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A Numerical Model of COP Radiolysis
(9) S. Korcek, J. Chenier, J. Howard, and K. Ingold, Can. J . Chem., 50, 2285 (1972). (10) D. L. Allara and R. R. Hiatt, unpublished results. (11) See R. R. Hiatt in "Organic Peroxides", Vol. 11, D. Swern, Ed., Wiley-Interscience, New York, N.Y., 1971, Chapter 1. (12) M. von Smoluchowski, Z. Phys. Chem., 92, 129 (1917). (13) S. G. Daniel, Trans. Faraday SOC.,47, 1345 (1951). (14) A. B. Hart and R. A. Ross, J . Catai., 2, 121 (1963). (15) D. Edelson, J. Chem. Ed., 52, 642 (1975).
(4) D. L. Allara and R. F. Roberts, J . Catai., 45, 54 (1976). (5) D. L. Allara, T. Mill, D. G. Henry, and F. R. Mayo, Adv. Chem. Ser., No. 76, 40 (1968). (6) T. Mill, F. R. Mayo, H. Richardson, K. Irwin, and D. L. Allara, J. Am. Chem. SOC.,94, 6802 (1972). (7) D. VanSickle, T. Mill, F. R. Mayo, H. Richardson, and C. Gould, J . Org. Chem., 38, 4435 (1973). (8) For a review, see J. A. Howard in "Free Radicals", Vol. 11, J. Kochi, Ed., Wiley, New York, N.Y.,1973, Chapter 12.
A Numerical Model of Carbon Dioxide Radiolysis R. Kummler," C. Leffert, K. Im, R. Piccirelll, L. Kevan, Department of Chemical and Metallurgical Engineering, Wayne State University, Detroit, Michigan 48202
and C. Wlllis National Research Council of Canada, Ottawa, Ontario, Canada (Received April 26, 1977) Publication costs assisted by Physical Dynamics, Incorporated
An extensive experimental literature on the radiolytic decomposition of C 0 2 to CO and 1 / 2 0 z has been developed over the last 20 years. The results have been conflicting and inadequately documented in many cases because the important variables determining the reaction yield have not been understood. In this work, we give a brief review of the significant published experiments and present a comprehensive numerical model, including the energy deposition process, prescribed diffusion, and the extensive chemical kinetics for both homogeneous and heterogeneous conditions (occurring in high linear energy transfer), which quantitatively explains this extensive literature. The model for pure C 0 2includes 76 reactions and 19 species which describe the real time concentrations of ionic and neutral constituents in the irradiated medium. This model utilizes the Keneshea version of the Kutta-Merson integration procedure coupled with a steady state algorithm. This combination has been demonstrated to be both efficient and accurate for a wide range of problems, including those characterized by long problem times and reactions with exceedingly short time constants. Results of the modeling provide the first prediction of the change in carbon monoxide yield which results when the dose rate is changed from 1014to 102*eV/g s at 1 atm pressure, and explains the differences observed for a and proton irradiation as compared to fission fragment irradiation.
I. Introduction The radiolysis of carbon dioxide (C02)began with the studies of Cameron and Ramsayl in 1908. Such studies continue to be of scientific and engineering interest today. A complete understanding of the chemistry of this radiolytic process has eluded all investigators. For much of this time span, neither the basic mechanistic information such as kinetic rate constants, thermodynamic heats of formation, and cross sections for ionization and excitation, nor the experimental work has unequivocally and unambiguously defined the phenomenological chemistry. Much of the earlier discussions of C 0 2 radiolytic data proceeded in the absence of a knowledge of the rate constants for oxygen atom recombinations with CO and 0, and in the complete absence of any insight with respect to cluster ions. We now know that the yield of carbon monoxide from COz radiolysis, which is normally expressed as the number of molecules of CO produced per 100 eV deposited, a quantity called the G value of CO, is influenced strongly by the dose rate, i.e., the amount of energy deposited per unit mass per unit time, the dose, Le., the amount of energy deposited per unit mass, the pressure and temperature, the composition of the irradiated medium, and the type and energy of the ionizing radiation employed. Very few of the experimentalists measuring G(C0) values over the past 70 years have carefully de-
termined the values of each of the input parameters which we now know to be significant in influencing the G(C0). Anderson and Dominey2 have presented an excellent review of all of the C 0 2 radiolytic experiments and theory prior to 1968. In that review, the stability of gaseous COz toward ionizing radiation at low dose rates is documented through a review of the early COz radiolysis work. In the presence of additives such as NOz, SOZ, CH4,and H2, COz decomposes to form CO and generally 02.In the presence of NO2, the G(C0) is approximately 4.5 under low dose situations. Because the ultraviolet photolysis of COz is not fraught with difficulties associated with ionic recombination, it is concluded that the back reaction of CO to COz which gives rise to the apparent C 0 2 radiation stability [i.e., G(C0) = 01, must be ionic in character. This ionic mechanism was not identified by Anderson and Dominey.2 The more recent review article by Willis and Boyd3 provides an updated summary of the COz radiolysis literature. This review provides primary process yields based upon the relative cross sections for ionization and excitation by 100 eV electrons. Such primary yields can be utilized to immediately obtain the asymptotic behavior of the chemical kinetics leading to the production of CO and can be utilized as input information to a more detailed model, which permits calculation of G values under actual experimental situations. Willis and Boyd illustrate with The Journal of Physical Chemlstty, Vol. 8 1, No. 25, 1977
Kummler et ai.
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their review of experimental data a low dose rate regime where the G(C0) is 4.5 f 0.5, and a high dose rate regime where the G(C8) is 7.8 f 0.3. It is our belief that the recent data from numerous laboratories around the world have enabled us to formulate a quantitative model which will permit the analysis of most of the experimental data that exists to date, and will suggest crucial experiments necessary to test the model. Thus, in this work, we attempt a more detailed review of previous experimental results identifying all of the important parameters, and utilize the numerical analysis of the chemical kinetics to predict the G(C0) under a great variety of conditions which can be tested against experimental data.
IB. Experimental Results The major experimental results on COP radiolysis are presented in Table I. Our current understanding of the radiolysis mechanism assumes that G(C0) is strongly dependent on the nature of the charge neutralization PTQC~SS. If the positive species, C02+ or (C02)n+,is neutralized by an electron, CO is produced: GO,' or (CQ,),+
t e-
-
CO
(1)
If COzs or (CO,),' is neutralized by a negative ion, there is no breakup to form CO: CO,' or (COz)n+t A-
-+
CO,
(2)
where A- is a molecular anion. Thus, if dissociative neutralization is to be a major path, charge neutralization must precede electron attachment. This will require a high local ion concentration. Such local concentrations can be achieved by either a high homogeneous volumetric dose rate or in the tracks behind high linear energy transfer (LET) particles. Homogeneous Dose Rate Effects. Willis et a1.,4 using single pulses from a Febetron 705 at a dose rate of 2 X loz7 eV/g s and single pulses from a Febetron 706 at 2 X eV/g s, show that dissociative neutralization dominates at these dose rates. Their results also agree fairly well with Meaburn et ale,5who used a dose rate of 2 X eV/g s. Thus, we can summarize:
Quartz cells4 Room temps
*
G ( C 0 ) = 7.8 0.3 G(CO)SF6= 4.8 t 0.2 G(CO) = 7.4 k 0.4 G(CO)sF6 = 5.2 0.4
0.5-2 a t m The dosimetry in these papers is based on G(N&,o = 12.4, which is referenced against an absolute calorimetric determination which seems valid. G(02) 1/2G(CO)in all cases. Both sets seem valid and mutually consistent. It is also noteworthy that the G(C0) averaged over a few pulses 1 min apart has dropped significantly, by about 20%; see Willis et aL4 Lower dose rate experiments with 1.5-MeV protons (we will later comment that proton irradiation has too low a LET to cause eq 1 to dominate) by Anderson et al." at 1.3 X 1019-6.6 X lozoeV/g s also seem to give valid, internally consistent results. The dosimetry is based on measuring the total charge input and incident proton energy in the irradiation cell for sample pressures that absorb the entire beam energy. We can summarize: G(C0) = 4.25 It 0.25 with no additives in flow system; G(O2) = 2.24 f 0.1, Pyrex and quartz cells, GC analysis, C02 was purified: 1-2 ppm of 02,P = 0.4 atm,
