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J. Phys. Chem. 1883, 87, 4564-4565
Decomposition of Water by Very High Linear Energy Transfer Radiations' Jay A. LaVerne and Robert H. Schuler' Radiation Laboratory and Department of Chemistry, University of Notre Dame, Notre Dame, Indiana 46556 (Received: August 19, 1983)
The yields for ferrous oxidation in aerated and deaerated 0.8 N HzS04by 20-MeV 7Li,9Be,llB, and lZCions, as measured in the present study, indicate that the limiting yield for the radiation decomposition of water by low-energy heavy ions is -2.8 molecules/100 eV. Appreciable yields of H atoms are produced by these radiations even though the linear energy transfer varies from 10 to 100 eV/A.
It is well-known2 that with increasing particle linear energy transfer (LET)3intratrack radical processes become increasingly important in the heavy particle radiolysis of water and aqueous solution^.^ In acid solutions the yields of H atoms and OH radicals which escape from the radiation track tend toward zero at very high LETS and the yields of molecular products, H2 and H202,markedly increases2As a corollary one expects that the recombination of H atoms and OH radicals will also increase in importance so that the net yield for water decomposition by heavy particles will decrease from the value of 4.6 molecules/100 eV observed for fast electrons.2 For purposes of modeling track effects it is of interest to establish the limiting yield for net water decomposition at high LETs. Previously5 it was suggested, from measurements of the yield of oxidation of ferrous ion in aerated and deaerated solutions by lOB(n,c~)~Li, that for 0.8 N H2S04this limit was -3.6. Other estimates have varied from 2.5 to 4.2.&13 We are in the process of carrying out extensive studies of the oxidation of ferrous ion by low energy 4He, 7Li, 9Be, llB, and 12C ions in order to provide a comprehensive description of the dependence of the differential yields of radical production and water decomposition as these particles approach the ends of their tracks. We report here preliminarily yields as measured for each of these particles at 20-MeV energy for both aerated and deaerated ferrous sulfate solutions. The results obtained suggest that at very high LETs the limiting yield for decomposition of water in -2.8 molecules/100 eV. Experimental Section The methods used were very similar to those employed in earlier studies with cyclotron radiation^.^.^ In the present case particles were accelerated with the tandem (1) The research described herein waa supported by the Office of Basic Energy Sciences of the Department of Energy. This is Document No. NDRL-2507 from the Notre Dame Radiation Laboratory. (2) A. 0. Allen, "The Radiation Chemistry of Water and Aqueous Solutions", Van Nostrand, Princeton, 1961. (3) The linear energy transfer, LET, is equal to the stopping power (-dE/dr) of a medium for a particle at a given energy. (4) See J. A. LaVerne, R.H.Schuler, A. B. Ross, and W. P. Helman, Radiat. Phys. Chem., 17, 5 (1981), for a bibliographic summary of radiation chemical studies with heavy particles. (5) R. H.Schuler and N. F. Barr, J . Am. Chem. SOC.,78,5756 (1956). (6) R.H.Schuler and A. 0. Allen, J . Am. Chem. SOC.,79,1565 (1957). (7) N. F. Barr and R. H.Schuler, J. Phys. Chem., 63, 808 (1959). (8) M. Lefort and X. Tarrago, J. Phys. Chem., 63, 867 (1959). (9) M. V. Vladimivova, Adu. Chem. Ser., No.81, 280 (1968). (10) A. R. Anderson and E. J. Hart,Radiat. Res., 14, 689 (1961). (11) M. Imamura, M. Mataui, and T. Karasawa, Bull. Chem. SOC.Jpn., 43, 2745 (1970). (12) N. E. Bibler, J. Phys. Chem., 79, 1991 (1975). (13) C. N. Trumbore and E. J. Hart, J. Phys. Chem., 63, 867 (1959). 0022-3654/83/2087-4564$0 1.50/0
FN Van de Graaff operated by the Notre Dame Physics Department. The particle characteristics and the dosimetry approaches used have previously been described.l4 The particles available from this instrument have a well-defined energy (iO.01 MeV) and charge state so that radiation chemical yields can be measured accurately. Beam currents were -lo4 A and total doses in the range of iOi8-iOi9 eV/g. The solutions were 10 mM ferrous ammonium sulfate (reagent grade, G. Frederick Smith Chemical Co.) in 0.8 N sulfuric acid (Fisher Scientific, reagent grade). Chloride was absent. Water was triply distilled from acid permanganate and alkaline dichromate solutions saturated with oxygen and stored in quartz vessels until use. These solutions were sufficiently pure that even at 10 mM ferrous ion the autooxidation rate was very low and did not interfere. Irradiations were carried out in a closed Pyrex loop (-30 cm3) so that solutions could be purged with N2. Irradiation was through a mica window (-4 mg/cm2) and the beam current collected with a platinum probe in contact with the solution. Solutions were circulated through the irradiation cell with a magnetic stirrer. Optical measurements were made in a l-cm quartz cuvette in the radiation loop. The ferric yield was determined at 304 nm with a Beckman DU-2 spectrometer thermostated at 25.0 i 0.2 "C. The extinction coefficient of ferric ion was taken as 2194 M-I 12m-l.l~ Results and Discussion The yields observed for ferric production by the various particles at 20-MeV energy are given in Table I. At this energy the measurements are very reproducible ( i 2 % ) so that for a given particle the yields in aerated (Gaer) and deaerated (Gdeaer)solutions can be compared quite accurately. It is seen that the ratio of these values decreases from 1.88 observed for y-rays and fast electrons7J6J7and slowly approaches a value near to 1as the atomic number, 2, increases. It is particularly noted that the ratios observed for '%e, llB, and 12Cradiations, where all the LETS are above the 4He ion maximum of 23 eV/& are considerably greater than the value of 1.12 previously reported for 'OB(n,a)'Li recoil radiation^.^ The present results, therefore, indicate that this latter ratio is somewhat low, possibly by as much as 10%. The yields measured in aerated solution are reasonably in accord with the absolute yield of 4.22 measured for the lOB(n,~t)~Li case so that we presume that the yield given for the deaerated solution is (14) J. A. LaVerne and R. H.Schuler, J. Phys. Chem., in press. (15) R. H. Schuler and A. 0. Allen, J. Chem. Phys., 24, 56 (1956). (16) N. F. Barr and C. G. King, J. Am. Chem. SOC.,76,5565 (1954). (17) W. Rothschild and A. 0. Allen, Radiat. Res., 8, 101 (1958).
0 1983 American Chemical Society
J. Phys. Chem. 1983, 8 7 , 4565-4567
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TABLE I: Ferrous Oxidation and Net Water Decomposition Yields by 20-MeV Ionsa energy b
uncertainty, particle 4He 'Li 9Be
MeV k0.1 i0.2
B '*C
k0.9 i1.2
t0.5
LET range in water 3-23 11-42 24-59 42-78 60-102
GaerC
GdeaerC
7.83
4.97 3.88
5.34
4.56 3.95 3.73
3.59
3.28 3.16
GaerjGdeaer
GH
1.57
1.43
1.38
0.73 0.49 0.34
1.27 1.20 1.18
0.29
G-H20
3.52
3.15 3.10 2.92 2.87
G-H20 '/&H
2.81 2.78 2.85 2.75 2.72
Interpolated from measurements in the 15-25-MeV region. Corresponding to t0.3 mg/cm2 in range. Ferric ion yields (molecules/100eV) in aerated and deaerated 0.8 N H2S0, containing 1 0 mM ferrous ammonium sulfate. somewhat high, possibly because an insufficient correction was applied for the background oxidation. The stoichiometry of these systems is such that the difference between the aerated and deaerated yields provides a direct measure of the H atoms which escape from the track core, i.e.2v7Je (1) G H = %[Gam - Gdeaerl As expected the H atom yields, as determined from eq 1, tend toward zero with increasing 2 and increasing LET. However, it is seen that with the IlB and 12Cradiations, where the LETS are above 40 eV/A, there is a significant fraction of the H atoms which escape into the bulk of the solution. At a given LET the density of energy deposition decreases as 2 increases.14 As a result the H atom yield decreases somewhat more slowly than might otherwise be expected and one can expect a small yield of H atoms with even the highest 2 radiations. The net water decomposition can be obtained from the data of Table I with the r e l a t i ~ n s ~ > ~ J ~ (2) G-H20 = Gdeaer G H '-
= 3/2Gdeaer - l/zGaer
(3)
(18) Equation 1 neglects the effects of scavenging of H atoms by O2 within the track in aerated solutions. Previous investigations with 510-MeV helium ions (see ref 7 and 13) indicate that thia equation results in an overestimate of G H by -0.2 for radiations of moderate LET. However, for very high LET radiations other track processes should dominate and this effect is expected to be small. (19) Tertiary intratrack reactions of OH and HzOz to form Hot, which is of modest importance at high LETS,will not affect the ferrous oxidation stoichiometrybut will lead to re-formation of water. Donaldson and Miller [Tram. Faraday SOC., 52,252 (195611 have estimated G H Oto ~ be about 0.25 using 21"Po a particles. The net water decomposition yields given here neglect these tertiary reactions and are, therefore, upper limits.
The values observed for 20-MeV %e, IIB, and ions are all in the range of 3.1-2.9 and are substantially lower than the limiting value of 3.6 indicated by the previous study with lOB(n,~x)~Li radiatiom6 This discrepancy parallels that for the ratio of yields in aerated and deaerated solutions. Because of the factor of 3/2 in eq 3 any errors in this ratio (or difference in the yields) will be magnified in the derived value. A yield ratio of 1.25 for 'OB(n,a)'Li radiations would correspond to a net water decomposition yield of 3.0. A value of G,, in the vicinity of 3 indicates that at very high LETS approximately 50% of the H atoms initially produced are lost to re-formation of water within the track, i.e., that H and OH recombination occurs very nearly statistically. By extrapolation of this argument one can, at least approximately, correct the observed net water decomposition yields to infinite LET by subtracting half the remaining H atom yield. Such an approach gives values indicated by the final column in Table I. These values are, within experimental error, independent of the particle (2.79 f 0.05) and very similar to this quantity for fast electrons (2.7). We suggest, therefore, that the net yield for water decomposition at very high LETS can be reasonably represented by a common limit of 2.8 f 0.1 molecules/100 eV for all radiations.
Acknowledgment. The authors thank Dr. C. P. Browne of the Notre Dame Nuclear Structure Laboratory for making the facilities available. They also thank Dr. E. D. Berners for his assistance with the accelerators and particularly for developing an ion source for the beryllium ion studies. The Nuclear Structure Laboratory is funded by the National Science Foundation.
Fractal Reaction Kinetics: Exciton Fusion on Clusters P. W. Klymkot and R. Kopelman' Depattmnt of Chemistry, The University of Michigan, Ann Arbor, Michigan 48109 (Received: August 29, 1983)
Bimolecular and pseudo-unimolecularreactions of random walkers on large clusters are presented via simple, analytically soluble, rate equations. The rate coefficient has a simple dependence on time: K ( t ) = t-h where 1 1 h 1 0 and h = 1 - f where 2f is the effective fracton (phonon on fractal) dimension of Alexander and Orbach. h measures the degree of local heterogeneity. In the l i t of local homogeneity h = 0. Triplet exciton homofusion rates on isotopic mixed naphthalene crystals are consistent with the formalism,giving classical diffusive behavior (h = 0) above the percolation threshold and nonclassical local heterogenous behavior below it (h = 0.48 for 4% c ~ in ~ c&H ). ~ We present a simple formalism for reactions in locally heterogeneous environments, based on cluster-limited kinetics. We apply this formalism to molecular exciton t Present address: IBM,East Fishkill, Hopewell Junction, NY 12533.
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kinetics and test it via homofusion experiments with neutral Frenkel triplet excitons on clusters of naphthalene in an isotopic alloy crystal, naphthalene-he in naphthalene-d,. Heterogeneous chemical reactions may be controlled either by diffusion or by percolation (motion in a micro@ 1983 American Chemical Society
