J. Phys. Chem. 1986, 90, 5974-5984
5974
Reaction of T2 and O2 Gas: A Model R. A. Failor,* P. C. Souers, Lawrence Livermore National Laboratory, Livermore, California 94550
and S. G. Prussint Department of Nuclear Engineering, University of California, Berkeley, California 94720 (Received: April 8, 1986)
+
-
The kinetics of the homogeneous gas-phase oxidation of tritium (2T2 O2 2T20) have been studied by use of a model which accounts explicitly for the radiolysis of the major species and the kinetics of the subsequent reactions of the ionic, excited-state, and neutral species. This report includes a detailed calculation of the radiolysis product distribution due to the tritium @ decay with special attention given to oxygen radiolysis. Adjustments were made to hydrogen-based rate constants obtained from the literature to account for kinetic isotope effects. Results from model calculations are given for 104-1.0 mol % pure T2 in pure 0,at 298 K and 1 atm, from time of mixing to beyond the l / e conversion time. As the reaction evolves, three different mechanisms control the T 2 0 production. Each mechanism has a different overall rate expression with a different order with respect to the T2 concentration. From the predicted mechanisms the importance of the radiolysis products and subsequent ion reactions is evident.
Introduction The rate of oxidation of molecular tritium to tritiated water is of great concern for the safe operation of tritium handling and nuclear fusion facilities. Two of the main reasons for concern are the increased health hazard of HTO over HT and the difference in chemical behavior of the two forms in tritium containment and removal systems. Tritiated water can form by the tritium oxidation reaction at room temperature because of the tritium @ radioactivity. This stands in contrast to H2 and 0, which usually require elevated temperatures to provide the intermediate free radicals. Experimental work on the T2-02 reaction to T20 has been carried out on for 30 years.’” However, the results are fragmentary and inconsistent. No good time-dependent curve of water yield has been obtained to date. This is partly because of the considerable difficulty in collecting the T 2 0 at the low tritium concentrations of general interest. The data have recently been reviewed by Robins et al.’ To date, the only attempt to model the T2-03reaction pathways was by Papagiannakopoulos and Easterly in 1982.’ They presented a good overview of the formation of tritiated water in three gas mixtures using hydrogen-based reaction rate data. In order to examine three very different gas mixtures they simplified the problem by neglecting many of the ions and excited states formed by the @ irradiation of the gases and their subsequent reactions. They further simplified the problem by assuming steady-state concentrations of certain radical species and neglecting the kinetic isotope effects. In this paper we present a comprehensive, non-steady-state model for the oxidation kinetics of molecular tritium. By restricting our attention to pure T2 in pure 0, we include a more detailed description of the reaction process than has been reported previously. Gas-phase oxidation of T2 occurs when the tritium-decay fi particle interacts with the species present in the gas, forming atomic, ionic, and excited-state radiolysis products of these species. The radiolysis products proceed through a series of steps to form the reaction intermediates which subsequently react to form T20. For a simple system containing less than a few percent T, in pure 0, we have developed a model which includes the tritium-@radiolysis of 02,T2, and TzO, and a series of reactions of the ionic, excited-state, and ground-state neutral species. We adjusted the reaction rate constants for hydrogen reactions to reflect the tritium kinetic isotope effect (KIE). In this model we assume that pure T2 and pure 0, are mixed in zero time. Ionic and atomic radiolysis products present in ‘Consultant to Lawrence Livermore National Laboratory.
0022-3654/86/2090-5974$01.50/0
TABLE I: Summary of Radiolysis Parameters Used in This Calculation‘
Probability of Direct Radiolysis Production Per Electron Formed hydrogen oxygen water H,+ 0.88 O,t 0.27 H,O+ 0.58 OH+ 0.21 Hi. 0.12 (d,+)* 0.48 H 0.89 O+ 0.17 H+ 0.21 0.08 H 0.73 H* 0.25 (O+)* 0.58 H* 0.13 H2* 1.00 O(’P) e1.00 O*(’D) 0.80 OH 0.86 5.2 x 10-4 o 0.13 O2*(a) 2.6 X IO4 Hz 0.13 O2*(b) e1.oo H20* 0.85 e-
1.oo
Energies and Stopping Powers ionization potential, eV eV/electron formed, eV/eelectrons formed/@particle re1 stopping power, ai
T2
02
T20
15.4 36.4 157.1
12.1 30.8 185.5
1.000
5.850
12.6 29.6 193.0 3.90
“The top portion lists the probability that a tritium p particle slowing down in a pure gas of either hydrogen, oxygen, or water vapor will produce a given species as a direct product of radiolysis. The probabilities are normalized to the number of secondary electrons formed. Asterisks indicate excited electronic states. The bottom portion lists physical parameters of the gases used in our calculations. tritium gas can be removed by flowing the gas through a metal capillary between charged plates prior to mixing with oxygen. This would give a mixture of pure T2 and 0,. The initial T2 concentrations modeled range from lo4 to 1.0 mol %. The calculations are performed for conditions of 1 atm pressure and 298 K. We L. M.; Hemmer, B. A. J . Chem. Phys. 1954, 22, 1555. (2) Casaletto, G. J.; Gevantman, L. H.; Nash, J. B. The SeljRadiation Oxidation of Tritum in Oxygen and Air; U. S.Naval Radiological Defense Laboratory: San Francisco, 1962; Report NRDL-TR-565. (3) Yang, J. Y.; Gevantman, L. H.J . Phys. Chem. 1964, 68, 3115. (4) Eakins, J. D.; Hutchinson, W. P. “The Radiological Hazard from the Conversion of Tritium to Tritiated Water in Air by Metal Catalysts”. In Tritium; Moghissi, A. A., Carter, M. W., Eds.; Messenger Graphics: Phoenix, AZ, 1971; pp 392-399. ( 5 ) Belovodskii, L. F.; Gaevoi, V. K.; Grishmanovskii, V. I.; Nefedov, N. N. Sou. A t . Energy (Engl. Transl.) 1975, 38, 488. ( 6 ) Phillips, J. E.; Easterly, C. E. Tritium Oxidation and Exchange: Preliminary Studies; Oak Ridge National Laboratory: Oak Ridge, TN, 1978; Report ORNL/TM-5963. (7) Robins, J. R.; Bartoszek, F. E.; Woodall, K. B. Reuiew of Tritium Comerston Reactions; Canadian Fusion Fuels Technology Project Report No. F84027; Ontario Hydro: Mississauga, Ontario L5J 1K3, Canada, 1984. (8) Papagiannakopoulos, P. J.; Easterly, C. E. In?. J . Chem. Kine!. 1982, (1) Dorfman,
14, 11.
0 1986 American Chemical Society
Reaction of T2 and O2 gas
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5975 TABLE II: Detailed List of Directly Formed Radiation Debris in the Radiolysis of Molecular Oxygen, according to Green*"
b 42g-(18.2)
-0' a
ground state
411u 118.2)
OZtexcited states
t
l5
E
c' w
+ +
'xu+ (9.4)
1-
1: 1 0
excited level transition integrated band state energy cross sect. branching (eV) (relative) ratio products name name X n=3 8.4 1.o 1.o 10.5 n=4 0.18 1.o o(3pj oi'sj 11.6 0.13 n>5 1.o O(3P) O(1S) 1.OO" x 2n8 12.1 1.o 02+(X) + e12.7 n=3 0.53 0.5 O('D) + O('S) 0.53 0.5 o,+(x) e' 0.1 1 14.6 n=4 0.5 O('P) 0(3ssS) 0.1 1 0.5 O,+(X) e0.21 0.68 15.6 n>5 Oi3P) + 0(3ssS) 0.10 0.32 02+(X) + e2.2 1.o a 4nu 16.1 02+(a) + e0.46 n=3 13.2 0.5 O('D) + O(lS) 0.46 0.5 02+(X) en=4 0.10 0.5 15.3 'P) + 0(3s5S) 0.10 0.5 ::+(XI + en=5 16.2 0.23 0.68 OOP) 0(3ssS) 0.11 0.32 02+(X,a) e1.3 1.o A211u 16.9 O2+(A) e0.15 n=3 15.7 0.50 OOP) + 0(3s3S) 0.15 0.50 02+(X) + en=4 16.9 0.045 0.50 O(jP) 0(3s2S) 0.045 0.50 02+(X,a) + e0.11 0.68 n>5 17.7 O('P) 0(3P3P) 0.053 0.32 02+(X,a,A) + e0.88 1.o b4Z,+ 18.2 02+(b) + eB, c n =-3 0.075 19.6 0.5 o(3~) 0(3SSP,3P'P) 0.075 0.5 02+(X,a,A,b) e0.019 0.5 n=4 21.5 O('P) + 0(3sSP,3p3P) 0.019 0.5 O2+(X,a,A,b) + en>5 22.5 0.034 0.68 o(3~) 0(3SSP,3P'P) 0.016 0.32 02+(X,a,A,b) e0.53 1.o 02+(B,c) e23.0 0.12 9.4 20(lD) 1.o 0.4 est 6.2 o ( 3 ~+ ) o(~D) 1.o 4.4 0.42 1.o 20(3~) 0.002 1.6 1.o 02* 0.004 1.o 1.o 02*
+ + +
O2 excited states b
'X.,'
(1.6)
J
+
O2 ground state
Figure 1. Energy levels used in calculating the @ particle energy deposition in oxygen. The two dashed levels at the left are for molecular dissociation, where the products are 2O('P) at 5.1 eV and O('P) 0 (ID) at 7.0 eV. The numbers in parentheses are the energies in electronvolts as referenced to the O2ground state. The lower Rydberg states (labeled with n in Table 11) are not shown here.
+
base much of the radiolysis calculation on an assumption that the tritium /3 energy spectrum is adequately approximated by tHe average /3 energy. We also assume that the reaction takes place only in the gas phase. The importance of the surface-induced reaction in both T2 and H2 oxidation is well established4 but is not considered in the work reported here. In the following sections we describe more of our assumptions, sources, and calculations for the data included in the model's reaction list and the model predictions. In a later paper we will publish a detailed comparison of our model predictions and experimental results in the literature. Energy Deposition and Direct Radiolysis Products
The interaction of tritium /3 particles (and secondary electrons) with molecular Tz, 02,and T 2 0 results in the direct formation of a wide range of ionic, atomic, and molecular species in various excited states. We refer to these as radiolysis products. By direct formation we mean only the net effects of the electron interaction and the deexcitation mechanisms (e.g., dissociation, ionization, and excited-state decay) which occur prior to collisions with any other chemical species. Table I summarizes the probability of producing specific radiolysis products from the /3 irradiation of H,,02,and HzO as obtained from calculations based on literature data."' The only excited states included in Table I are electronic excitations. We do not consider vibrational excitation induced by radiolysis in this model. The effects of this simplification are discussed in a later section. The values given in Table I are probabilities normalized with respect to the total number of electrons formed due to the fl thermalization process, including the /3 electron. This means that if X electrons are produced when a (3 particle of energy ( E B ) is ions will released in Oz,then we predict that, overall, 0.27X02+ (9) Watson, C. E.; Dulock, V. A., Jr.; Stolarski, R. S.; Green, A. E. S . J. Geophys. Res. 1967, 72, 3961.
(10) Porter, H.S.; Jackman, C. H.; Green, A. E. S. J . Chem. Phys. 1976, 65, 155.
(11) Jackman, C. H.; Garvey, R. H.; Green, A. E. S. J. Geopbys. Res. 1977.82, 5081.
(12) Oktizaki, K.; Sato, S . Bull. Chem. SOC.Jpn. 1975, 48, 3523. (13) Okazaki, K.; Sato, S.; Ohno, S.-I. Bull. Chem. SOC.Jpti. 1976, 49, 174. (14) Ohno, S.-I.;Nagayama, H.; Okazaki, K.;Sato, S . Bull. Chem. SOC. Jpn. 1975,48, 2153. (15) Wojcik, L.; Bederski, K.; Adamczyk, B.; Pleszczynski, M. Ann. Univ. Mariae Curie-Sklodowska Lublin Polonia 1973, 28, 421; in Polish. (16) Turner, B. R.; Rutherford, J. A.; Compton, D. M. J. J. Chem. Phys. 1968, 48, 1602. (17) Combecher, D. Radiot. Res. 1980, 84, 189.
+ + +
+ + +
+
+
+
+
"Integrated cross sectiobs calculated relative to this level. See Figure 1 for the position of many of the excited states. The energies are referenced to ground-state 02(X3Z,-) at 0 eV. The levels above 18.8 eV can dissociate h t h e r to form O+ ions.
be formed and 0.17X O+ ions will be formed, etc. We assume that the same product distributions are obtained when tritium is substituted for protium because the electron-induced ionization cross sections for H2 and D2are virtually identical at all energies.'*-,O The electronic level scheme of hydrogen is sufficiently wellknown that a fairly complete understanding of T, radiolysis is possible. We use the results of Okazaki and Sato12 for energy loss of 100 keV electrons in hydrogen without change. The problem of determining the yields of species produced by radiolysis of oxygen and water is more difficult. For oxygen we base our calculations on results of Green and co-w~rkers.~-'' Briefly, the values in Table I for O2were derked by (1) calculating the relative integrated cross Sections for formation of the main excited states, (2) estimating the branching ratios for dissociation product formation from each excited state, (3) calculating the amount of each specie formed relative to the total number of ionization electrons created, and (4) slight adjustment of these calculated values to reflect experimental data. The probability that a single electron impact produces a given excited state is determined by the cross section for such a reaction. (18) Schram, B. L.; DeHeer, F. J.; van der Wiel, M. J.; Kistemaker, J. Physica (Amsterdam) 1965, 31, 94. (19) Rapp, D.; Englander-Golden, P. J. Chem. Phys. 1965, 43, 1464. (20) Cowling, I. R.; Fletcher, J. J. Phys. E 1973, 6, 665.
5976
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
Green and c o - w o r k e r ~ ~have - ’ ~ published comprehensive lists of cross sections for inelastic electron energy transfer in many gases, including 0,. The cross sections, which are energy-dependent, give the probability that an electron of a given energy will produce a certain excited state when interacting with ground-state 0,. From Green’s reports we integrated the energy-dependent cross section for each level from 0 to 18.6 keV to obtain the integrated cross section for tritium /3 radiolysis. We were able to simplify the calculations by considering only relative integrated cross sections. The values in Table I1 are listed relative to a value of 1.00 for the band head of the X Rydberg series at 12.1 eV. The energy level diagram for O2is shown in Figure 1. The functional form of the energy dependence is quite similar for all the cross sections. They differ mainly in magnitude and threshold. From this observation we assumed the relative magnitude of the cross sections did not vary significantly from 1 to 18.6 keV. The values in Table I1 do not include integration over the electron energy distribution. This is valid because this similarity in energy dependence of the cross section allows this term to cancel when the relative integrated cross sections are calculated. Only where the threshold energies vary significantly will any error be introduced by this approximation. In a complete calculation, the relative integrated cross sections for levels with low energy thresholds would increase. The magnitude of the error due to this approximation in likely to be negligible. Most of the excited states in Table I1 are unstable with respect to dissociation, ionization or both. The last two columns of Table I1 give the probability that the excited state will decompose via a certain mode and what the products of the dissociation will be. As written in Table 11, a total of 7.68 secondary electrons are formed. To obtain the probability of formation of a given specie per electron one adds up each of the products and divides by the 7.68 electrons. We include all this detail for /3 radiolysis of oxygen by tritium because no such summary seems available elsewhere. We note in Table I1 that Green includes a series of excited 02+ states with energies more than 18.8 eV above the ground state of 0,. These states are unstable with respect to dissociation to 0 atoms and O+ions.2’ We combined our calculated 02+ values with data from two experiments. First, mass spectroscopy of and 0.25 electron-bombarded oxygen shows a split of 0.75 02+ O+ ions, with 02+ and Oz2+ions being in negligibly small conc e n t r a t i o n ~ . We ~ ~ must, therefore, take some of the Oz+ and (02+)* ions of Green’s model and dissociate them into O++ 0. Next, the fraction of O+ ions that are excited was measured:I6 0.27 at 50 eV and 0.30 at 100 eV, and we include this split. This results in the following formation probabilities per electron: 02+ 0.27; (02+)* 0.48; 0’ 0.17; (O+)* 0.083; O(3P) 0.58; O(lD) 0.42; and O* (higher states) 0.38. The O* (higher states) generally decay to the O(lD) state. We combine these together and use a value of 0.80 for the O(lD) formation probability per electron (See Table I). The radiolysis of water irradiated by electrons has also been modeled.13J4 The results shown in Table Ii3 include two excited species, although more doubtless exist. We must guess the quantity of one of them, the H20*. We consider the dissociative reaction H20* H OH (la)
+ H* + O H
-+
HzO*
(1b) and assume that half the H-OH pairs reported in ref 14 came from HzO*. We, therefore, restore half the HzO* as a direct radiolysis product. We have assumed that the singlet states of H 2 0 * are stable and that the triplet states dissociate; hence the estimate of one-half. To determine the total production of species due to radiolysis we next need the average energy taken from a kilovolt p particle needed to form secondary electrons in each of our three substances. The average energy per electron formed (ion pair) is more than the ionization potential by about a factor of 2 because a significant -+
(21) Huber, K. P.; Herzberg, G . Molecular Spectra and Molecular Structures. IV. Constants of Diatomic Molecules; Van Nostrand and Reinhold: New York, 1979; pp 504-506.
Failor et al. portion of the /3 energy goes into the nonionizing processes such as excitation and dissociation. The electron formation (ion pair) energies are listed in Table I.” This energy decreases with increasing initial electron energy, and it is constant in the kilovolt range, where the tritium’s mean energy lies. The best value for the decay heat of tritium is 1.954 f 0.0054 W/mol of T2.,, We combine this with the tritium half-life of 12.3232 f 0.0043 yearsz3 and we obtain a mean tritium beta energy of 5682 f 17 eV. We then divide this number by the electron formation (ion pair) energy to obtain the number of electrons per tritium /3 particle for a pure substance. We must add one to account for the initial /3 particle. These values are listed in Table I. In the model we used a radiolysis rate expression. This is written as the rate of seconary electron formation (ion pair) eR- for each species
SIi
5682 eV Fi = 2XcfT2)Op
i = 02,T,, or T 2 0 (2)
( e v / e-) i
where X = tritium decay constant = 1.784 X lO-’s-’, = initial mole fraction of T2, (eV/e-)i = electron formation energy for each species (seeTable I), 5682 eV = average tritium /3 energy, and Fi = fraction of /3 energy absorbed by species i. The term 2xcfT,)O gives the initial rate of /3 production. For the relatively short times we cover with this model, this is not significantly reduced by the tritium decay and is held constant in our calculations. We next need the relative amounts of /3 particle energy imparted to the 02,T2, and T20in a mixture with an initial mole fraction of tritium (fTJ0. The fraction of energy deposited into gas i is assumed to be given by 3
.h/Xffif;
Fz =
(3)
I
where the summation is over the three components and 3
Vi = 1
(4)
I
aiis the stopping power, andJ is the mole fraction of species i.
The stopping power is defined as
at a given energy E. Here, p is the mass density of the material being considered and x is the distance traveled by the /3 particle. We use the stopping powers at the tritium mean /3 particle energy of 5682 eV. The stopping powers were calculated from recently published formulas.24 The stopping powers in this reference are given in units of MeV/(g-cm-,). When we adjust the Z / A dependence in the dE/dx expression to the tritium values, the density in g/cm3 is also adjusted resulting in essentially the same relative stopping power ratios for T2:02:T20as for H2:02:H20.We converted the stopping power to MeV/(mol.cm-2) units and list the relative results (with T2 = 1.0) in Table I as ai. The assumption that the relative stopping power is independent of energy introduces some error in our calculations. The relative oxygen stopping power is 15% less at 1 keV and 7% more at 20 keV than at 5.68 keV. For water vapor, the corresponding numbers are -12% and 5%, respectively. For a given cfTt)o the denominator of eq 3 is approximately a constant. So, using eq 3, we can write eq 2 as
%Ii
= ki[i]
where kicombines all the constant factors and depends on
cfTJ0.
(22) Pillinger, W. L.; Hentges, J. J.; Blair, J. A. Phys. Rev. 1961, 121, 232. (23) Rudy, C. R.; Jordan, K. C. Tritium Half-Life; Monsanto Research Corp.: Mound Laboratory, Miamisburg, OH, 1977; Report MLM-2458. (24) Selzer, S . M.; Berger, M. J. Int. J . Appl. Radiat. Isot. 1984, 35, 665.
Reaction of T2 and O2gas
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5911
TABLE 111: Gas-Phase Reactions Used in this Model rate const! multiplier of rate const: multiplier of reaction cm'/(mohs) lit. valuek ref notes reaction cm'/(mobs) lit. valuek Ions Radicals-Tritium Atom 02' + T2-T02+ + T 1.7 X the concentrations of OT, O ' , 0, and O('D) are constant during zone IC, other radicals are building up in concentration in this zone. The T atoms, produced by the above reactions (26,28, and 16) and also by T2 radiolysis, react to form the hydroperoxo radical (TO,) T
+0 2
M
TO2
(29)
The relative contribution of each production pathway for T, OT, and TO2 is shown in Figure 5. For ozone and peroxide the production routes are simpler. The 0 atoms, formed by oxygen radiolysis, react to form ozone 0
+ O2
M
O3
(30)
This is the only important ozone production route. Peroxide is formed mainly via 2T02 T202 + 0 2 (31)
-
and a small contribution from
M
20T
T202
(32)
5982
Failor et al.
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
El
Production routes
100 50
0
02
T2
2
0
-2
4
6
Loglo time (sec)
Figure 5. Main production reactions for T, OT, and TO2 for a 1% T2 in O2system. The reactions are shown as the percent contribution to that radical vs. log time. The times of the zones are shown at the top. For T 2 0 2the production route is almost 100%2T02, and for O3 100%0 + 02,these are not shown here. 100 I
I
I
I
I
I
I
2
I
Figure 7. Schematic for water production in zone 11. Notice the added
c
.-
OT + TO2
+,
a
complexity. Ions still figure prominently. The OT production route shown in Figure 4 remains important but is not shown here. Notice the increased importance of the TO2, T202,and O3intermediates. The heavy dots indicate that the two species shown are both reactants. The bold lines indicate the main routes of direct T 2 0 production for zone 11.
0
The presence of ozone is important in these T 2 0 production pathways. The ozone introduces a new hydroxyl production route
O3 + TO2
-
OT
-
+ 202
(35)
In zone I1 several reactions combine in the following series 50
x
I-
-\. .
I1
0 3 + TO2
i O3 + 2 T 0 2
OT + TO
-
OT
+ TO2
T20+ 302
and 0
0
4
2
O3 + TO2
6
--*
OT
+ 202
(35)
+0 2
(33)
T20
(sum of eq 35 and 33)
-
OT
+ 202
(36)
(35)
Loglotime (sec)
Figure 6. Production reactions for T 2 0 for the 1% and lo4 T2 in O2 cases. The I and I1 refer to the change in mechanism from zone I to zone 11. Note the difference in the relative importance of the OT + TO2 vs. OT T 2 0 2routes in the two cases in zone 11.
+
The second transition zone begins when the concentrations of hydroperoxo and peroxide become sufficient for two new water production reactions to become important
+ TO2 OT + T202 OT
--*
+0 2 T2O + TO2 T20
(33)
O3 + 2 T 0 2
-
+ T202 T20+ 302 OT
giving for these two cycles
O3 + 2 T 0 2
+
T20
+ TO2
(34)
(sum of eq 35, 31, and 34) (36)
-
T20+ 302
(36)
in addition to
(34)
Zone IIt is present for all [T2I0shown in Figure 3. Figure 6 shows the relative contribution of the three water production reactions vs. time for two [T2I0concentrations. At the higher [T,], the concentration of T 2 0 2relative to TO2 makes eq 34 the dominant pathway.
as the overall main routes of water formation. The mechanisms active in zone I1 are shown schematically in Figure 7. The T and 0 atoms are formed by ion-electron recombination. The O3and TO2 chains are shown in parallel. The OT and T 2 0 production pathways shown in Figure 4 for zone I
The Journal of Physical chemistry, Vol. 90, No. 22, 1986 5983
Reaction of T2 and O2 gas
Heavy lines, T 2 0
Light lines, T2
03
TO2 OT
0
0
I
T
2
3
4
Time (lo6 sed
-
Figure 9. During the latter part of zone I1 and zone I11 most of the T2
O+
-16
-14
-12
-8
-10
-6
-4
-2
T 2 0conversion takes place. Shown here are Tz (light lines) and T 2 0 (heavy lines) as a percent of the [T,], vs. linear time. For the 1% T, case the third constant zone is reached near lo6 s. Here the maximum conversion has taken place. The lo4% T2 case has not reached zone IIC by 5 X lo6 s.
0
{ [species concentration] / IT2] }
Loglo
Figure 8. Bar graph of the species concentrations predicted for 1% and lo4% T2 in Ozduring zone IIc. These are the values for 2.3 X lo4 s for 1% T2 and 3.5 X lo5 s for lo4% T2. Notice these times are the center of zone IIc for each (see Figure 3). The increased importance of the OT + TOz vs. OT + T2Q2route is seen by the difference in the TOz concentration.
are still occurring but are of lesser importance and are not shown in Figure 7. In addition to the zone I mechanism, note that OT is formed increasingly by
O3 + TO2
-
+ 202
(35)
T20
+0 2
(33)
T20
+ TO2
(34)
OT
-
As shown in Figure 6, the reactions
OT OT
+ TO2
+ T202
are now the main water production routes. These are shown with bold lines in Figure 7. The net rate of T 2 0 production in zone I1 can be expressed as (37) The values of n and k vary with time in zone 11; early in zone IIt the values are on the order of 0.7 and 10l6 (with appropriate units), respectively, whereas in zone IIc they are closer to 0.5 and 3 X 10'7. The beginning of the second constant zone, IIc, occurs when the ozone and hydroperoxo concentrations reach steady state. The main hydroperoxo destruction routes are
- + - + + - + + - +
+ TO2 TO2 + O3
TO2
T202
OT
0 2
202
(31) (35)
The ozone destruction occurs via the reaction in eq. 35 and also by
0
O3
02(12,)
202
(38)
02('2,)
(39)
The 02('Z,) is produced by O(lD)
0 2
0
(Undesignated states imply the electronic ground state.) The relative importance of the various intermediate species is shown graphically in Figure 8. Plotted here is the logarithm of the specie concentration divided by the initial T2 concentration for and 1.0% [T2I0. These are the values for the systems in the middle of zone IIc. As mentioned before, the [T202]/[T02] ratio is greater at the higher T2 concentration. This explains the differences in the importance of the different pathways shown in Figure 6.
The ion chain shown at the top of Figure 7 contributes to three TO2+, features of zone 11. The ion-electron recombination of 02+, and T3+ are sources of 0 and T atoms which are important in ozone and hydroperoxo production. The T3+ion is important in T 2 0 removal. The reaction T3+ + T 2 0
-
T 3 0 + + T2
T3+ + T 2 0
-
T30+
(20) is one of the reasons for the eventual decrease in dT20/dt seen in zone 111. The decline in the net T 2 0 rate marks the beginning of zone 111. The bulk of the T2 reacts and ultimately forms T 2 0 between lo5 and lo6 s. This is shown graphically in Figure 9. The T2 and T 2 0 concentrations are shown as a percent of the initial T2 concentration. The decline in T2 decreases the OT and T formation, which affects the TO2 and T 2 0 2concentrations with the decrease in these main species. In zone I11 the T 2 0 production is essentially over. Several T 2 0 depletion reactions become significant as the T 2 0 concentration increases. These depletion reactions are O('D)
+ T20
-
+ T2
20T
(20) (40)
T 2 0 radiolysis (41) The rate of decline in the T2 concentration varies significantly with the initial T2 concentration (see Figure 9). As shown in Figure 3 a third constant zone is reached for 1% [T2I0at about lo6 s. In this zone the system reaches a dynamic equilibrium where T2 depletion and production balance. The model has not been run to times necessary to reach zone IIIc for T2concentrations less than 1%. Since the model was not constructed to handle the details of the system when the [T20]/[T2] ratio is large, our results for very long reaction times should be viewed with caution. Summary This report contains the first detailed mechanistic analysis of the homogeneous gas-phase oxidation of tritium. Certain oxygen radiolysis products and ions which were never before considered, O+,O[lD), and OT', proved to be crucial in the mechanisms. Three major mechanisms and their time zones were identified. Two zones are responsible for the major T2to T20conversion with the last zone being the approach to equilibrium between T 2 0 destruction and production. In the first two zones, the rate expressions for T 2 0 were determined. Briefly, the mechanism for zone I is shown in Figure 4. During the transition part of zone I the rate expression for water formation is
d[T2O] /dt = k[OT] [T2] For initial concentrations T2 greater than 1.7 X
(24) a zone is
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J . Phys. Chem. 1986, 90, 5984-5989
reached where the hydroxyl concentration is at steady state. The rate expression remains the same as in eq 24 but is constant in zone IC. The mechanism changes as the hydroperoxo, peroxide, and ozone concentrations increase. This marks the beginning of zone I1 whose mechanism is shown in Figure 7. The rate expression in zone I1 is
In future publications we will address the effects of initial concentration of tritium radiolysis products on the production of T 2 0 and make direct comparisosn of our modeling results and existing experimental data. The latter is of great interest because results in the experimental literature do not agree on the order, with respect to [TJ, of the overall T2to T 2 0 conversion kinetics. This work shows that no simple expression is valid over the entire time of the oxidation reaction in the gas phase.
(37)
Acknowledgment. We thank C. K. Westbrook, F. Magnotta, W. L. Morgan, and M. L. Koszykowski for their helpful discussions; c. Gatrousis, R. W. Buddemeier, and W. J. Shotts for their continued support of this research; and M. A. Litterst for her clerical efforts. This work was performed under the auspices of the U S . Department of Energy by the Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48.
where n varies from 0.7 in zone IIt to 0.5 in zone IIc. A sharp decrease in d[T20]/dt marks the beginning of zone I11 and essentially the end of the T2to T 2 0conversion. Depletion reactions for T20become more important at this time. Eventually an equilibrium between T 2 0formation and depletion is achieved.
A Laser Flash Photolysls Study of 2,6-Dlmethyl-3,5-diphenyl-4-pyrone and Related Chromones. Evidence for Triplet State Structural Relaxation from Quenching Behaviors‘ K. Bhattacharyya,t D. Ramaiah,t P. K. Das,*+ and M. V. George*+*# Radiation Laboratory and Chemistry Department, University of Notre Dame, Notre Dame, Indiana 46556, and Chemistry Department, Indian Institute of Technology, Kanpur 208016, India (Received: April 14, 1986)
The 308- or 337.1-nm laser excitation of 2,6-dimethyl-3,5-diphenyl-4-pyrone( l ) , 2-phenylchromone (2), and 2,3-diphenylchromone (3) results in the formation of short-lived triplets (T: = 1-5 ps, Af, = 330-365 nm) in high yields (0.5-1.0 in benzene). From phosphorescence spectra at 77 K, the spectroscopic triplet energies of these aromatic enones are estimated at 69,62, and 67 kcal mol-’, respectively. However, in fluid solutions at room temperature, the triplets of 1 and 3 (as monitored by transient absorption) are poorly quenched by 1-methylnaphthalene (ET= 59.6 kcal mol-’), dienes (ETz 59 kcal mol-’), and ferrocene (ETz 40 kcal mol-’). In spite of the apparent exothermicity, the energy-transfer processes are inefficient; this suggests geometric distortion in these triplets, very probably in the form of partial twisting about the ene double bonds, causing a lowering of vertical energy (at relaxed geometry) by -30 kcal mol-’. The quenching behavior of the triplet of 2, however, is “normal”, the rate constants for quenching by the above-mentioned quenchers being in the limit of diffusion control. A major reason for the excited-state torsional distortion in 1 and 3 appears to be the steric interaction between adjacent substituents (phenyl and methyl) on the carbon atoms of the ene double bond.
Introduction The interesting photochemical rearrangement of hindered 4pyrones (I) to 2-pyrones (11) under steady-state irradiation has been studied quite extensively by Ishibe and c o - w ~ r k e r s ~(see -~ Scheme I). Mechanistically, the photoreaction has been shown to be singlet-mediated.4 It apparently involves initial photo1-one (111) through isomerization to a 4,5-epoxycyclopent-2-enthe intermediacy of a dipolar species (IV). The photorearrangement of I to I11 is analogous to that of cyclohexa-2,5-dienones to bicyclo[3.1 .O]hex-3-en-2-ones6 and has been suggested’ as a sequence in the phototransformation of 2,6-disubstituted 4-pyrones to 2,6-disubstituted 2-furaldehydes. The intermediacy of the zwitterionic species, IV, and epoxycyclopentenone, 111, is also indicated by steady-state photochemical of several methyl- and methoxy-substituted 4-pyrones in nucleophilic solvents (alcohols). In order to shed light on the intermediates participating in the photochemistry of 4-pyrones, we have carried out a nanosecond laser flash photolysis study of 2,6-dimethyl-3,5-diphenyl-4-pyrone (1) and two related chromones (2 and 3). Although our original interest lay in the spectral and kinetic properties of the zwitterionic ‘Radiation Laboratory, University of Notre Dame. !Chemistry Department, Indian Institute of Technology. Chemistry Department, University of Notre Dame.
0022-3654/86/2090-5984$01.50/0
0
I
u
0
2
0
3
u
intermediate, IV, the transient absorption phenomena resulting from laser flash excitation of 1 in various solvents were found to be dominated by its triplet and very little information could be obtained about the zwitterionic species. Interestingly, however, (1) The work described herein was supported by The Office of Basic Energy Sciences, Department of Energy. This is Document No. NDRL-2846 from the Notre Dame Radiation Laboratorv. (2) Ishibe, N.; Odani, M.; Sunami, M. Chem. SOC.,Chem. Commun. 1971. 1034-1035. (3) Ishibe,~N.;Sunami, M.; Odani, M. J . Am. Chem. SOC.1973, 95, 463-468. (4) Ishibe, N.; Yutaka, S. J . Org. Chem. 1978, 43, 2138-2143. (5) Ishibe, N.; Yutaka, S.; Masui, J.; Ihda, N. J . Org. Chem. 1978, 43, 2144-2 148. (6) For reviews, see Zimmerman, H. E. Angew Chem., Int. Ed. Engl. 1969, 81,45-55. Kropp, P. J. In Organic Photochemistry, Chapman, 0. L., Ed.; Marcel Dekker: New York, 1967; Vol. 1, pp 1-90. (7) Yates, P.; Still, I. W. J. J . Am. Chem. SOC.1963, 85, 1208-1209. (8) Barltrop, J. A.; Day, A. C.; Samuel, C. J. J . Chem. SOC.,Chem. Commun. 1977, 598-599. (9) Pavlik, J. W.; Pauliukonis, L. T. Terrnhedron Lett. 1976, 1939-1942.
0 1986 American Chemical Society
