± 0.028

0.514 ± 0.026 0.502 ± 0.025

0.344 ± 0.024 0.325 ± 0.023

0.500 ± 0.025 0.528 ± 0.026

0.487 0.343 0.307 0.305

± ± ± ±

0.024 0.017 0.015 0.015

Byakov showed23 that for high concentrations, the inhibiting effect of the scavenger on the formation of H2 in water can be described by an equation of the Stern−Volmer form: ⎛ ⎞ G(H 2) 1 ⎟⎟ = ⎜⎜ Go(H 2) ⎝ 1 + k H2[S] ⎠

(8)

Here G(H2) is an observed yield of molecular hydrogen in the presence of concentration [S] of the scavenger, Go(H2) is the yield in the absence of a scavenger, and kH2 is a constant characterizing the scavenging efficiency. In Figure 2 we plot 1/ G(H2) vs molar concentration of the scavengers as demonstrated by Byakov.23 The concentrations of scavenger should be high enough to suppress spur recombination reactions 2 and 3 (ks[S] > 1 × 109 s−1 at room temperature, corresponding to at least 0.1 M NO3−), so that Go(H2) corresponds to a presolvation yield of H2. The intercepts of the fitted lines give us 1/Go(H2) values, and the slope should represent kH2/ Go(H2), from which we can calculate the scavenging efficiency. Figure 2 clearly shows that our experimental data (for Cr2O72−, NO3−, Cu2+, and Cd2+) are in very good agreement with previous literature data (NO3−, H2O2). The fitted lines for all of the scavengers converge to an intercept corresponding to

Figure 2. Plot of 1/G(H2) vs the scavenger concentration: ●, Cr2O72− (this work); ▲, Cd2+(this work); ■, NO3− (this work); red box, NO3− (ref 15); blue box, NO3− (ref 25); ◇, NO3− (ref 23); △, H2O2 (ref 15); +, H2O2 (ref 26); ×, H2O2 (ref 27), ☆, H2O2 (ref 23).

Go(H2) = 0.344. Pastina et al.15 estimated the yield of H2 from the presolvation process of about 0.34 molecules/100 eV at 25 °C, in excellent agreement with this value. C

DOI: 10.1021/acs.jpca.5b12281 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A In Figure 3 we plot data for NO3− and Cr2O72− scavengers to demonstrate that the same analysis can be carried out up to 350

Figure 4. Radiolysis yields of H2 generated in presolvation events (···) and spur recombination reactions (---). The solid line () represents the total H2 escape yield (Elliot and Bartels).9

The Special Case of Cd2+. It is important to point out that the estimated Go(H2) yield for Cd2+ at 25 °C up to 0.3 M [Cd2+] is in very good agreement with experimental data for the other scavengers. Some previous workers15,27 using Cd2+ have reported room temperature H2 yield (at 1.0 M Cd2+ concentration) that does not fit this trend. Pastina et al. suggested15 this was due to an additional mechanism for H2 production in the bulk Cd+ recombination chemistry. However, Kelm et al.28 studied the pulse radiolysis of room temperature Cd2+ solutions with optical and conductivity detection, and also measured yield of cadmium metal precipitated in γ radiolysis. The mechanism they propose for Cd+ recombination, involving Cd22+ dimer, does not suggest any production of H2. Elliot et al.29 found no additional H2 yield for γ radiolysis of 0.001 M Cd2+/0.01 M MeOH solutions below 200 °C. Above that temperature the yield increased dramatically to reach ca. 6/100 eV at 300 °C. Radiolytic production of H2 after the physicochemical stage requires a combination reaction of two reducing equivalents. The G(H2) of 6/100 eV at 300 °C implies that all of the radicals recombined, with nearly quantitative H2 formation. In all likelihood this comes from CH2OH radical produced from OH, reducing the Cd+ or Cd22+ formed from (e−)aq, and followed by hydrolysis of the product.

Figure 3. Plot of 1/G(H2) vs the scavenger concentration for Cr2O72− (●) and NO3− ions (■): () 25 °C; (···) 150 °C; (---) 250 °C; (−·−) 350 °C. The inset illustrates the temperature dependence of the intercept.

°C. The density of the water was corrected on the basis of the IAPWS 1997 equation of state.24 Table 2 shows the measured breakdown of H2 yields for presolvation processes and the spur recombination reactions, based at elevated temperatures primarily on the most reliable NO3− data. The results definitively show that early time processes are the major source of H2 for the whole range of temperature. The contribution of “presolvation” H2 increases with temperature to reach ∼76% of the total H2 yield at 350 °C. The contributions of H2 generated in spur recombination reactions fall in the range 17%−29%. The temperature dependence of total H2 escape yield and the breakdown into presolvation processes and recombination reactions is plotted in Figure 4.

Table 2. kH2 Values and the Escape Yield Fractions of H2 Originating from Early Time Event Processes and Diffusive Spur Reactions G(H2) [molecules/100 eV]

kH2 [M−1]

% of the total H2

temp [°C]

total Gesc(H2) [molecules/ 100 eV]

presolvation processes

spur recombination reactions

presolvation processes

spur recombination reactions

NO3−

Cr2O72−

Cd2+

25

0.44

0.344 ± 0.017

0.096 ± 0.017

78.2 ± 3.9

21.8 ± 3.9

2.11 ± 0.11

11.02 ± 0.13

1.41 ± 0.08 (0.93 ± 0.11)a

100 150

0.47 0.49

0.331 ± 0.019 0.346 ± 0.017

0.139 ± 0.019 0.144 ± 0.017

70.4 ± 4.0 70.6 ± 3.5

29.6 ± 4.0 29.4 ± 3.5

1.46 ± 0.21 1.11 ± 0.06

7.60 ± 0.14

≥1.71 ± 0.10 (0.93)a

200 250

0.51 0.56

0.377 ± 0.022 0.413 ± 0.021

0.133 ± 0.022 0.147 ± 0.021

73.9 ± 4.3 73.8 ± 3.8

26.1 ± 4.3 26.2 ± 3.8

0.89 ± 0.14 0.85 ± 0.02

5.03 ± 0.05

≥1.78 ± 0.12 (1.13)a

300 350

0.64 0.76

0.529 ± 0.031 0.581 ± 0.029

0.111 ± 0.031 0.179 ± 0.029

82.7 ± 4.8 76.4 ± 3.8

17.3 ± 4.8 23.6 ± 3.82

0.66 ± 0.09 0.41 ± 0.01

a

Cu2+ 0.64 ± 0.09 ≥0.67 ± 0.09 ≥0.66 ± 0.14

Values estimated from Cd2+ + 0.1 M NO2− data. D

DOI: 10.1021/acs.jpca.5b12281 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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mechanism at high temperature. We conclude by discussing implications for modeling of water radiolysis. A. Possible H2 Sources. Several processes that may contribute to the formation of H2 at early times have been suggested over the years31,32 and incorporated into radiolysis models.33,34 One suggested prompt source of H2 is dissociation of electronically excited water:

The hydrolysis reaction must have a high activation energy, because it is not evident below 200 °C. Using the phenol scavenger for H and OH, we obtained Cd2+ results similar to other presolvated scavengers up to 150 °C, but at 250 and 350 °C additional H2 was certainly generated as the Cd 2+ concentration was increased. The excess H 2 production is evidenced by the curvature of the plots of 1/G(H2) vs [Cd2+] in Figure 5. A second set of experiments

H 2O* → H 2 + •O(1D)

Dissociation to give this product requires at least 7 eV (adiabatic) excitation in the gas phase. Dissociation of a triplet state to give •O(3P) and H2 requires at least 5 eV. Even though in Figure 3 we demonstrate a strong correlation involving presolvated electron scavengers, the possibility exists that these scavengers also effectively quench the water excitons with nearly the same relative efficiency. Though we cannot rule it out, this possibility seems remote, and in any case process (10) is not expected to be a very significant source of H2.33,34 LaVerne and Pimblott35 studied formation of H2 in the radiolysis of water with use of γ-rays, 10 MeV protons and 5 MeV helium ions. They demonstrate that G(H2) in the high LET helium ion radiolysis is significantly more sensitive to presolvated electron scavengers than the low LET γ case. On the basis of their data, we can estimate that the subpicosecond Go(H2) value for 5 MeV He radiolysis is 1.0 molecules/100 eV in contrast to 0.34 for γ radiolysis. This sensitivity to LET implies, given the large change in local density of ionization events, that a “second-order” kinetic process involving the presolvated electron and another radiation-generated transient is responsible for a large fraction of the hydrogen formation. They consider that dissociative charge recombination (10) of presolvated electrons with presolvated H2O+ “holes” is the most obvious second-order reaction occurring on the fast time scale that can lead to formation of H2:

Figure 5. Stern−Volmer plots for Cd2+ scavenging of presolvated electrons. The open circles and squares are intercepts predicted on the basis of data from the other scavengers.

was carried out, in which 0.1 M NaNO2 was used to ensure that all primary radicals are scavenged by nitrite, and also to scavenge Cd+ by reaction 9, whose rate constant is 2 × 109 M−1 s−1 at room temperature.30 Cd+ + NO2− ⇒ Cd2 + + NO2 2 −

(10)

H 2O+ + e−(pre) → H 2 + (•O3P or •O(1D))

(11)

The vertical ionization potential of room temperature liquid water is estimated to be36 ca. 11.7 eV, so that even recombination of presolvated electrons with zero kinetic energy could provide enough energy for the H2 production. The demonstrated existence of a second-order kinetic process at high LET does not rule out simultaneous operation of the “first-order” dissociative electron attachment (DEA) to a water molecule. (Here we denote the unstable transient as (H2O−*), and assume its lifetime is measured in femtoseconds.) The mechanism could generate an intermediate (H−)aq hydride anion (reaction 11c), whose lifetime must be on the order of picoseconds or less before it reacts with the water solvent to give the H2 product:

(9)

It should not be possible to form H2 outside of spurs in these NO2− solutions. As seen in Figure 5, we have linear Stern− Volmer plots in these experiments up to 150 °C. The intercepts are consistent with the other scavenging experiments if we correct for the presence of 0.1 M NO2− as an additional presolvated electron scavenger. (The kH2 value for NO2− is assumed to change with temperature just like that of NO3−). At 250 °C, the plot deviates from linearity just as with the phenol scavenger. We conclude that the nonlinearity results from additional H2 generation in the spurs. In both the phenol and NO2− solutions, we will be generating the reduced Cd+ ion by capturing a presolvated electron. In spurs of all temperatures, there could also be a double reduction giving some Cd0. We suggest that at high temperature, some of these doubly reduced ions hydrolyze water to give the additional H2.

H 2O + e−(pre) → (H 2O−*)

(11a)

(H 2O−*) → H 2 + (O−)aq

(11b)

or

IV. DISCUSSION The data we have presented adds to a large body of evidence that shows a precursor of the hydrated electron is involved in formation of much of the molecular hydrogen, but the exact mechanism is still debated. We first review what is known about presolvated electron scavenging and the mechanisms for H2 formation at room temperature. The temperature derivative of the scavenging efficiency can then be used to infer the

(H 2O−*) → (H−)aq + •OH −

(H )aq + H 2O → H 2 + OH

(11c) −

(11d) −

In 1972 Melton observed generation of H anion using negative ion mass spectrometry during low-energy electron irradiation of water vapors.37 Rowntree et al.38 confirmed the condensed phase dissociative electron attachment process E

DOI: 10.1021/acs.jpca.5b12281 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A (DEA) in a thin layer of condensed amorphous water film deposited onto a polycrystalline Pt foil. They report the onset for H− detection with low energy electron irradiation at 5.5 eV, with a maximum yield for anion desorption at ∼7.4 eV. The absolute cross sections were later reported by Michaud et al.39 However, it appears the absolute amplitude has simply been used as a fitting parameter in Monte Carlo simulations34,40,41 to obtain the subpicosecond hydrogen yield. B. Presolvated Electron Scavenging. Which mechanism is responsible for the presolvation H2 generation at room temperature, and for the increasing Go(H2) with temperature? The nature of the scavenging should help us answer this question. Both Byakov23,42 and Pastina et al.15 noted the strong correlations between presolvated electron scavenging and presolvated H2 scavenging efficiency of various scavengers. However, there is significant difference in the scavenging mechanism. In picosecond pulse radiolysis experiments, the absorption of hydrated electrons in concentrated scavenger solutions is generally found to be described by functions of the form16 A(t ) = Ao exp( −[S]/C37) exp( −ks[S]t )

Let us now consider the limit that the intrinsic reaction rate k is much greater than the rate of solvation 1/τ. The first-order rate of solvation is determined in femtosecond laser experiments46 to be on the order of 2.5 × 1012 s−1. In this case we require k > 2.5 × 1013, which is perfectly reasonable for an electron transfer process near the peak of the Marcus parabola.45 In this limit each term of eq 13 reduces to just the probability Θi, and Qs reduces to the total probability that there is at least one scavenger within the volume Vs. It follows that the fractional probability for actually observing (i.e., not scavenging) the solvated electron is (1 − Qs) = Θ0 = exp(−Ns). When we compare this analysis to eq 12, we see that 1/C37 is just the molar scavenging volume LVs. To recover the Stern−Volmer form from eq 13 and understand the attenuation of H2 product, we need to acknowledge a hierarchy of presolvated electron states on the basis of electron energy. It is accepted that secondary electrons are most often generated with kinetic energies in the range 10− 100 eV, high enough to ionize and/or electronically excite water molecules.3,34,40,47−49 They quickly (within around 5 fs50) lose their energy in large quanta by these electronic excitation processes until they reach energies below about 6 eV. These subexcitation electrons (e−)se can only lose energy by scattering into vibrations and librations of the water molecules. Monte Carlo simulations50 suggest that the lifetime of the subexcitation electrons is of order 50 fs. Eventually, the electrons slow down enough to be trapped or localized, (e−)loc. The water then reorganizes around the trapped charges, and this is the solvation process leading to (e−)aq characterized by ca. 400 fs time constant.46 On the basis of eq 13, the presolvated scavenging product yield will only have the exponential concentration form for k ≫ 1/τ. C37 is characteristic for scavenging of localized electrons, (e−)loc. For mobile high energy or subexcitation electrons, the effective reaction radius R is likely to be larger, and lifetime τ is likely to be much shorter than for the trapped electrons. In the limit of large R and large Ns, the Poisson coefficients Θi tend toward a Gaussian distribution around the average number Ns. The most probable value of i is Ns, and eq 13 tends to the Stern−Volmer form

(12)

where we see that both the time-decay profile and the initial amplitude are functions of the scavenger concentration [S]. The time decay profile immediately allows determination of the hydrated electron reaction rate constant ks, but the effects of scavenging presolvated electrons on a femtosecond time scale are hidden in the apparent “initial” amplitude, where 1/C37 is a constant characterizing the presolvation scavenging efficiency.16,17,43,44 It is important to understand that the pulse radiolysis initial (ca. 1 ps) solvated electron yields definitely are characterized by an exponential form G(e−)aq/Go(e−)aq = exp(−[S]/C37) rather than the Stern−Volmer form characterizing H2 inhibition. Nevertheless, there is a much stronger correlation of kH2 with 1/C37 than with the hydrated electron reaction rate constant ks.17,23,42 Kee et al.45 have suggested a model that qualitatively explains the difference between the different scavenging equations for (e−)aq and H2 or positronium inhibition. For very high scavenging rates, we can define a hard-sphere reaction radius R for electrons in the same spirit as the Smoluchowski equation for diffusion-limited reactions and define a corresponding scavenging volume Vs = 4πR3/3. A presolvated electron will be created by an ionization event somewhere in the solution, and we assume it will have lifetime τ prior to its solvation. If the electron is created within the reaction radius R of a scavenger, instead of solvating, it may react with the scavenger with the intrinsic reaction rate k. At higher concentrations of scavenger, there may be more than one scavenger within the reaction radius of the electron. The total probability of scavenging the electron before it solvates should be given by45 ⎛ A(t =0) ⎞ Q s = ⎜1 − ⎟= Ao ⎠ ⎝

∞

∑ i=1

ik Θi ik + 1/τ

Qs =

Nsi exp( −Ns) i!

(15)

Consequently, the Stern−Volmer scavenging dependence follows from the shorter lifetime and greater delocalization of the high energy and subexcitation electrons relative to the trapped electrons.45 It seems fair to conclude that the presolvated H2 yield does not come from any reactions of the trapped or localized electrons, but rather from reactions involving (e−)se. C. Evidence from Positron Annihilation Lifetime and High LET Measurements. In principle, it might be possible to establish the dominant mechanism for the presolvated H2 scavenging on the basis of analogy with the inhibition of positronium formation.23,42,51 Positronium “atoms” formed at the end of a positron track from a positron−electron pair, can be detected using nuclear counting techniques via positron annihilation spectroscopy. Their formation can be inhibited by various scavengers of presolvated electrons, and characterized by a Stern−Volmer form17,23,52 with efficiency constant kpi. Byakov23 first noted the similarity of kH2 and kpi for the scavengers H2O2, NO3−, and NO2−. Byakov and Firsov42

(13)

where Θi is the probability for having i scavengers within the reaction radius of the electron. The average number of scavengers within the reaction radius is simply Ns = [S]LVs, where L is Avogadro’s number. The probabilities Θi are given by the Poisson distribution Θi =

Nsk Nsk + 1/τ

(14) F

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The Journal of Physical Chemistry A Table 3. Go(H2) and kH2 for Several Scavengers vs LET of the Radiation kH2 [M−1] type of radiation and LET

Go(H2) [molecules/100 eV]

Cr2O72−

γ: (0.2 eV/nm) H+: 10 MeV (13 eV/nm) He2+: 5 MeV (156 eV/nm)

0.34 ± 0.02 0.37 ± 0.06b 1.04 ± 0.13b

11.0 ± 0.1 7.1 ± 1.0d 6.1 ± 0.4d

a

SeO42−

H2O2 c

0.8 ± 0.1 0.7 ± 0.1d 0.5 ± 0.2d d

1.4 ± 0.2d 1.8 ± 0.3d 1.9 ± 0.3d

a Go(H2) calculated from the data in this work. bGo(H2) calculated based mainly on H2O2 data from ref 35. cCalculated from the low-LET data in this work. dCalculated from the data in ref 35.

Table 2 we show that kH2 for both NO3− and Cr2O72− scavengers decreases by more than 2 times with temperature up to 250 °C. However, the values of kH2 for Cd2+ or for Cu2+ barely change with temperature. We suggest the differing behavior of the charged presolvated electron scavengers is consistent with Coulombic repulsion or attraction as a result of the change in dielectric constant with temperature. For example, the Debye−Smoluchowski equation for diffusionlimited reaction of ions is53,54

compiled data for a large number of scavengers to demonstrate the near-equivalence of scavenging efficiency for H2 and positronium inhibition, and the strong correlation with presolvated electron scavenging. Stepanov and Byakov argue that to form quasi-free (unsolvated) positronium, the combined kinetic energy of a presolvated electron and positron must be below ca. 1 eV, because this is the approximate binding energy49 of the quasi-free positronium “atom”. This same scavenging efficiency should also roughly correspond to kH2, if the H2 formation is dominated by the charge recombination process. We have already noted that it should be energetically possible to generate H2 via charge recombination even with electrons of zero kinetic energy. On the contrary, if H2 generation is dominated by dissociative electron attachment, which has maximum cross section at 7.2 eV,38,39 electrons must be scavenged at energies above the threshold energy of 5.5 eV to have any effect at all. One expects that it should be much more difficult to inhibit the DEA process than the charge recombination pathway. Given the qualitative argument of Byakov and Stepanov49 noted above, it is difficult to see how any scavengers could provide similar scavenging efficiency of DEA and positronium formation processes. It is far more likely that charge recombination is the primary source of presolvation H2. A more definitive comparison to make is the kH2 values obtained for high-LET He2+ ion vs γ radiolysis in the experiments of LaVerne and Pimblott.35 Our fit of their (high concentration) data for three scavengers is tabulated in Table 3. The presolvation H2 yield in 5 MeV He2+ ion tracks is 3 times larger than for low-LET γ radiation, and this must be because the charge-recombination is much more probable in the dense tracks. The presolvation yields have only slightly different sensitivity in the kH2 toward various scavengers, which suggests that the H2 formation mechanism is dominated by charge recombination in low LET radiolysis as well. If DEA inhibition was happening with low LET γ radiation, then the much more probable scavenging of charge recombination in high-LET He2+ tracks ought to result in a dramatically larger value of kH2. This is not seen. D. Presolvated H2 Formation at High Temperature. On the basis of the foregoing analysis of literature data for presolvation scavenging, we conclude that the room temperature presolvation Go(H2) is completely dominated by the electron−hole charge recombination mechanism rather than DEA. What about at high temperature? As we showed in Figure 4, the yield of presolvated H2 increases at elevated temperature, by nearly a factor of 2 between room temperature and 350 °C. If the temperature effect was due to a large increase in DEA cross-section at higher temperature, we might expect a significant decrease (ca. 2 times) in all of the presolvated scavenging efficiencies kH2 (because DEA is hard to inhibit). In

kDS =

4πrcD r exp⎡⎣ Rc ⎤⎦ − 1

(16)

where D is relative diffusion and R is the hard-sphere reaction distance, at which recombination is certain to occur. The Onsager radius rc, where Coulombic potential energy equals kT, is given by rc =

Z1Z 2 4π ϵoϵkT

(17)

Depending on the sign of the charges Z1 and Z2, the rate constant will increase or decrease relative to the uncharged case, and the sensitivity depends on the dielectric constant ε. (These equations apply only qualitatively, because although the scavenger ion charges are fully screened by the solvent dipoles, the subexcitation electrons are screened only by the highfrequency electronic polarization of the medium.) The behavior of the charged scavengers is a definitive indication of the mechanism for the H2 generation at high temperature. The DEA process involves the resonant capture of electrons with energies in the range 6−8 eV. In contrast, the energy kT of thermalized electrons is ca. 25 meV at room temperature and increases to ca. 51 meV at 350 °C. It is impossible that increasing the absolute water temperature by a factor of 2 would significantly change the trajectories of the 6− 8 eV electrons. If charged scavengers were able to capture electrons at these higher energies (presumably by a competing very efficient dissociative attachment process, or by their ionization), the ambient temperature could have no significant effect on the relative cross sections. The scavenging of presolvated electrons must occur at kinetic energies near ambient, to demonstrate a different temperature effect on positively and negatively charged scavengers. The only possible conclusion is that most of the subpicosecond H2 yield comes via electron−hole charge recombination of low energy, nearly thermalized (but not localized) electrons. E. Implications for Track Structure Modeling. Serious attempts to describe temperature-dependent water radiolysis have been most recently made by Jay-Gerin and co-workers,40 using as reference the G value and reaction rate data compiled in the review of Elliot and Bartels,9 and recent high temperature picosecond radiolysis measurements of the hydrated electron G

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The Journal of Physical Chemistry A spur recombination.55,56 The most significant finding of these authors is that the average thermalization distance of electrons relative to their geminate partners must significantly decrease above 100 °C, to fit the hydrated electron decay kinetics.40 The theoretical justification is that increasing disorder of the water at higher temperature correspondingly increases the scattering of low energy electrons, such that they do not travel as far from their origin. The physicochemical model used by this group34,41 includes direct excitation of A1B1 or B1A1 water excited states, dissociative electron attachment, and dissociative charge recombination. At low temperature, the branching ratios for dissociative charge recombination producing (H2 + •O), (2•H + •O), or (•H + •OH) were considered to be the same as for directly excited B1A1 state. The branching ratios are postulated to change with temperature above 100 °C in a manner analogous to the thermalization distance. For lack of data, the DEA cross-section and the branching ratios were assumed to be equal to the gas phase values at 350 °C. In this model, the probability for dissociative charge recombination giving H2 increases from 13% at room temperature to 21% at 350 °C, at the expense of the (•H + •OH) channel. They postulated the DEA cross-section more than doubles from 2.8 × 10−18 to 6.7 × 10−18 cm2 at 350 °C. Apparently the (45%) probability of nondissociative de-excitation remained independent of temperature in the model. The simulations of Sanguanmith et al. with this model40 appear to be reasonably successful in matching escape yield and picosecond kinetics data over the 25−350 °C temperature range, except for Gesc(H2) at temperatures above 250 °C. A monotonic increase in Gesc(H2) with temperature is recovered, but the increase in yield only reaches Gesc(H2) = 0.6 molecules/ 100 eV as opposed to the experimental result of 0.76. Rather than reparametrizing the (>7) variables of their physicochemical model, Sanguanmith et al.40 followed Swiatla-Wojcik and Buxton57 in postulating the relatively slow reaction of H atoms with water H + H 2O ⇒ H 2 + OH

to change the initial local concentration of transient species in the particle tracks. In high LET radiolysis, the second-order recombination processes are emphasized more strongly, both on the subpicosecond physicochemical time scale and on the later diffusive recombination time scale. Rather than doubting the experimentally measured maximum in second-order diffusive recombination rate, we conclude from this high-LET simulation result that the second-order process of dissociative charge recombination has been underestimated at high temperature. Decrease in the second-order diffusive recombination above 150 °C is compensated and exceeded by increase in the second-order charge recombination giving H2. In light of our H2 scavenging results showing sensitivity to both temperature and charge of the scavenger, it seems probable that most if not all of the increase in “presolvation” H2 yield comes from increasing the charge recombination process, and not from a large increase in the DEA cross-section. We cannot completely rule out some DEA contribution at elevated temperature, because we only succeeded in “scavenging” half of the H2 with 1 M NO3− at 350 °C. Nevertheless, room temperature parameters in the simulation program of Jay-Gerin and co-workers40,59 will need to be reworked. Indeed, except for the simulation of Stepanov and Byakov,49 it seems that all of the popular water radiolysis simulation codes60,61 need to be modified to properly account for the charge recombination. The simplest benchmark to use for the H2 formation should be the simultaneous simulation of low-LET and high-LET radiolysis G(H2) data, which is sensitive to a large difference in the charge recombination probability.35 The recent review of Elliot and Bartels9 makes it clear that there is very little highLET data available for this purpose at high temperature. Work in our laboratory is presently aimed at providing this information.

V. CONCLUSIONS Our experimental results clearly show that some early time “presolvation” process is responsible for the major part of the molecular hydrogen generated in low-LET water radiolysis, up to 350 °C. The presolvation H2 can be attenuated with high concentrations of presolvated electron scavengers, and the efficiency for preventing either (e−)aq or H2 (or positronium) product formation is strongly correlated. The Go(H2) from the presolvation process increases with temperature from 0.344 at 25 °C to 0.581 at 350 °C, corresponding to ∼78% and ∼76% of the total H2 escape yields, respectively. The efficiency for scavenging of the presolvation H2 depends on temperature and on the charge of the scavenger. Anion scavengers become less efficient at high temperature, whereas cation scavenger efficiency changes little. This behavior can only be explained if the scavenging occurs at near thermal energies of the electrons, so we are able to conclude that the H2 is mostly generated in electron−hole charge recombination events of nearly thermalized electrons, rather than via dissociative electron attachment. The different concentration dependence (exponential vs Stern Volmer) of presolvated (e−)aq and H2 scavenging indicates that the electrons are not yet trapped when charge recombination occurs to yield the H2.

(18)

to make up the H2 yield deficit. This is unfortunate because they had in their possession, and cited (as ref 47), an unpublished manuscript that demonstrates the impossibility of this explanation.57 Very briefly, the data that give the Gesc(H2) = 0.76 result are derived from solutions containing the H atom scavenger phenol, so that reaction 18 cannot possibly contribute to the escape yield of H2. (In a publication that appeared when our work was ready for submission, Meesungnoen et al. revised the model as is necessary to fit this data, by further increasing the DEA cross sections to 10 × 10−18 cm2 at 350 °C.58) Sanguanmith et al. described at some length40 the necessity to increase the DEA and dissociative recombination cross sections above 150 °C, because the spur recombination production of H2 decreases when the reaction (e−)aq + (e−)aq ⇒ H 2 + 2OH−

(2)

abruptly “turns off” above this temperature. To compensate, the subpicosecond H2 yield clearly must increase at higher temperature to give the monotonically increasing total yield. However, Jay-Gerin and co-workers have doubted that this bimolecular recombination rate actually decreases. In a more recent note,59 they complain that for simulations of high LET radiolysis, the simulated maximum in G(H2) at 150 °C reappears, contrary to experiment. The major effect of LET is 9

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AUTHOR INFORMATION

Corresponding Author

*D. M. Bartels. E-mail: [email protected]. Phone: (574) 6315561. Fax: (574) 631-8068. H

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The Journal of Physical Chemistry A Notes

(19) Takahashi, K.; Bartels, D. M.; Cline, J. A.; Jonah, C. D. Reaction Rates of the Hydrated Electron with NO2-, NO3-, and Hydronium Ions as a Function of Temperature from 125 to 380 Degrees C. Chem. Phys. Lett. 2002, 357, 358−364. (20) Sedigallage, A. P.; Freeman, G. R. Solvent Structure Effects on Solvated Electron Reactions in Mixed-Solvents - Negative-Ions in 1Propanol-Water and 2-Propanol-Water. Can. J. Phys. 1990, 68, 940− 946. (21) Kanjana, K.; Courtin, B.; MacConnell, A.; Bartels, D. M. Reactions of Hexa-aquo Transition Metal Ions with the Hydrated Electron up to 300 degrees C. J. Phys. Chem. A 2015, 119, 11094− 11104. (22) Bonin, J.; Janik, I.; Janik, D.; Bartels, D. M. Reaction of the Hydroxyl Radical with Phenol up to Supercritical Conditions. J. Phys. Chem. A 2007, 111, 1869−1878. (23) Byakov, V. M. Nature of Precursors of Radiolytic MolecularHydrogen in Water, and Mechanism of Positronium Formation in Liquids. Int. J. Radiat. Phys. Chem. 1976, 8, 283−288. (24) Wagner, W.; Kruse, A. Properties of Water and Steam: The Industrial Standard IAPWS-IF97 for the Thermodynamic Properties of Water; Springer: Berlin, 1998. (25) Mahlman, H. A. Activity Concept in Radiation Chemistry. J. Chem. Phys. 1959, 31, 993−995. (26) Anderson, A. R.; Hart, E. J. Hydrogen Yields in the Radiolysis of Aqueous Hydrogen Peroxide. J. Phys. Chem. 1961, 65, 804−811. (27) Peled, E.; Czapski, G. Molecular Hydrogen Formation G(H2) in the Radiation Chemistry of Aqueous Solutions. J. Phys. Chem. 1970, 74, 2903−2911. (28) Kelm, M.; Lilie, J.; Henglein, A. Pulse Radiolytic Investigation of Reduction of Cadmium(II) Ions. J. Chem. Soc., Faraday Trans. 1 1975, 71, 1132−1142. (29) Elliot, A. J.; Chenier, M. P.; Ouellette, D. C. G-Values for Gamma-Irradiated Water as a Function of Temperature. Can. J. Chem. 1990, 68, 712−719. (30) Meyerstein, D.; Mulac, W. A. Reductions by Monovalent Zinc, Cadmium, and Nickel Cations. J. Phys. Chem. 1968, 72, 784−788. (31) Cobut, V.; Jay-Gerin, J.-P.; Frongillo, Y.; Patau, J. P. On the Dissociative Electron Attachment as a Potential Source of Molecular Hydrogen in Irradiated Liquid Water. Radiat. Phys. Chem. 1996, 47, 247−251. (32) Kimmel, G. A.; Orlando, T. M.; Vezina, Ch.; Sanche, L. Low Energy Electron-Stimulated Production of Molecular Hydrogen from Amorphous Water Ice. J. Chem. Phys. 1994, 101, 3282−3287. (33) Swiatla-Wojcik, D.; Buxton, G. V. Modeling of Radiation Spur Processes in Water at Temperatures up to 300-Degrees-C. J. Phys. Chem. 1995, 99, 11464−11471. (34) Cobut, V.; Frongillo, Y.; Patau, J. P.; Goulet, T.; Fraser, M. J.; Jay-Gerin, J. P. Monte Carlo Simulation of Fast Electron and Proton Tracks in Liquid Water - I. Physical and Physicochemical Aspects. Radiat. Phys. Chem. 1998, 51, 229−243. (35) LaVerne, J. A.; Pimblott, S. M. New Mechanism for H2 Formation in Water. J. Phys. Chem. A 2000, 104, 9820−9822. (36) Swiatla-Wojcik, D.; Mozumder, A. Assessment of Hydrogen Bonding Effect on Ionization of Water from Ambient to Supercritical Region-MD Simulation Approach. Radiat. Phys. Chem. 2014, 97, 113− 117. (37) Melton, C. E. Cross-Sections and Interpretation of Dissociative Attachment Reactions Producing OH-, O-, and H− in H2O. J. Chem. Phys. 1972, 57, 4218−4225. (38) Rowntree, P.; Parenteau, L.; Sanche, L. Electron-Stimulated Desorption via Dissociative Attachment in Amorphous H2O. J. Chem. Phys. 1991, 94, 8570−8576. (39) Michaud, M.; Wen, A.; Sanche, L. Cross Sections for LowEnergy (1−100 eV) Electron Elastic and Inelastic Scattering in Amorphous Ice. Radiat. Res. 2003, 159, 3−22. (40) Sanguanmith, S.; Muroya, Y.; Meesungnoen, J.; Lin, M.; Katsumura, Y.; Kohan, L. M.; Guzonas, D. A.; Stuart, C. R.; Jay-Gerin, J. P. Low-linear Energy Transfer Radiolysis of Liquid Water at Elevated

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Jay Laverne for sharing tables of his published G(H2) yields for high-LET radiolysis, and for useful discussions. This work is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under award number DE-FC02-04ER15533. This is manuscript number 5089 of the Notre Dame Radiation Laboratory.

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