J. Phys. Chem. 1984,88, 5057-5061 effects (different head groups and counterions) are small but definitely significant. With a bulkier and more rigid hydrophobic part and with a less distinct separation of hydrophobic and hydrophilic parts the behavior is markedly different as demonstrated for the case of sodium cholate.
Acknowledgment. This work has been supported by the
5057
Swedish Natural Sciences Research Council. Prof. B. Brun is thanked for advice and discussions. Registry No. ’Li, 13982-05-3;sodium octanesulfonate, 5324-84-5; sodium dodecyl sulfate, 151-21-3;lithium dodecyl sulfate, 2044-56-6; hexadecyltrimethylammonium chloride, 1 12-02-7;hexadecyltrimethylammonium bromide, 57-09-0.
Computer Modeling of Data from Pulse Radlolysis Studies of Aqueous Solutions Containing Scavengers of Spur Intermediates Conrad N. Trumbore,* Walter Youngblade, and David R. Short Department of Chemistry, University of Delaware, Newark, Delaware 19716 (Received: January 3, 1984)
With the calculations reported here, all of the data from a comprehensive study of the kinetics of hydrated-electron decay in the 14-MeV-electron pulse radiolysis of pure water and aqueous solutions have been modeled within experimental error. The overlapping-spur model utilized employs a constant-energyfraction (0.2) of high, constant spur density regions (representing blobs/short tracks) and another constant-energy fraction (0.8) of a low, variable spur density region (representing isolated spurs) whose spur density is proportional to the pulse dose. The model also contains a new hydrated-electron probability density distribution function with the maximum in the probability density displaced from the center ofthe spur. Adjustments made to fit experimental data from different aqueous-solution pulse radiolysis studies have been minor. In this paper, hydrated-electron decay kinetics have been modeled within experimental error for a variety of scavengers of transient reactive intermediates originating in the spur. Thus, this new spur model has been successfully tested against experimental data for 14-MeV electrons over a wide range of pulse doses (0.5-80 Gy), time regimes (10-”-10-5 s), and types of scavengers of the major spur transients (eaq-, .OH, and H’).
Introduction The kinetics and yields in the radiolysis of water and aqueous solutions have been explained on the basis of energy deposition by ionizing radiation resulting in localized, nonhomogeneous regions of relatively high concentrations of reactive intermediates called spurs.’ The deposition of energy along energetic electron tracks in condensed media has been further modeled in terms of isolated-spur, “blob”, and “short-track” regions.z The latter are regions of increased spur density at track ends or where relatively large amounts of energy are deposited in a small region along the electron track. The introduction, at the center of the spur, of a minimum in the hydrated-electron (eaq-) probability distribution function in our computer modeling program3 has produced excellent fits between calculations and experimental data for hydrated-electron and OH radical decay for pure water in the nanosecond time regime following the pulse under a variety of pulse radiolysis condition^.^ The use of a spur model with two different spur density regions has enabled us to model qualitatively the anomalous decay kinetics of the hydrated electron following low radiation pulse doses in pure water.5 The two spur density regions are introduced in our calculations as first-order approximations of (1) the isolated spurs (C100-eV energy deposited)’ along the electron track (low spur density) and (2) the higher LET (linear energy transfer) blob and short-track regionsZnear track ends and in regions along the electron track in which larger amounts of energy ( > l o 0 eV) are deposited in a nonhomogeneous fashion. The average energy per spur (60 eV) used to attain the desired fit between our computer calculations and experimental data is
more in accordance with that assumed by Magee and Chatterjee (40 eV)6 than that suggested by Kuppermann (273 eV).’ Our modeling efforts thus far have concentrated primarily on pure-water pulse radiolysis results. We now wish to report further results in modeling the remainder of the pulse radiolysis hydrated-electron decay data of Fanning* taken with 14-MeV electrons from the Argonne linac and employing a series of scavengers of the reactive intermediates (ea;, .OH, and Hf). These data were taken by using 14-MeV pulsed electrons under conditions where the average distance between isolated spurs is equal to or greater than the average distance between electron tracks. This allows the assumption of a random distribution of isolated spurs, blobs, and short tracks. Our hydrated-electron calculations are within experimental error of nearly all the data tested over a wide range of pulse dose and concentrations of scavengers of the predominant reactive intermediates produced in water by ionizing radiation.
(1) Samuel, A. H.; Magee, J. L. J . Chem. Phys. 1953, 21, 1080. (2) Mozumder. A,: Maeee. J. L. Radiat. Res. 1966. 28. 203. (35 Fanning, J: E.,’Jr.;?rumbore, C. N.; Barkley, P. d.;Short, D. R.; Olson, J. H. J . Phys. Chem. 1977, 82, 1026. (4) Trumbore, C. N.; Short, D. R.; Fanning, J. E., Jr.; Olson, J. H. J . Phys. Chem. 1978, 82, 2762. (5) Short, D. R.; Trumbore, C. N.; Olson, J. H. J . Phys. Chem. 1981,85, 2328.
(6) Magee, J. L.; Chatterjee, A. J . Phys. Chem. 1978, 82, 2219. (7) ,Kuppermann, A. In “Physical Mechanisms in Radiation Biology”; Technical Information Center, Office of Information Services, NRC: 1974; p 155. (8) Fanning, J. E., Jr. Ph.D. Thesis, University of Delaware, Newark, DE,
0022-365418412088-5057$01.50/0
Computations and Experiments Computer simulations were performed in the same manner as previously r e p ~ r t e d .Pulse ~ radiolysis experiments on the Argonne linac were generously performed by W. Mulac in essentially the same manner as that reported by Fanning et aL9 We have found that in almost all cases the fits between computations and experimental data are much better in the 10-6-10-5-s region if we include in the program a contribution for hydrated-electron scavenging by small amounts (2 Mm) of dissolved oxygen. Since Fanning reports* that the 2-hm value is the upper limit of oxygen concentration found in his spot-checks of oxygen concentration
1975.
(9) Fanning, J. E., Jr.; Trumbore, C. N.; Barkley, P. G.; Olson, J. H. J . Phys. Chem. 1977, 81, 1264.
0 1984 American Chemical Society
Trumbore et al. I I llllli~ I
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Figure 1. Comparison of experimental and computed hydrated-electron and OH radical decay kinetics in the 14-MeV pulse radiolysis of pure water. Initial spur parameters are those in Table I, ref 4. Solid lines are from a single calculation for e,, and -OH; pulse dose: 79 Cy (1 Gy = 100 rd). Computer model includes a novel initial hydrated-electron spur distribution and a spur-overlap feature: (0)hydrated-electron data of Jonah et al.;" (+) hydrated-electron, 79-Gy pulse data of Fanning;*(0)
OH radical data of Jonah and Miller; I2 ( I ) hydrated-electron data of Sumiyoshi and Katayama.lo
in the so-called "oxygen-free" solutions, we believe the use of this practice is justified. In any case, the inclusion of such small amounts of oxygen in the program only affects the kinetics on this relatively long time scale.
Results and Discussion Agreement with a New Picosecond Value of G(e,,;). Figure 1 illustrates the agreement between our previous calculations of hydrated-electron G values and a new value obtained by Sumiyoshi and Katayamaxoa t 30 ps using the stroboscopic pulse radiolysis method. Our calculations are within the experimental error of this new value which is also in good agreement with extrapolations from the data of Jonah et al." Therefore, we have continued to use all of the previously reported model parameters derived from fitting hydrated-electron decay data of Jonah et al." and the hydroxyl radical decay data of Jonah and Miller'* for the pulse radiolysis of pure water (Figure 1). Modeling High Spur Density Regions in Pure Water. We have demonstratedJ that in order to model data from the pulse radiolysis of pure water, a high spur density contribution is needed on an individual electron track in addition to a contribution from widely distributed spurs. In our model, the fraction of the total energy deposited in this high spur density region is constant. The spur density in this region is presumed constant and independent of dose. The remainder of the energy is deposited in regions of lower spur density in which spur density is proportional to the dose. The calculations of electron decay kinetics are performed for the high and low spur density regions separately, each is weighted according to an appropriate energy fraction, and the weighted electron decay kinetics are added linearly. Thus, two additional fitting parameters are introduced by this feature of the model: (1) the fraction of energy expended in the high spur density region and (2) the spur density of that region. Short et al.5 achieved a qualitative fit with pure-water pulse radiolysis data employing a value of 0.3 for the first parameter above with a spur density corresponding to that of a pulse dose of 120 Gy (1 Gy = 100 rd). This dose represents an average interspur distance of approximately 510 A. The current work has refined these parameters to provide quantitative agreement between calculation and experiment for irradiated aqueous solutions. Figure 2 illustrates the effect of pulse doses and thus variable spur densities on the predicted decay kinetics of the hydrated electron in pure water. The kinetics of the hydrated-electron loss (10) Sumiyoshi, T.; Katayama, M. Chem. Lett. 1982, 1887. (11) Jonah, C. D.; Matheson, M. S.;Miller, J. R.; Hart, E. J. J . Phys. Chem. 1976, 80, 1276. (12) Jonah, C . D.; Miller, J. R. J . Phys. Chem. 1977, 81, 1974.
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Figure 2. Calculated decay curves for the hydrated electron in the 14MeV-electron pulse radiolysis of pure water at different high pulse doses and therefore at different high spur densities. Calculations utilize the same initial spur parameters as in Figure 1.
(represented as G values-number of hydrated electrons per 100 eV deposited) is independent of the pulse dose and therefore of the spur density up to approximately 5 ns. As the initial spur density increases in pure water, there is earlier spur overlap and therefore faster electron decay in the vicinity of lo-* s following the pulse. Thus, the effect of mixing a high spur density contribution into the calculations is to cause faster electron decay at times greater than s following the pulse. As the experimental pulse dose is decreased, the contribution of the high spur density region to electron decay in the region of lO-*-lO-'s becomes more important and eventually dominates at very low pulse doses in pure water at times greater than s. We attribute our ability to model low pulse dose data from pure water to this combined high and low spur density feature. This is most readily illustrated in Figure 3, where linear combinations of various high and low spur density calculations are shown with typical experimental data for very low and medium pulse doses. Figure 3 illustrates the typical sensitivity of the calculations to various mixes of electron decay for different high spur densities at low and medium pulse doses. Low pulse dose calculations are much more sensitive at later times to the two fitting parameters than are the higher dose calculations. Small deviations between data and calculations of the type shown in Figure 3 are anticipated at about loT7s because of possible early spur overlap with randomly distributed spurs (see ref 5 for a more extensive discussion of this point). Extensive combinations of the two spur density fitting parameters have given us a best fit over the full matrix of the Fanning pulse radiolysis data* utilizing a 20% contribution (energy fraction of 0.2) of a spur density equivalent to that of a 500-Gy pulse dose and a remaining energy fraction of 0.8 of a spur density which is directly proportional to and calculated from the experimental pulse dose. (The 500-Gy pulse dose corresponds to an average interspur distance of approximately 330 A.) All results reported hereafter utilize these fitting parameters and are encoded in Figure 3 and subsequent figures as 80/20(500 Gy). Modeling Data from the Pulse Radiolysis of Pure Water. Figure 4 illustrates the close fit between experimental data and
Computer Modeling of Pulse Radiolysis Data
The Journal of Physical Chemistry, Vol. 88, No. 21, 1984 5059
5
G(e;,)
5 4 3
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Figure 3. Comparison of typical experimental and computed hydratedelectron decay in the 14-MeV-electronpulse radiolysis of pure water at various pulse doses. Initial spur parameters same as in Figure I . Upper curves: Calculated and experimentals G values for e, for a 0.5-Gy pulse
irradiating a pure H20sample. Calculations of hydrated-electron decays in combined high (500 Gy) and low (0.5 Gy) spur density regions with the following percentage ratio (low/high) weighting factors (from top to bottom): 100/0(500 Gy) (see text for explanation of symbols), 90/ lO(SO0 Gy), SS/lS(SOO Gy), 80/20(500 Gy), 70/30(500 Gy). Lower curves: typical calculated and experimentals hydrated-electron G values for pure water irradiated with a 17-Gy pulse of 14-MeV electrons. Weighting factors (from top to bottom): 80/20(250 Gy), 90/10(750 Gy), 80/20(500 Gy). calculations when the new fitting parameters described above are applied to calculations for pure water subjected to different pulse doses. The fits between calculation and Fanning's data8 are within the experimental error at all doses. Other calculations and data not shown fit similarly. Modeling Pulse Radiolysis Data with Scavengers of Spur Intermediates. Fanning8 conducted a series of pulse radiolysis experiments with aqueous solutions containing scavengers (OH-, 2-propanol, 02)of each of the major reactive intermediates in the spur (H', .OH, and ea;). Faraday cup dosimetry was not available for this series of experiments because of equipment malfunction. Instead, the G value of the hydrated electron at s was used as an internal dosimeter with an assumed G value at s of 2.7 taken from the work of Jonah et al." New equations representing the reactions of homogeneously distributed, dissolved solutes which are reactive with spur intermediates were introduced into our computations. The spur fitting parameters from the pure-water calculations were employed without change in the calculations with reactive solutes present. For oxygen-containing solutions in the range 0-88 jtM O2(Figure 5 ) and for oxygen-free, high-pH solutions (Figure 6), the fit between calculations and hydrated-electron decay data from pulse radiolysis experiments was within experimental error. However, poor agreement resulted when 2-propanol data, using the same parameters, were compared with our calculations, as illustrated in Figure I . The relatively high concentrations of 2-propanol and hydroxide ion used in the above experiments should be effective scavengers of OH radicals and H+ ions, respectively. A decreased concen-
2
1 ~ 1 0 - 1 0I ~ I O - ~1 ~ 1 0 - 81 ~ 1 0 . I~ ~ I O - ~I ~ I O - ~ TIME ( s e c )
Figure 4. Comparison of typical calculated and experimentalshydrated-electron decay following 14-MeV-electronirradiation of pure water samples with pulse doses listed. Calculations are based on a 80/20(500 Gy) weighting factor (see text for the meaning of weighting factors) and the same initial spur parameters as in Figure 1. Upper curves are each displaced upward 2 G units.
tration of the latter two reactive species should slow the rate of reactions 1 and 2, thereby increasing the eaq-concentration and
+ H+ eaq- + .OH eaq-
-
-
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therefore the radiation chemical yield of the hydrated electron at a given time following the pulse, when cornpared with the eaqyield at the corresponding time in pure water. Thus, we reasoned that Fanning's assumption8 of a G(eaq)of 2.7 at s was not appropriate in cases where there were high concentrations of scavengers of H+ and O H radicals. Data from subsequent experiments, to be discussed later, confirmed this assumption. Since only hydrated-electron concentration data and not G(e,,-) values were available at the time of our calcidations, we decided to use the model as a predictive tool to estimate C(e,;) for the following conditions: pH 7 with 0.1 M 2-propanol, pH 9.5 with and without 0.1 M 2-propanol, and pH 11 with and without 0.1 M 2-propanol. The procedure used was as follows: The calculated value of G(e,;) at s was found to be independent of pulse dose for each of the above solute systems. These calculated G(eJ values were used with experimental values of eaq-concentrations s to calculate a revised pulse dose for the Fanning 2at propanol data. This revised pulse dose was then used to predict new calculated hydrated-electron G(eaq-) values and decay data to be compared with experimental values at times other than s, where experimental data and calculated curves are normalized. The middle column of Table I lists predicted values of C(eaq-) at s for each solute system. The lack of experimental data at s to support the use of adjusted G values warranted further attention. Consequently, arrangements were made with W. Mulac of the Argonne National Laboratory to measure G(ea -) at s employing the same 14-MeV linac accelerator and experimental conditions used by
5060 The Journal of Physical Chemistry, Vol. 88, No. 21, 1984
Trumbore et al.
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Figure 5. Comparison of typical calculated and experimental*hydrated-electron decay following 14-MeV-electronirradiation of water containing 8.9 p M O2with pulse doses listed. Calculationsare based on an 80/20(500 Gy) weighting factor (see text) and the same initial spur parameters as in Figure 1. Top two curves are displaced upward 2 G units each.
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sec) Figure 6. Effect of pH and pulse dose on agreement between typical calculated and experimentals hydrated-electron pulse radiolysis data. Same modeling parameters as in Figure 5, 80/20(500 Gy); pH of sample and pulse dose listed in figure under calculated curves and to the left of experimental pulse radiolysis data taken under these conditions.s Upper curves displaced upward by 2 G units. TIME (
TABLE I: G(e,-) Values at lO-'s
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predicted 2.70 2.70 2.7+ 3.42 3.15 3.10
exptl' 2.70 2.70 2.77
3.18 2.92 2.84
Argonne linac. 5
TABLE I 1 Experimental vs. Calculated G Value RatiosD PH ratiob 1119.5 9.517 1117
Argonne exvt 1.09 1.03 1.12
model mediction 1.09 1.02 1.10
0.1 M 2-propanol. Ratio of pHs of G values being compared. Fanning,* with the dose determined by direct Faraday cup dosimetry rather than by calculations using an estimated G(eJ. Results of this later experimental study also are shown in the last column of Table I as G(e,;) values at lO-'s. These results showed the revised model predictions parallel trends demonstrated by the experimental data: (a) A small correction in pH 11 G value was apparently justified. (b) G values higher than 2.7 were required for the 2-propanol experiments. Predicted values were within 9% or less of those obtained from experiment. (c) The predicted trend of decreasing G value as a function of decreasing pH (0.1 M 2-propanol) was confirmed. Although absolute experimental and predicted values differed slightly, the ratios of G values were quite similar, as shown in Table 11.
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Figure 7. Disagreement between typical calculations and experimental datas of hydrated-electron decay from the 14-MeV-electronpulse radiolysis of 0.1 M 2-propanol solutions at the indicated pH and pulse doses = 2.7 at s. Upper two curves calculated by using an assumed G(e,;) displaced by 2 G units. Figure 8 presents the results Of calculations using the revised dose estimates and comparing predicted hydrated-electron G values
Computer Modeling of Pulse Radiolysis Data
I x 10-10
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I x 10-8
I x 10-7 TIME ( s e c )
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The Journal of Physical Chemistry, Vol. 88, No. 21, 1984 5061
I x 10-5
Figure 8. Recalculation of typical 0.1 M 2-propanol data using calculated G(e,;) at lo-’ s (Table I) as the basis for dosimetry of all experimental values. This has the effect of normalizing data and calculations at lO-’s. Other assumptions and conventions identical with those made in Figure 7. Upper curves displaced by 2 G units.
with the data of Fanning8 for solutions containing 2-propanol at pH 7 and above. The excellent quantitative agreement with data s appear to justify our assumption of solute conbeyond s. Other 2-propanol centration-dependent G(eJ values at data at different pulse doses are in equally good agreement with model calculations. Figure 9 represents the results achieved by utilizing the G values for solutions containing 0.1 M 2-propanol, obtained from the Argonne data (Table I) to recalculate dosimetry for the Fanning data. The good agreement between calculations based on the new dosimetry and experimental data reflected in Figure 9 concluded the modeling of Fanning’s experimental data. The close quantitative agreement between experimental data and modeling results for Fanning’s pure water (Figure 4), O2solute (Figure 5), high pH (Figure 6), and high pH, 2-propanol solute data (Figure 9) demonstrated 80/20(500 Gy) as a suitable linear combination to simulate contributions from a higher spur density component in 14-MeV-electron irradiations. These results did not require any other changes to the model parameters utilized by Short et aLs
Conclusions The spur model described above, consisting of a model which includes a feature for Spur Overlap and which distinguishes between regions of high and low spur density, has been tested successfully
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Figure 9. Recalculation of data similar to those presented in Figure 7 using new Argonne dosimetry as the basis for calculating G(e,-). Other assumptions and conventions identical with those in Figure 8.
against hydrated-electron decay data from the 14-MeV pulse radiolysis of pure water and aqueous solutions containing scavengers for all the important reaction spur intermediates. Results are modeled over a time range of 10-11-10-5s during which the following processes may take place: intraspur reaction and spur expansion, overlap of high spur density regions (representing overlapping of spurs in blobs and short tracks), reaction of spur intermediates with dissolved solutes, overlap of isolated spurs, and homogenization of reactive intermediates. Computations with the above model are now being compared with 14-MeV-electron pulse radiolysis data on the molecular yields (H2 and H202). Results are highly encouraging and will be reported e1~ewhere.I~
Acknowledgment. We thank the University of Delaware for financial support of this project. We also acknowledge continuing discussions with Dr. J. H. Olson and thank W. Mulac and the staff of the Argonne linac for performing the most recent pulse radiolysis experiments described in this paper. Registry No. OH-, 14280-30-9;O,, 7782-44-7; H+, 12408-02-5; .OH, 3352-57-6; water, 7732-18-5; 2-propanol, 67-63-0. (13) pumbore, C. N.; Youngblade, W.; Short, D. R.; Olson, J. H., in preparation. See also: Trumbore, C . N.; Youngblade, W. In “Proceedings of the Workshp on the Interface between Radiation Chemistry and Physics, Argonne National Laboratory, Sept 9-10, 1982”, ANL-82-88 (TID),pp 82-90.
