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Spur Decay of the Solvated Electron in Picosecond Radiolysis Measured with Time-Correlated Absorption Spectroscopy †

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Spur Decay of the Solvated Electron in Picosecond Radiolysis Measured with Time-Correlated Absorption Spectroscopy †
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  Spur Decay of the Solvated Electron in Picosecond Radiolysis Measured withTime-Correlated Absorption Spectroscopy † David M. Bartels,* Andrew R. Cook, Mohan Mudaliar, and Charles D. Jonah Chemistry Di V  ision, Argonne National Laboratory, Argonne, Illinois 60439 Recei V  ed: August 2, 1999; In Final Form: No V  ember 17, 1999 Spur decay kinetics of the hydrated electron following picosecond pulse radiolysis of water have been measuredusing a time-correlated transient absorption technique with an asynchronous mode-locked laser. The 11 nstime window afforded by this signal-averaging technique is ideal to match up with more conventional transientabsorption measurements taken to microsecond time scales. The precise data recorded in this study requirea revision downward of the “time zero” solvated electron yield to approximately 4.0 per 100 eV of energyabsorbed, to match the best available scavenger product measurements. Introduction The practical importance of understanding radiolysis of waterwith fast electrons and  γ  radiation can hardly be overemphasizedin fields such as radiation biology and nuclear engineering. Mostof the details have been worked out for neat water near roomtemperature. 1 - 3 High-energy electrons and  γ  photons ionizemolecules to produce low-energy secondary electrons, whichproceed to ionize and electronically excite other molecules nearthe primary ionization site.The water radical cations immediately react with other watermolecules to give (OH, H 3 O + ) pairs. Secondary electronsquickly thermalize, trap, and become solvated electrons.Thus, well-separated clusters of ionization/excitation events(referred to as spurs) are generated on subpicosecond timescales, and diffusive recombination of the free radicals thenoccurs in competition with scavenging by other species insolution. The most important recombination reactions involvethe dominant OH, H 3 O + , and (e - ) aq  species:The effective yield of scavenged product s the chemical con-sequence of the radiation s depends on the scavenging rateconstant and scavenger concentration ( k  s [S], often referred toas scavenging power). If one knows the time-dependent survivalprobability of the primary radicals in neat solution, then onecan predict scavenger product yields from the scavenging power.Similarly, through a Laplace transform relationship, the productyields vs scavenging power have been used to infer the time-dependent survival of the primary species. 4 In a recent publication 5 a reexamination of the time-dependentyield of solvated electrons in radiolysis was undertaken toreconcile existing picosecond and nanosecond transient absorp-tion measurements, scavenger yield measurements, and large-scale computer simulations. Upon reviewing older pulse radi-olysis work, it was realized that stroboscopic kinetics measure-ments on the time scale 30 ps to 3 ns 6 and measurements usingfast photodetectors on nanosecond and longer time scales 7 hadnever been carefully and convincingly matched together.Significant problems are the secondary response nonlinearitiesof fast-rise-time light detectors, and the limited time scale anddrifts of the accelerator beam, which might distort the strobo-scopic experiment based on Cerenkov probe light. The experi-ments reported here have been undertaken to provide a  fullylinear   baseline measurement of the solvated electron kineticsfor the time range 100 ps to 10 ns, following a 30 ps radiolysispulse. To complete the study, kinetics were recorded with afast digitizer/photodiode combination out to microsecond timescales. The new results show that the synthesis achieved in ref 5 was a reconciliation between several sets of flawed data. Experimental Section The experimental arrangement for picosecond radiolysis/time-correlated absorption spectroscopy is shown in Figure 1. Thebeam from a mode-locked Ti:sapphire laser is passed througha hole in the thick radiation shield wall, crosses a 1 cm flowcell in front of the 20 MeV electron beam (60 Hz, 30 ps pulses),and returns for detection by a Hamamatsu S5972 siliconphotodiode. The basic idea is to measure absorption of the onelaser pulse that arrives nearly coincident with the 30 ps electronpulse and to simultaneously measure the time delay betweenthe electron and laser pulses. A histogram of absorption vs timeevents can then be constructed.The long path traveled by the laser introduces 10 - 20%fluctuations in the light intensity, and a precise measurementof both transmitted and incident light is essential. The idea usedhere is that all fluctuations in intensity occur on a time scale † Work performed under the auspices of the Office of Basic EnergySciences, Division of Chemical Science, US-DOE under contract numberW-31-109-ENG-38. H 2 O 9 8  γ e - + H 2 O + (1)H 2 O + H 2 O + f  OH + H 3 O + (2)e - f  (e - ) aq  (3)(e - ) aq + OH f  OH - (4)(e - ) aq + (e - ) aq f  H 2 + 2OH - (5)(e - ) aq + H 3 O + f  H + H 2 O (6)OH + OH f  H 2 O 2  (7) 1686  J. Phys. Chem. A  2000,  104,  1686 - 169110.1021/jp992723e CCC: $19.00 © 2000 American Chemical SocietyPublished on Web 02/05/2000  much longer than the 11 ns laser pulse spacing. Thus, we setthe (  I  t  ) gate of one gated integrator to measure the laser pulsenearly coincident with the electron pulse and the (  I  o ) gate of asecond integrator to measure an average intensity of severalpulses just prior to the electron pulse. The details of thisarrangement are nontrivial. We first require a detector whosesignal decays completely to baseline before the arrival of anotherlaser pulse at the 90 MHz repetition rate. Second, a gatingarrangement must be found that allows for two very fast high-precision measurements on the pulse train without distortingthe information. We measure the single (  I  t  ) pulse amplitude ina Stanford Instruments SR255 fast sampler with 1 ns gate width.This instrument is designed such that the fast signal is fed inand then out on 50  Ω  cable, to be terminated in 50  Ω  at theend of 2 m of cable. We use a feed-through 50 Ω termination,and measure an average intensity signal at this point with ahigh impedance (1000  Ω ) operational amplifier circuit of 20ns rise time. This signal is fed into a Stanford Instruments modelSR250 gated integrator set to integrate a 60 ns window justbefore arrival of the electron pulse.To provide triggers, a 90 MHz clock signal synchronous tothe mode-locked Ti:sapphire laser is derived from a beampickoff and photodiode. The photodiode signal is fed into aconstant fraction discriminator, whose output is a very stablenear-sine-wave used for the external clock of a BNC 7050 digitaldelay generator. A synchronization trigger from the Linac RFsystem arrives roughly 100 ns prior to the electron pulse. Thispulse triggers both the BNC 7050 and the start of a time-to-amplitude converter (TAC). The prompt and delayed outputsof the BNC 7050 (now synchronized to the laser pulse train)are used to stop the TAC, and to trigger the two gated integratorsfor  I  t   and  I  o  measurement. For each incident electron pulse, a12 bit A/D converter records the time delay (TAC) voltage andthe  I  t   and  I  o  signals. On the basis of the TAC voltage, the  I  t   and  I  o  signals are summed into appropriate channels. The ratio  I  t   /   I  o and the number of samples acquired in each channel ismonitored as the experiment proceeds.Sample solutions of ca. 300 mL volume were recirculatedthrough the 1 cm square Suprasil flow cell using a Teflon/ stainless steel gear pump, at a flow rate sufficient to replacethe irradiated volume every two or three Linac shots. Duringthe experiments argon was bubbled to remove oxygen, but nogreat precautions were taken to ensure sample purity given theshort 10 ns time scale of measurement. All solutions werechecked to ensure that the solvated electron lifetime was at least1  µ s before and after a run. Under these conditions no morethan 1% of the initial signal can decay within 10 ns due toimpurity scavenging or second-order chemistry, and the short-time spur kinetics of interest are minimally distorted. We weresurprised to find that pure water gave typically a 300 - 500 nselectron lifetime at the 60 Hz repetition rate, while solutions of OH scavenger such as 0.1 M NaOAc or 0.02 M EtOH alwaysgave a 1 - 3  µ s lifetime or longer. We can only ascribe thisobservation to peroxide buildup in the flow cell due to inefficientflushing of some dead volume near the windows. The additionof even small amounts of hydroxyl radical scavenger greatlyreduces the peroxide yield and lengthens the average electronlifetime.At this point it is appropriate to comment on the advantagesof the time-correlated absorption technique over other transientabsorption methods. The first and most obvious advantage isthe very high photon flux available with the laser-based probelight source. A stroboscopic technique based on Cerenkov lightgenerated with part of the electron pulse has been usedsuccessfully for many years, 6 but the signal-to-noise ratio islimited by shot noise. Even worse, strong Cerenkov lightgenerated in the sample inevitably is scattered into the detector,making signal/background very tiny in the UV spectral region.The implementation of this technique at Argonne has beenlimited to 3.3 ns full scale. A double pass delay stage mighthave been implemented to extend the time range, but alignmentof the divergent Cerenkov light is difficult even for the 3.3 nsdelay path. The Cerenkov light is also quite sensitive to theproper tune-up of the Linac itself, and any number of experi-ments failed due to poor initial tune or drifting over the courseof a day. Because one is randomly collecting the entire kineticswindow, time-correlated absorption is largely immune to anydrifts of Linac operating parameters. Very fast transient digitizer/ photodetector techniques have also been used over the years toobtain subnanosecond kinetics, but large corrections have tobe made for the detector nonlinear response, and in general,one is always limited by shot noise. Time-correlated absorptionspectroscopy has the advantage of complete linearity overwhatever full scale is chosen (which could be any integermultiple of the laser repetition rate). For the first 10 ns of kinetics, time-correlated absorption is an ideal technique. Onlonger time scales, transient digitizer methods can be made moreefficient.To measure the spur decay at longer times, deoxygenatedsamples of neutral water from a Barnstead Nanopure cartridgesystem were irradiated with the same 30 ps Linac pulses in a 2cm quartz cell. Transient absorption was recorded on a 1  µ stime scale and longer using a Tektronix 645A digitizer with250 MHz band-pass filter and 5 GHz sampling. Two detectorsgave excellent agreement from 10 ns to longer time scales: anEG&G FND100 silicon photodiode with detection at 750 nmand a vacuum photodiode with detection at 600 nm. The lightsource was a 75 W xenon arc whose intensity was pulsed 50 to100 ×  for 300  µ s for the measurement. Wavelengths wereselected using 40 nm band-pass interference filters. Figure 1.  Schematic diagram for the time-correlated absorptionmeasurement, as described in the text. Spur Decay of the Solvated Electron in Radiolysis  J. Phys. Chem. A, Vol. 104, No. 8, 2000  1687  Results and Discussion Figure 2 illustrates the quality of the raw data obtained inthe laser experiment. The two traces shown represent transmis-sion of a water sample following a full charge Linac pulse anda half-charge pulse. The full charge pulse has two clearly visiblesatellite pulses at ( 760 ps. The half-charge pulse has one tinysatellite (typically 0.5%) following the main pulse. The ratioof   I  t   /   I  o  in the baseline was measured with a standard deviationof 0.5% per shot. The full 11 ns time scale was divided into440 channels of 25.64 ps average width. Small corrections forthe differential nonlinearity of the TAC were included in thefitting but made little difference. An average of 30 shots wererecorded in each channel to produce the data illustrated here.At 60 Hz repetition rate of the Linac, this required some 4 minto acquire. A small amount of Linac RF noise was subtractedout by recording a dark baseline just before or just after thekinetics run. The rise time of the kinetics is ca. 100 ps, whichmust be limited by trigger jitter in the Linac/laser synchroniza-tion, because the Linac pulses are known to be 30 ps fwhm,and the 1 cm sample width should be too small to introducethis much distortion from walkoff of the electron and light beams(the relativistic electrons travel near the vacuum speed of light c , while the phase velocity of light in the water is  c  divided bythe refractive index). Cross-correlation of the laser pulse trainwith itself, using a second BNC 7050 unit, demonstrated theelectronics are capable of 12 ps time resolution.Numerous cross-checks were made to ensure the signal waslinear. A solution of 0.5 M NaNO 3  was used to check fortransient absorption of the cell walls. The nitrate ion efficientlyscavenges electrons both prior to and after their solvation, sothis solution has only a tiny short-lived absorption at 780 nm.No change of the cell transmittance was detected after theelectron pulse. The transient absorption in 0.1 M HClO 4  decayedto baseline with the time constant expected for the reaction of solvated electrons with hydronium ion. 8 Identical (but noisier)kinetics were obtained with half the laser intensity and, at otherwavelengths, to check detector linearity.To fit the raw data, transient decays were described as thesum of two exponential functions plus a constant. The rise timewas reproduced by convolution of this decay with a Gaussianfunction. To account for the satellite fine structure in the Linacpulses, data sets were represented by the sum of two or moreof these functions, which were time-shifted relative to each otherby 760 ns (known from the Linac RF frequency). Fittingparameters included the four (exponential) parameters neededto describe the kinetics shape, a time shift and a Gaussian widthparameter to fit the signal rise, and individual scaling parametersfor the charge in each fine structure pulse. The kinetics followingboth the full and half-charge Linac pulses were found to beidentical after correction for the satellite pulses, as indicatedby the almost invisible fit traces in Figure 2. In this example,the fundamental decay parameters were first obtained from thehalf-charge Linac data, which only requires a small correctionfor one satellite pulse. The fundamental decay parameters werethen held fixed, and only the fine structure amplitude parameterswere adjusted to fit the full-charge Linac pulse to well withinthe noise in the data. The exponential parameters found todescribe multiple data sets in neat water at three differenttemperatures are reported in Table 1. (Note that these coef-ficients are only meant to represent the first 10 ns, as spurrecombination continues out to hundreds of nanoseconds. Thefit parameters have no mechanistic significance.)In Figure 2, we have included for comparison the spur decaykinetics reconstructed from old data in ref 5. It can be seen thatthe new time-correlated absorption result disagrees with thereconstructed kinetics of ref 5, showing a substantially slowerdecay. The conclusions of ref 5 are, in fact, largely incorrect(see below). Reexamination of the stroboscopic absorption dataused in ref 5 reveals that the best “clean” data set chosen torepresent the first 3 ns for that publication was actually an outlierresult with relatively fast decay. Other data sets from theCerenkov light stroboscopic radiolysis experiment that havesince been examined, including the srcinal report in ref 6, agreevery well with the first 3 ns of decay in the present study.To check other results of ref 6, the effect of severalconcentrated scavengers on the spur kinetics were recorded andquantified. Results are illustrated in Figure 3, and the fitparameters are included in Table 1. As shown in ref 6,scavengers for either protons or hydroxyl radicals have a similarimpact on the spur kinetics of solvated electrons, becausesolvated electrons react with both hydronium and hydroxyl withsimilar rate constants. The decay kinetics in 1.0 M ethanol andin 0.1 M NaOH are nearly identical on this time scale. A stilllonger electron lifetime is found in 1.0 M NaOH/25% methanolsolution where both OH and hydronium ion are quicklyscavenged. It was noted in ref 6 that concentrated hydroxideion is more effective in preventing intraspur loss of solvatedelectrons than are other proton scavengers. Several effects mustbe considered in this comparison. First, the ionic strength effect Figure 2.  Transient absorption of solvated electron at 780 nm recordedfollowing (A) full pulse and (B) half-charge Linac pulses. The solid-line fit curves include convolution with a Gaussian response functionand include the time-shifted satellite pulses. The spur decay parametersfit to the half-charge pulse have been applied without modification tothe full charge pulse. The dashed line indicates for comparison theincorrect result given in a recent publication. 5 TABLE 1: Fitting Parameters for Solvated Electron SpurDecay in the First Ten Nanoseconds  a solution:  A 1  T  1  /ns  A 2  T  2  /nswater, 25  ° C 0.1119 0.5195 0.2754 4.508water, 6.5  ° C 0.1370 1.1482 0.3308 9.361water, 46  ° C 0.2092 0.4200 0.3251 4.6201.0 M ethanol 0.1081 0.5410 0.1807 5.0900.1 M NaOAc 0.0909 0.5525 0.2350 4.0790.1 M NaOH 0.0864 0.5451 0.1910 4.4490.05 M NaOH 0.1436 0.5802 0.1928 5.6690.01 M NaOH 0.1644 0.7513 0.1912 5.29520% MeOH, 0.1 M NaOH 0.0772 0.2495 0.1200 5.128 a Fit equation: 1  +  A 1  exp( - t   /  T  1 )  +  A 2  exp( - t   /  T  2 ). 1688  J. Phys. Chem. A, Vol. 104, No. 8, 2000  Bartels et al.  on reaction of ions will change both recombination rates andscavenging rates. Second, the ionic strength will alter diffusionrates of the ions, in particular slowing the diffusion of solvatedelectrons and hydronium ions. Finally, as a strong base thehydroxide ion will react with the hydroxyl radical, producingthe oxide radical anion O - . The anion reacts more slowly thanthe hydroxyl radical, both with itself and with solvatedelectrons. 3 Acetate and other weak bases do not effect thistransformation. In Figure 3 we present data for 0.1 M acetatein comparison with 0.01 M NaOH and 0.05 M NaOH. Theneutralization rate constant of acetate with hydronium ion is4.5  ×  10 10 M - 1 s - 1 , while the hydroxide ion rate constant is 9 1.4 × 10 11 M - 1 s - 1 . In the 0.01 M NaOH solution, hydroniumions are scavenged in roughly 1 ns, while in the 0.05 M solution,hydronium is gone within several hundred picoseconds. In theacetate solution, after taking the primary ionic strength effectinto account, the hydronium ion should be gone within ca. 500ps. Hydrated electron kinetics in the acetate solution areintermediate between the two hydroxide solutions, but the slopeis somewhat greater, especially at longer times. The differenceseems to be qualitatively consistent with the OH/O - equilibrium.In ref 5 the (outlier) stroboscopic data were matched to anearly study 7 of spur decay performed with a fast-rise vacuumphotodiode and sampling oscilloscope that recorded kineticsfrom 200 ps to 35 ns. The splicing of data sets was performedby matching slopes at ca. 3 ns, on the assumption that secondaryresponse nonlinearity distorted the vacuum photodiode data atearlier times. However, the new time-correlated absorption datareported here are not consistent with the older vacuum photo-diode data. To extrapolate a solvated electron yield back to“zero” time, we made new measurements of the solvatedelectron absorption following our 30 ps pulse in a 2 cm Suprasilfused silica cell filled with Argon-bubbled water. In Figure 4we show the first 50 ns of data recorded at 600 nm with thesame vacuum photodiode used in ref 7. Superimposed is the(suitably scaled) fit of the time-correlated absorption data, whoseslope matches the new digitizer data well from 3 to 10 ns. Alsosuperimposed is the kinetic trace from ref 7, whose decay isclearly too fast. We have no explanation at this late date whyref 7 was incorrect. Perhaps the sampling oscilloscope used torecord the data malfunctioned.For quantitative analysis, data from an EG&G FND100photodiode detector with 750 nm analyzing light was digitizedevery 200 ps out to 1  µ s. (An identical but noisier result wasobtained at 600 nm with the vacuum photodiode mentionedabove.) We presume that all secondary response nonlinearitiesof these detectors have decayed away within 9 or 10 ns afterthe pulse. The slope of the laser time-correlated absorption datais consistent with these new transient digitizer measurements,as shown in Figure 4. The limiting lifetime of the solvatedelectron after the first 500 ns was ca. 5 - 10  µ s for the first shot,limited by second-order recombination and some impurities(probably dominated by oxygen). The decay became progres-sively shorter as peroxide built up in the cell with each shot.To perform the most precise measurements, 5 - 15 shots wereaveraged, giving an average limiting lifetime of ca. 3 - 3.5  µ sdue to the peroxide. In the spirit of the isolated spur model 1 - 4 the survival of the hydrated electron in the presence of scavengerwill follow the formwhere  k  s [S] is a scavenging rate. In the multiple shot experiment,the peroxide product acts as the dominant scavenger. The minorsecond-order homogeneous recombination can be subsumed intothe “scavenger” exponential for fitting purposes.To fit both the short time (laser) kinetics and the long time(lamp) kinetics at room temperature (25  ° C), it was foundnecessary to use a functional form for  G ° ( t  ) containing no lessthan four exponentials plus a constant:The first 10 ns of the lamp/digitizer data were replaced by the(appropriately scaled) fit to the laser data, and then thecombination was fit with the four-exponential sum, multipliedby a scaling factor and a “scavenging” exponential to fit thelimiting decay. A good separation of spur and homogeneouskinetics is achieved because the “scavenging” time constant isgreater than 3  µ s, and the longest component of spur decay is140 ns in this representation. Identical results are again obtainedwith the full and half-charge Linac pulses and in experimentsrun on several different days. By inspection of eq 9, the yieldof hydrated electron at  t   )  0 is 1.59 times the escape yield Figure 3.  Transient absorption of solvated electron in severalconcentrated scavenger solutions following the half-charge Linac pulse.Raw data, corrected to remove the contribution of the 0.5% satellitepulse, are shown for the 0.01 and 0.05 M NaOH solutions. Normalizedbest-fit curves for the other solutions and pure water are superimposedfor the sake of clarity. Figure 4.  Matching of new vacuum photodiode/transient digitizer data(dots) with the result obtained from laser time-correlated absorption(line). Good matching of slopes is obtained between 3 and 10 ns. (Thebump at ca. 20 ns is from a 1% reflection on the signal cable.) Olddata from ref 7 recorded with the same vacuum photodiode (circles)are superimposed for comparison. G ( t  ) ) G ° ( t  ) exp( - k  s [S] t  ) (8) G ° ( t  )/  G inf  ) 1 + 0.090 exp( - t   /139 ns) + 0.128 exp( - t   /24.4 ns) + 0.255 exp( - t   /3.51 ns) + 0.118 exp( - t   /0.480 ns) (9) Spur Decay of the Solvated Electron in Radiolysis  J. Phys. Chem. A, Vol. 104, No. 8, 2000  1689  G inf  . Perturbation of the fit parameters (e.g., forcing the longesttime constant to 250 ns, then refitting the remaining parameters)suggests the ratio  G ° ( t  ) 0)/  G inf   must be correct to within about3%. However, we have not carried out a formal sensitivityanalysis.Using this form for  G ° ( t  ) allows easy prediction of productyield in hydrated electron scavenger experiments by integrationof eq 8 over time. In Figure 5 we plot this prediction as afunction of   k  s [S] together with product yield data for methylchloride, 10,11 glycylglycine, 12 N 2 O, 13 - 15 tetranitromethane (TNM), 15 nitrate, 16,17 and methyl viologen 17 scavengers. Taking  G inf   ) 2.5, we obtain  G ( k  s [S])  )  2.7 for a scavenging power of 1  × 10 7 s - 1 , a result which the most precise scavenger studies haveconverged upon, with scatter of only 2 - 3%. 18 All of thescavenger results shown in Figure 4 lie within about 5 - 10%of the curve based on transient absorption, with residual scatterprobably due to systematic errors in calibration. We considerthe work of Elliot et al. 17 using both nitrate and methyl viologenscavengers, as perhaps the most reliable in the literature. Recentwork of Buxton et al. 15 has shown good agreement for bothN 2 O and tetranitromethane scavengers. The precise methylchloride measurement of Schmidt et al., 11 which was basedentirely on conductivity including a T-jump for dosimetry, isalso in superb agreement with the predicted curve.We should emphasize that we have not carried out anydosimetry in the present work. We have only measured the shapeof the solvated electron decay, and used the integral over timeto match the most reliable scavenger yields in Figure 5. Equation9 accurately represents the data to produce random residuals of the fit from 100 ps to 1  µ s, for several data sets collected ondifferent days. The fitting parameters are not unique, in thatcovariance of individual exponential decay time constants andcoefficients is significant. However, the basic shape of the  G ° ( t  )decay is quite robust, independent of dose and scavenger(peroxide) concentration. The combination of laser and lamptransient absorption reported here almost certainly gives thecorrect ratio  G ° (0)/  G inf   to better than 5%, with most of theuncertainty in the lamp/digitizer data. Further cross-checks onthe transient digitizer data could reduce this uncertainty.The new extrapolated yield of   G ° (0)  )  4.0  (  0.2 issignificantly (ca. 20%) lower than the yield of 4.9 suggested inref 5. As noted above, the previous number was based onerroneous old data, combined with the methyl chloride data 10 in Figure 4, which now appears to be about 10% high. Theglycyl glycine data, 12 which seem to agree with ref 10, may besomewhat high at the largest concentrations used s glycine itself is known to scavenge electrons prior to solvation, which couldinflate the product yield. 19 This effect of presolvated electronscavenging makes it essentially impossible to accurately deter-mine  G ° ( t  ) 0) by inverse Laplace transformation of the scav-enger data, 4 and no doubt accounts for some of the scatter inthe product yield literature.Older numbers quoted for the solvated electron yield at 30ps ( G ° (30 ps) ) 4.6 in ref 6) were based on the dosimetry andthe erroneously fast decay data in ref 7. The dosimetry used inref 7 was based ultimately on the solvated electron extinctioncoefficient reported by Fielden and Hart, 20 which has since beenshown to be 8% low. 21 (This correction alone would reducethe yield to 4.2 from 4.6.) The yield of   G ° (30 ps)  )  4.0estimated by Wolff et al. 22 referred to a limiting “microsecond”yield of 2.7 and so really should have been higher to agree withthe present experiment.It is worth noting that the often-cited estimate 23 of   G OH  ) 5.9 for the OH radical at 200 ps was based on an estimate of  G ° (200 ps) ) 4.5 for the solvated electron. This number shouldapparently be reduced to  G OH (200 ps) ) 5.1 on the basis of thepresent results.At the low end of scavenging power, it must be recognizedthat the existence of an “escape” yield  G inf   is an idealizationbased on the concept of isolated spurs in three dimensions. Inreality, even low LET  γ  and electron radiation leaves a track of spurs, and ultimately in very low dose rate situations thediffusion of radicals will result in overlap of the spurs to forma diffuse track. (At a higher dose rate (i.e., track density), as inthis study, diffusion may lead first to overlap of the separatetracks and a homogeneous concentration of species.) There isno diffusive escape ( G inf   )  0) from a cylindrical track. Theseparation we have made between homogeneous chemistry andspur chemistry is entirely empirical and might well be slightlydifferent if the dose per pulse in our experiment were reducedan order of magnitude or more. (Nevertheless very similar resultshave been found for the longest spur decay component usinglower dose 2 ns electron pulses at the Notre Dame RadiationLaboratory. 24 ) Some recent studies have called into questionthe utility of the  G inf   idealization for low dose rate and lowscavenger concentrations. 15,25 The very low scavenging powerdata of Buxton et al. 15 shown in Figure 5 could be matched byexchanging the constant 1 in eq 9 for an additional exponentialdecay with time constant of about 13  µ s. Our time-resolvedexperiment is insensitive to such a slow component of track chemistry. Conclusion Using a new asynchronous laser sampling method we havemeasured the radiolysis spur recombination kinetics for thehydrated electron from 100 ps to 10 ns. These data were foundto match up well at ca. 10 ns with new data collected with atransient digitizer and fast diode detectors. Fitting this combina-tion of results gives a ratio of   G ° (0)/  G inf  ) 1.59 for an isolatedspur model. Taking  G inf  ) 2.50 gives excellent agreement withproduct yield results of many scavenging experiments. Theextrapolated “time-zero” hydrated electron yield is  G ° (0) ) 4.0 (  0.2 electrons per 100 eV of deposited energy. Acknowledgment.  The authors would like to acknowledgeMr. Ed Kemereit for his contribution in operating and maintain-ing the Linac used in this work. We thank Dr. RichardFessenden of the Notre Dame Radiation Laboratory for sharingunpublished data on the long-time component of spur decay, Figure 5.  Comparison of experimental and predicted scavengedproduct yields, as a function of the scavenging power  k  s [S]. 1690  J. Phys. Chem. A, Vol. 104, No. 8, 2000  Bartels et al.
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