J . Phys. Chem. 1988, 92, 3011-3017 to a factor of 10 lower than at pH = pK(H2P04-) - 1.02, proving that H+ determines the overall rate of disappearance at all temperatures. At ambient temperature and up to 100 OC reaction 6 is rate determining with an activation energy of 7.6 f 0.8 kJ mol-l (1.8 f 0.2 kcal mol-') and a rate constant k6 = (9.6 1.0) X lo7 dm3 mol-' s-l at 20 O C . These figures are in agreement with reported data.6 Above 100 "C the rate constant calculated as k6 (Figure 5 ) increases drastically, and the linearity of the Arrhenius plot in the temperature region 20G320 OC suggests that a new reaction becomes rate determining. The activation energy determined at these high temperatures is very large, EA = 80 f 12 kJ mol-' (19 f 3 kcal mol-'). From eq V an overall decay rate constant of k7 = 1.0 X 1Olo mol-' s-l may be calculated at pH 5.64 and at 285 "C (reactor conditions). At higher pH's the rate constant decreases linearly with the H+ concentration. As a tentative explanation for this behavior, a mechanism of reaction 7a followed by reaction 7b is suggested:
*
+
- + - -
02- 02- 04*-
+
042- H+
H02-
O2
(7a) (7b)
The forward reaction in equilibrium 7a is slow at low temperature but may have a high activation energy. The back-reaction (-7a) may be fast as suggested18 from the reaction
+
03- 0-
(042-) 20,
(8)
(18) Sehested, K.;Holcman, J.; Bjergbakke, E.; Hart, Edw. J. J . Phys. Chem. 1982,86, 2066.
3011
where 02-is formed concomitantly to the disappearance of 03-. The rate constant k-7a may therefore be higher than lo4 s-I at room temperature. If the measured activation energy of 80 kJ mol-l is ascribed to the equilibrium 7a, the rate constant will increase by a factor of lo7going from 20 to 285 OC. This indicates that reactions 7a and 7b may be rate determining at high temperature but are negligible at room temperature, where reaction 6 is dominating. Reactions 7a and 7b exhibit the same pH dependency as reaction 6. However, at pH -7 with different buffer concentrations (10-3-10-1 mol dm-3 phosphate) the same 0; decay rate is observed. This is unexpected if reaction 7b was rate determining and indicates that the decay mechanism is more complex and involves an acid-base equilibrium. A plausible explanation may be based on an unstable intermediate
+
042- H+
HOC
-+
HOF
H04-
(9a)
+ 0,
(9b)
Reactions 6,7a, 9a, and 9b can account for all our experimental results in the pH region 5-9 and at temperatures from 20 to 300 OC.
Acknowledgment. T. Johansen and H. Corfitzen are gratefully acknowledged for technical assistance, and we thank J. Holcman for valuable discussions. H.C. gratefully acknowledges financial support from OKG, Sydkraft, and Vattenfall (The Swedish State Power Board). Registry NO. HOz, 3170-83-0; O,, 11062-77-4; 0:-,75968-88-6; H', 12586-59-3; HOZ-, 14691-59-9; 0 2 , 7782-44-7.
Pulse-Radlolysis Study on the Yield of Hydrated Electron at Elevated Temperatures H. Shiraishi,* Y. Katsumura, D. Hiroishi, K. Ishigure, Department of Nuclear Engineering, Faculty of Engineering, University of Tokyo, 7-3- 1 , Hongo, Bunkyo- ku, Tokyo, Japan 1 1 3
and M. Washio Nuclear Engineering Research Laboratory, Faculty of Engineering, University of Tokyo, Tokai-mura, Naka-gun, Ibaraki, Japan 319-11 (Received: September 16, 1987; In Final Form: December 28, 1987)
A pulse-radiolysis technique has been used to estimate G(e,[) at elevated temperatures up to 250 OC. Observation in pure water indicated that absorbance at A,, of e,; increases significantly with temperature, by 1.4 times in going from 20 to 250 OC, when compared at supposedly equivalent times by which most of spur decay probably finishes at each temperature. This temperature dependence was considered to arise primarily from variation in G(eaq-)itself. In another series of experiments Cd2+was used as an e,; scavenger. The estimated G(Cdf) in a dilute CdZ+solution was 3.5 and 3.8 respectively at 200 and 250 OC in accord with the above estimation on the temperature dependence of G(eaq-).
Introduction In the field of nuclear-reactor chemistry the necessity for a better understanding of the consequence of radiolysis in the primary cooling water has been widely Especially problems about the yield of oxygen and of hydrogen peroxide have been matters of concern, since these products may add a detrimental condition to the occurrence of stress corrosion cracking of 304 stainless steeL2v3 In this connection an effect of adding hydrogen to feed water of a boiling water reactor has recently (1) Burns, W. G.; Moore, P. B. Radiat. Eff. 1976, 30, 233. (2) Christensen, H. Radiat. Phys. Chem. 1981, 18, 147. (3) Indig, M. E.; Cowan, R. L. Proceedings of the 2nd International Conference on Water Chemistry of Nuclear Reactor System, Bournemouth, U.K., 1980; British Nuclear Energy Society: London, 1980; p 73.
0022-3654/88/2092-3011$01.50/0
been examined in real power plant^.^,^ Analysis of such experiments requires basic data on the radiolysis of water at high
temperature^.^,^ Although considerable efforts have recently been devoted, notably by Christensen and Sehested,8 to measurements on the (4) Magdalinski, J.; Ivars, R. Trans. Am. Nucl. SOC.1982, 43, 323. (5) Burley, E. L.; Wong, T. L.; Law, R. J.; Cowan, R. L. Trans. Am. Nucl. SOC.1982, 43, 322. ( 6 ) Ibe, E.; Uchida, S . Nucl. Sci. Eng. 1983, 85, 339. (7) Ishigure, K.; Takagi, J.; Shiraishi, H. Radiat. Phys. Chem. 1987, 29, 195. (8) Christensen, H.; Sehested, K. Radiat. Phys. Chem. 1980, 16, 183; Radiat. Phys. Chem. 1981, 18,723. Christensen, H.; Sehested, K.; Corfitzen, H. J . Phys. Chem. 1982, 86, 1588. Christensen, H.; Sehested, K. J. Phys. Chem. 1983, 87, 118.
0 1988 American Chemical Society
3012 The Journal of Physical Chemistry, Vol. 92, No. 10, 1988
temperature dependence of related reaction rates, the present knowledge on radiation chemistry of an aqueous system at high temperatures is still quite insufficient. Particularly, conflicting results have been reported on the G values of primary species. (A G value is taken here as a number of molecules produced per 100 eV of absorbed energy. A notation such as Geacrefers to the so-called G value corresponding to yield of the specles that escapes out of spurs to participate in homogeneous reactions in an experiment with low solute concentration. Another notation, G(eaq-), is used in a more general sense.) On the basis of a y-radiolysis study with various additives, Burns and Marsh9 have reported that the G value of hydrated electron, Ge,? reduces from 2.65 at room temperature to 0.4 a t temperatures above 300 "C, while GOH increases with the same change in temperature eventually through production of atomic oxygen. This result is contradictory to the previous observation by Jha, Ryan, and Freeman,lo who had measured Gee; up to 300 "C using SF, as an electron scavenger. These authors had obtained the result that Geaq-increases with temperature to a value of 4.8 at 300 OC.Io More recently, Christensen and Sehested" have reported about a pulse-radiolysis study on an alkaline solution pressurized with hydrogen and have suggested little change, or slight increase, with temperature for the sum of Geaq-and GoH. A few groups of researchers have made measurements on the temperature dependence of ferric ion yield in a Fricke dosimeter system above 100 0C.7912-14In deaerated ferrous solutions G(Fe3') is generally found to be almost independent of temperature up to 250 "C, while the reported results on G(Fe3+) in aerated solutions are comparatively scattered. Either little change7.l4or increase13 in Grd, namely Geaq'+ GH, has been suggested in this strongly acidic solution. The present study was undertaken primarily to contribute to the above problem on the yield of eaq- at high temperatures. A nanosecond-pulse-radiolysis technique was applied to observe variation in the intensity of e,; absorption in pure water up to 250 "C. The spectra of e,; at high temperatures have already been reported by several groups of worker^.^'^'^'^ In these studies attention has been paid mostly to change in the spectral characteristic, though some discussions have been made on the spectral intensity in a paper by Michael, Hart, and SchmidtI5 as well as in the above-cited study by Christensen and Sehested.]' Naturally, ambiguity persists in the interpretation of change in absorbance, because the absorption coefficient may vary with temperature. In the present work another series of pulse-radiolysis experiments were carried out to estimate the yield of e, -,utilizing cadmium ion, Cd2+,as an e,; scavenger. The reasons lor the choice of Cd2+ are that the scavenging rate is known to be very fast and that the produced monovalent Cd+ ion reportedly possesses strong absorption in the UV It was expected that uncertainty in variation of the absorption coefficient might be reduced in this case, if the spectral change of Cd+ with temperature is very little. Although this expectation was not completely met in reality, the stability of Cd+, which had been another concern, was found to be reasonably high even at 250 "C. Attempts were, therefore, (9) Burns, W. G.; Marsh, W. R. J. Chem. Soc., Faraday Trans. 1 1981, 77, 197.
(IO) Jha, K. N.; Ryan, T. G.; Freeman, G. R. J . Phys. Chem. 1975, 79, 868. (1 1) Christensen, H.; Sehested, K. J . Phys. Chem. 1986, 90, 186. (12) Kubota, H. J. Inorg. Nucl. Chem. 1966, 28, 3053. (13) Kabakchi, S . A,; Lebedeva, I. E. Khim. Vys. Energ. 1984, 18, 206; Khim. Vys. Energ. 1986, 20, 397. (14) Katsumura, Y.; Takeuchi, Y.; Ishigure, K. Radiat. Phys. Chem., in press. (15) Michael, B. D.;Hart, E. J.; Schmidt, K. H. J. Phys. Chem. 1971,75, 2798. (16) Gaathon, A.; Czapski, G.; Jortner, J. J . Chem. Phys. 1973,58, 2648. (17) Dixon, R. S . ; Lopata, V. J. Radiat. Phys. Chem. 1978, 1 1 , 135. (1 8) Baxendale, J. H.; Fielden, E. M.; Keene, J. P. Proc. R . Soc. London, A 1965,286, 320. (19) Buxton, G . V.; Sellers, R. M. J . Chem. Soc., Faraday Trans. 1 1975,
-.(20) Kelm, M.; Lilie, J.; Henglein, A. J . Chem. Sac., Faraday Trans. 1
71 558.
1975, 71, 1132.
Shiraishi et al. made to observe the scavenger-concentration dependence of G(Cd+) at 20, 200, and 250 OC.
Experimental Section The accelerator used is an S-band ML35-L linac (Nuclear Engineering Research Laboratory, the University of Tokyo), which produced a 2-11s electron pulse with an energy of 35 MeV within a diameter of 3 mm. The pulse beam entered perpendicularly to one of the nearly flat optical windows of a cylindrical pressure-resistant Suprasil cell, which was placed in the center of a heater unit that had two opposite apertures for the electron beam and analyzing light. For experiments up to 200 OC a cell that had an internal diameter of 7 mm and an external diameter of 12 mm was used, while at 250 "C it was replaced by a smaller cell of 4 mm in internal diameter and 9 mm in external diameter. The optical path length was 20 mm for the both types of cells, and the analyzing light was let pass parallel to, but in an opposite direction against, the electron beam. To introduce sample solution, the cell was joined with a branch tube, which was also used for pressurization during heating. The pressure was raised with argon gas to about 5 X lo5 Pa above the saturation pressure at each temperature. The dosimetry was made at room temperature with an aqueous KSCN solution of 1 X lo-* mol dm-3 saturated with N 2 0 . A value of 46400 (molecules/100 eV) mol-' dm3 cm-I was assumed for the product of yield of (SCN)T and its absorption coefficient at 472 nm.21 This measurement gave an average dose in a central region of sample solution, 3 mm in diameter, to which the analyzing light was limited. Scattering of an electron beam both by the cell window (3 mm thick) and by the sample itself was presumed to cause considerable dose inhomogeneity in the sample along the direction of an incident beam. It was anticipated that the extent of scattering might change with density of water, which decreases to 0.799 g cm-3 at 250 "C, resulting in variation in an average dose per unit beam input. The following reference experiment was performed to check this point. Model samples, each of which consisted of four pieces of blocks, were prepared from plastic materials with three different densities, ranging from 0.89 . were pulse-irradiated with a pair of 3to 1.38 g ~ m - ~These mm-thick quartz disks attached at both sides and with five sheets of Radiochromic film22inserted in each gap between the component blocks. Coloration of the films was then examined, and the result suggested that the average dose in fact increases by a factor of 1.04 for a density decrease from 1.O to 0.799 g cm-'. This effect of density was, therefore, taken into account in the estimation of pulse doses for water samples at high temperatures. It was also found at the same time that dose distribution along the axial direction was such that the ratio of doses at both ends of a 20-mm sample was 0.35 when the sample density was 0.89 g ~ m - The ~ . dose for each pulse was monitored by a current from a beam stopper placed downstream to the optical cell, and the accelerator was ordinarily readjusted when the pulse intensity decreased to about 70% of an initial setting. However, slight variation in the actual dosage per monitor reading, which is estimated to be less than &6%, was inevitable due probably to change in the position of beam input against the optical cell. The measurement of absorption was made with an optical assembly that consisted of a flash lamp (EG&G FX279U), collimating lenses, a pair of thin mirrors placed in the electronbeam path, and a monochromator (Ritsu Oyo Kogaku MC-10). In most experiments either a 100- or a 500-ns sweep was used, but the intensity of light from the flash lamp varied appreciably during the latter sweep. Although this variation was corrected in each time-profile run, a considerable error was inevitable when the absorbance was small. One had to choose reasonable data from repeated measurements. The light intensity decreased seriously below 290 nm and above 800 nm. The band-pass of the monochromator was ordinarily set to 10 nm.
-
(21) Schuler, R. H.; Janta, E.; Patterson, L. K. J . Phys. Chem. 1980, 84, 2088. ( 2 2 ) Radiochromic films are from Far West Technology, Ltd., U S A .
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988 3013
Yield of eaq- at Elevated Temperatures
a
t
I
2l I ' ~1
I
100
200
300
460
'
'
0
Time / ns
200
100
300
400
Time / n3
Figure 1. Time profiles of eag- absorption in pure water irradiated at 20 "C with three different pulse doses: (1) 3.8 Gy; (2) 8.8 Gy; (3) 20 Gy. The observation was made at 720 nm. The unit for GeT2,,is (molecules/100 eV) dm3 mol-' cm-'.
A PIN photodiode (Hamamatsu Photonics S1722-01) with a 300-MHz bandwidth was used as a detector for the measurement of e,; absorption, while it was replaced by a biplanar photodiode (Hamamatsu Photonics R1328U-02; 60-ps rise time) in the measurement of UV absorption of Cd+.23 The output of the detector was directly fed into a transient digitizer (Tektronix Type 7912 with a 7A19 amplifier), which had a bandwidth of 500 MHz. The signal was then processed by a minicomputer. The overall response of the system was such that e,, absorption rose completely to a maximum at 5 ns after the end of a 2-11s pulse. Triply distilled water was used in preparing sample solutions. Reagents C d S 0 4 (Nakarai Chemicals G R grade) and KSCN (Koso Chemicals GR grade) were used as received. Solutions were deaerated by bubbling Ar gas (Iwatani Sangyo), and a syringe technique was used for injection into an optical cell. In order to prevent bubble formation in the optical cell during heating, it was necessary to fill the branch tube so that a top portion of liquid was well out of the heater unit to be cooled down by ambient air.
Results and Discussion Observation of e,{ in Pure Water. In Figure 1 is shown the time variation of eaq absorption at 20 "C. The sweep range is 500 ns, and the measurements were made at 720 nm, near the absorption maximum of eaq-. The three traces in the figure are those measured with pulses of different doses varied approximately in a ratio 1:2:5 (these are referred to as low-, intermediate-, and high-dose traces). The ordinate is taken to be the product of the yield, G(eaq-), and the molar absorption coefficient of e - at 720 nm, ~ 7 2 3 . It is seen that there is a rapid initial decay of e", which is followed by a much slower decrease. During the first 70 ns the three traces almost overlap in this dose-normalized presentation, indicating that the initial decay is due primarily to intraspur reactions. Difference in the decay rate becomes apparent in the later stage, which must reflect an effect of spur overlapping. The measurements were also made with a faster sweep of 100 ns. Assuming €720 to be 1.85 X lo4 mol-' dm3 ~ m - ' , ' ~G(e,,3 at 5 ns after the end of a pulse was estimated to be 3.45 f 0.20 in reasonable agreement with the reported valueF5 The yield reduces to 85% in 70 ns, and after 300 ns G(e,,-) is 2.67 f 0.15 in the low-dose (3.8 Gy) trace in Figure 1. Trumbore et al. have studied pulse-dose dependence of e,; decay in pure water in a time range from 30 ns to 1 psZ6 The respective time profile in Figure 1 agrees very well with the corresponding result reported by them except that the absolute value is 6% larger in the present work. Since Trumbore et al. observed very little change in the decay profile below 3 Gy, the 3.8-Gy trace in Figure 1 is presumed to ap~
(23) Occasionally it was substituted by another PIN photodiode (Hamamatsu Photonics S1722-02) with a 100-MHz bandwidth. (24) Hart, E. J.; Anbar, M. The Hydrated Electron; Wiley-Interscience: New York, 1970 p 40. (25) Jonah, C. D.; Matheson, M. S . ; Miller, J. R.; Hart, E. J. J . Phys. Chem. 1976, 80, 1267 and references therein. (26) Trumbore, C . N.; Youngblade, W.; Short, D. R. J. Phys. Chem. 1984, 88, 5057 and earlier papers of this series.
Figure 2. Time profiles of ea; absorption in pure water irradiated at 100 O C with three different pulse doses: (1) 3.6 Gy; (2) 8.6 Gy; (3) 20 Gy. The observation was made at 800 nm. The unit of the ordinate is the same as in Figure 1, and in this figure 14% adjustment was allowed to equalize initial GeBWat 5 ns.
4
O
W
4
100
200 Time / n s
300
400
Figure 3. Time profiles of eaq-absorption in pure water irradiated at 200 OC with three different pulse doses: (1) 3.9 Gy; (2) 8.7 Gy; (3) 20 Gy. The observation was made at 800 nm. The unit of the ordinate is the same as in Figure 1.
proximate a decay pattern in the low-dose limit. Similar measurements were performed at 100, 150, 200, and 250 "C. The spectrum of ea,- is known to undergo large bathochromic shift with t e m p e r a t ~ r e , " ~ ' ~but - ' ~ in the present study observations were made only at 800 nm due to an instrumentational reason. Figures 2 and 3 show the observed results at 100 and 200 "C, respectively. It is clearly seen from the dose-varied traces that the decay by interspur reactions following spur overlap is sped up with temperature. This makes it difficult to estimate time variation of G(eaq-)ein the absence of spur overlapping. In principle one should lower the beam intensity until the normalized decay curve becomes independent of a pulse dose. Such measurements were difficult to be made in the present experimental setup,27 and we have to make reasonable estimation from the measured dose-dependent profiles. As mentioned above, at 20 "C the three dose-normalized traces overlapped for the initial 70 ns. Figures 2 and 3 show that such period of the same relative decay is much shorter at higher temperatures when a similar dose range was used. Yet, even at 250 "C the optical density at 5 ns after the end of a pulse was found proportional to pulse dose, indicating that the value at 5 ns may at least be regarded to be free from the effect of spur overlapping. Alternatively, decay due to interspur reactions was in fact not so fast even at 250 "C as to cause significant decrease of e,; within 5 ns. Unlike the decay profile at 20 "C no distinct initial fast decrease was seen at high temperatures, though slight indication of spur decay could be recognized at 100 "C for the first 20 ns. This suggests that most of the intraspur decay, if it exists, must have taken place before the rise of the absorption signal. In fact it was presumed that the observed decay after 20 ns at 100 "C and that after 5 ns at higher temperatures are due mostly to bulk interspur reactions even in the low-dose traces examined here. This presumption is based on the finding that the absolute decay rate in (27) The problem was mainly insufficient reproducibility in the temporal profile of the analyzing light (see Experimental Section).
3014
The Journal of Physical Chemistry, Vol. 92, No. 10, 1 F188
Shiraishi et al. Temperature / 250 200
150
-
OC
50
100
20
u)
I
-
._ 5 20
["
14
N 20
;
10
2
n \
; i
10
P)
2
50
0;
150
100
200
250
'
y
"C
Temperature /
1
Figure 4. Plot of Gc,, for e,, in pure water against temperature. The
points marked with 0 are values at 5 ns after the end of a pulse, while those marked with 0 are at t*'s by which most of spur decay is presumed to finish at each temperature. The assigned t*'s are 100, 22, 13, 10, and 7 ns, respectively, for 20, 100, 150, 200, and 250 OC. The data for t * ' s are from low-dose (-4 Gy) traces. each low-dose trace differs little from that in the later stage of the intermediate-dose trace, when e,, concentration is the same. Although this reasoning is not strict, the suggested extent of shortening in the period of intraspur decay is certainly as expected from the view that the spur processes, including reactions and diffusive motion, are accelerated proportionally to an increase in the rate of diffusion in water (see discussion below). The result of the scavenging experiment was also consistent with such a view. Figure 4 shows the temperature dependence of G(eaq-)tmaX at 5 ns after the end of a pulse, where -e is the maximum absorption coefficient at the respective temperature. The values for a ratio esOO/c,,, were evaluated from the published eaq-spectra at high temperature^.",'^ The employed ratios at 100, 150, 200, and 250 "C are respectively 0.99, 0.89, 0.77, and 0.68. These values are presumed to be accurate within f4%,28and probable errors for G(eaq-)emaxa t high temperatures are estimated to be *lo%, including an error in dose estimation. Also included in Figure 4 are the values of G(eq-)e- at tentatively assumed equivalent times by which most of the spur decay probably finishes at each temperature. These times, designated as t*'s, have been assigned inversely proportional to the setfdiffusion coefficient, D,of starting with 100 ns at 20 O C . The respective values of t*'s are given in the figure legend, and the low-dose traces were used for this plot. For convenience the temperature dependence of D, reproduced from an N M R study by Hausser, Maier, and N ~ a c k : ~ is shown supplementarily in Figure 5. It is seen in Figure 4 that though G(3-)emax a t 5 ns exhibits a minimum around 100 OC, the value at t increases monotonously with temperature. Michael et al. reported that in a range from 4 to 90 O C C(ea,)e,,, increased with a small temperature coefficient of (19 f 6)/OC,ls while Jou and Freeman noted that G(eq-)e, at 107 OC was nearly the same as, or 2-3% larger than, that at 25 Both of these studies are presumed to have measured the value near the end of the spur decay, and the present result at 100 "C is consistent with them. More recently, Christensen and Sehested have observed variup to 300 OC in an alkaline solution pressurized ation of G(e,Jt,, with hydrogen." In this solution OH radical is converted into eaq- through reactions 1 and 2:
OH H
+ Hz
+ OH-
-
HZ0
+H
eaq- + H 2 0
-
(1)
+ e,, + 2H+
H,
2 2.0
2.5
3.0
.E
3.5
T-1 ,/ 10-3.K-1
Figure 5. Arrhenius plot of kc,,,,;' (m), where k is an apparent secondorder rate coefficient for bulk decay of e,- in pulse-irradiated pure water. The values were obtained from analysis of high-dose (-20 Gy) traces. The point at 20 "C is probably overestimated because of overlapping of intraspur decay. Also included here are the values of the self-diffusion coefficient ( 0 )of water taken from ref 29.
imum at 150 "C. The decrease in the decay rate of eaq- above 150 O C seems to have facilitated observation of G(eaq-)c,,, free from the effect of interspur reactions, even though time resolution was of a submicrosecond order. According to them, G(eaq-)emax continues to increase up to 300 O C with almost the same slope as that below 100 "C, and the value at 250 OC is about 10% larger than that at 20 "C. An extent of increase in G(eag-)tmaxat t* is significantly larger in Figure 4. The situation is certainly different in this comparison, because contribution from OH radical is added to eaq-yield in their study. It was noticed, however, that a considerable part of the above difference may be ascribed to the probably unnecessary correction made in their study concerning intraspur scavenging of OH radical. That is to say, extrascavenging by hydrogen was supposed to take place because of an increase in the rate of reaction 1 at high temperatures, and accordingly each of the observed G(ea()emax above 100 OC was subtracted by an amount evaluated in reference to a relevant scavenging experiment at room temperature." This correction is probably unnecessary because the reported degree of increase in the net rate of reaction 1, the product of the rate coefficient and Hz concentration, is no more than the presently estimated acceleration in the rate of the spur process. Their raw data before the correction indicate that G(eaq-)e,,, at 200 and a t 250 OC are respectively aout 1.17 and 1.28 times as large as that at 20 OC. The corresponding ratios for G(eap)emaxat t* are 1.24 and 1.41 in the present work. Though the relative increase appears still somewhat larger here, the difference might be regarded to be within experimental errors. It then follows that the ratio of the yield of OH to that of eaq-is probably close to unity a t least up to 250 OC. This remark is not an obvious one, since variation in this ratio is not necessarily i m p r ~ b a b l e . ~ It is difficult to give a strict argument about temperature dependence of C(e,;) because of uncertainty in the variation of tHowever, the reported change in the spectral width of eq- suggests that ,e, is probably not very sensitive to temperature. At temperatures below 107 OC detailed analysis on the eaq-spectrum has been made by Jou and Freeman,3oaccording to whom normalized integrated spectral intensity, defined by Z = Se/e,,,
dE
(4)
(2)
Interestingly, at pOH below 4 the recombintion reaction of eaqe,,
2
(3)
was found to show non-Arrhenius behavior, the rate being max(28) The values at 150 and 250 OC were estimated by interpolation. (29) Hausser, R.; Maier, G.; Noack, F. 2. Naturforsch., A : Astrophys., Phys. Phys. Chem. 1966, ZlA, 1410. (30) Jou, F.-Y.; Freeman, G . R. J . Phys. Chem. 1979, 83, 2383.
where E is photon energy, increased by 3.5% in going from 20 to 107 O C . A slight increase in the red-side half-width is responsible for this change, and this tendency was also noted by Christensen and Sehested to continue up to 1.50 OC." On the other hand, Michael et al. have reported that in a range from 200 to 390 "C the full width at half-maximum was nearly constant and besides is smaller than that at 25 OC.15 The difference from the room temperature width was, however, at most 7%, and it might partly have arisen from the use of DzO in their high-temperature measurement^.'^,^^ Therefore, if the oscillator strength, which
Yield of eaq-a t Elevated Temperatures
The Journal of Physical Chemistry, Vol. 92, No. 10, 1988 3015
should be approximately proportional to Zemax,31 is taken to be nearly constant, so must be emax as well. The constancy of tmax has also been noted for solvated electrons in alcohols,32 though the examined temperature range is much lower. It thus seems quite likely that the temperature dependence of G(ea;)emax is dominated by that of G(eaq-). As described later, the results of the scavenging experiments turned out to reinforce the above view that emx of eaq-is nearly constant and that G(e,,-) at the end of the spur decay increases with temperature up to 250 O C . Although detailed analysis on bulk reactions after spur overlapping is difficult, a simple trial has been made by assuming a second-order decay for eaq-. The reciprocal plot of the optical density generally showed significant concave upward curvature except in the initial spur-decay period a t 20 and 100 "C, where reversed curvature was apparent. Further, at the same temperature the slope of the reciprocal plot increased with the decrease of a pulse dose, when compared in the same time region (about 1.5 time increase in going from 4 to 20 Gy). These probably indicate involvement of quasi-first-order reactions. Some impurity might have been present, but another possibility may be a reaction between e,; and H+ in the bulk phase. The dissociation of water is known to increase with temperature, and H+ concentration amounts to 2 X 10" mol dm-3 in pure water at 200 0C.33 Figure 5 shows an Arrhenius plot of k/emax,where k is an apparent second-order decay rate, which was evaluated from early 100-ns decay in each high-dose (20 Gy) trace, excluding naturally the spur decay period. The content of k is not clear, and considerable inhomogeneity exists in the dose distribution, as mentioned under Experimental Section. Nevertheless, if emax is nearly independent of temperature, one can roughly estimate temperature dependence of eaq-reactions common with those taking place in spurs. The observed increase in k/tmaxat 200 OC is roughly of the same magnitude as estimated by Michael et al. from e,; signal ~ Arrhenius plot in Figure 5 intensity during a 3-ps p ~ 1 s e . lThe appears to be nonlinear and it looks as if this nonlinearity parallels with that of D, the self-diffusion coefficient of water. Alternatively, if one simply calculates an activation energy from the two data a t 20 and 200 "C, the result is 13 kJ mol-'. Scavenging Experiment with Cadmium Zon. It has been known that while CdZ+hardly reacts with atomic h y d r ~ g e nor ~ ~with .~~ hydroxyl radical,I9 it is readily reduced by e , ~ : l s - z o -
-
+ CdZ+
Cd+
(5)
The produced Cd+ possesses an intense UV absorption band, and it was expected that this absorption may be used to estimate G(e,,-) at high temperatures. The analysis of the observation, however, requires knowledge on the temperature dependence of various related properties such as the rate of reaction 5, stability or decay of Cd+, and of course, the absorption coefficient of Cd+. The results of examination on these properties are described first. The rate coefficient of reaction 5, k5,was measured at 20, 200, and 250 OC by observing the rise of Cd+ absorption in dilute and 4 X mol dm-3). The monC d S 0 4 solutions (2 X itoring was made at 300 nm, where, as detailed later, the absorption was maximum independent of temperature. Examples of data at 20 and 200 "C are shown in parts a and b of Figure 6 together with those for a more concentrated solution, which are added for the convenience of later discussion. The values of k5,evaluated assuming a first-order reaction, were (4.7 f 0.4) X lolo, (5.5 f 0.6) X lo", and -8.1 X 10" dm3 mol-' s-I, respectively, at 20,200, and 250 "C. The corresponding decay profiles of eaq-were found consistent with these rate coefficients, and the value at 20 "C agrees well with the literature data.18,35 The observed increase in k5 corresponds to an activation energy (31) The proportionality coefficient may vary with the refractive index, which is slightly temperature dependent (cf. Mulliken, R. S.; Rieke, C. A. Rep. Prog. Phys. 1941, 8, 231). (32) Jha, K. N.; Bolton, G. L.; Freeman, G. R. J . Phys. Chem. 1972, 76, 3876. (33) Holzapfel, W. J . Chem. Phys. 1969, 50, 4424. (34) Hayon, E.; Moreau, M. J . Chim. Phys. 1965, 62, 391. (35) Anbar, M.; Hart, E. J. J . Phys. Chem. 1965, 69, 973.
61
I
Time / ns
6 w
0
200
100
b
0
t
f
300
400
2 I
--I
Time / ns
Figure 6. (a) Time profiles of Cd+ absorption observed at 20 O C for CdS04 solutions in concentration of ( 1 ) 2 X lod mol dm-3 and (2) 1 X mol dm-'. The measurements were made at 300 nm and with a pulse dose of 15 Gy. The unit for G(Cd+)s,, is (molecules/lOO eV) dm3 mol-' cm-I. (b) The same as the above except that the temperature is 200 O C .
of 15.5 kJ mol-', though it is not certain whether an Arrhenius plot is strictly linear in the examined temperature range. At any rate the temperature dependence of k5 is consistent with the presumed diffusion-controlled nature of reaction 5. It is known that various complexes or ion pairs are formed in a concentrated CdS04 solution such as expressed by Cd2+
+ S042- F! CdS04
(6)
The equilibrium constant K6at 25 OC is -250 so that the fraction of free Cdz+is about half when the total concentration is 1 X lo-* mol dm-3.36 It has been reported from a measurement with exces sulfate ion that the rate coefficient of reaction 5' is about oneeaq-
+ CdS04
-
Cd+
+ S042-
(5')
fourth of k5.19,37This evaluation may, however, be an underestimate, because the presence of other forms of the complex is neglected.3s One has to note that considerable uncertainty exists mol dm-3 in the later in the net scavenging rate above 2 X plot of Cd+ yield against solute concentration and further that this effect of complexation may also be present at higher temperatures. (The problem is, however, not so serious in the logarithmic scale for the abscissa in Figure 8.) We now turn to the problem of decay of Cd+ after its formation. Ideally, the product of scavenging should be stable or unreactive, but it is clear that Cd+ is not stable in a long time scale. One has to be satisfied if the decay of Cd+ is much slower than that of eaq- in pure water. In pure water the decay of ea,-, both to intraspur and interspur decay, occurs mainly through three reactions:
-
+ H+ H e,, + ea,- + 2H+ H* eaq- + OH OHea,-
-
(7) (3)
--L
~
~~~~
(36) Smith, R. M.; Martell, A. E. Critical Stabiliry Constanrs; Plenum: New York, 1976; Vol. 4, p 84. (37) Peled, E.; Czapski, G. J . Phys. Chem. 1970, 74, 2903. In this paper the decrease in the scavenging rate is ascribed to the effect of ionic strength. (38) An effect of adding sodium sulfate was examined in both ref 19 and 37, but the presumed presence of Cd(SO4)?- or Cd(SO&& was unfortunately ignored.
3016 The Journal of Physical Chemistry, Vol. 92, No. 10, 1988 340
Shiraishi et al. 6 r
Wavelength / nm 320 300 280
S
3
I
I
0.15F
4.0 4.5 Photon Energy / eV
I
lCdS041 /
Figure 7. Spectra of Cd+ observed in a 2 X mol dm-' CdS04 solution. @, 20 OC;A, 200 OC;W, 250 OC. Each of the plotted points
is absorbance in the plateau region of the respective time profile, corrected to an average pulse dose of 15 Gy.
Conversion of e,; these by
into Cd+ will result in replacement of each of
+ + + +
Cd+ + H+ Cd+
Cd2+
Cd+
H
Cd22+
(9) (10)
OH Cd2+ OH(11) The reported rate data at room t e m p e r a t ~ r eindicate ~ ~ , ~ ~that k9/k7
