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Communications to the Editor
(21)E. N. Cain and R. K. Solly, J. Am. Chem. Soc.,94, 3830 (1972); Ausf. J. Chem., 28, 2079 (1975). (22) J. E. Douglas, B. S. Rabinovitch, and F. S. Looney, J. Chem. Phys., 23, 315 (1955). (23) A referee has called attention to a paper by H. M. Frey, A. M. Lamont, and R. Walsh, J. Chern. SOC. A , 2642 (1971), which presents evidence to show that the cis-trans isomerization of 2,3-dimethyl-l,3-pentadienealmost certainly proceedsvia the intermediate formation of 1,2,3-trimethyIcyclobutane and not via a biradical mechanism. These workers also studied the cis-trans isomerization of 1,3-pentadiene. The skiation was less clear but again intermediate formation of a cyclobutane seemed more likely than a biradical mechanlsm. A similar pathway for 3-methyl-l,3-pentadiene seems likely. This paper was overlooked by Marley and Jeffers.
Keith D. Klng
Department of Chemical Engineering University of Adelaide Adelaide, South Australia 500 1 Received JuV 19, 1976
Reply to the Comment on Resonance Stabilization Energies from Cis-Trans Isomerization Studies
Sir: There is little we can challenge in Professor King’s communication, except perhaps its tone. We feel that the differences in derived stabilization energies may well be within the stated experimental error limits, in most cases. A discussion of the 2-butene rate constant was presented in J. Phys. Chem., 78, 1469 (1974). However, since the stabilization energies under criticism are derived from relative rate measurements, the absolute value chosen for 2-butene isomerization seems irrelevant. Most of the cis-trans isomerization results reported in our series of papers were based on about 10-20 shock experiments. Perhaps what is really needed is a more extensive (and perhaps more careful) set of experiments. Our studies appear to be the most complete and generally reliable set of results on the kinetics of systems which from all indications are difficult to study by other techniques. We would urge further experiments before challenging the shock tube relative rate techniques on the basis of existing cis-trans isomerization results. Department of Chemistry State University of New York at Cortland Cortland, New York 73045
Peter M. Jeffers
Received September 15, 1976
Preliminary Report of a Spur Model Including Spur Overlap
Sir: Experimental results from picosecond pulse radiolysis studies’ have prompted Kupperman2 to introduce significant changes in certain parameters of the spur model in aqueous radiation ~hemistry.~-~ Using the stroboscopic method, Wolff et a1.6 found there was very little, if any, decay of the hydrated electron concentration in pure water during the time period from 20 to 350 ps following the delivery of a short, high-energy electron pulse. Jonah et al.7 have suggested the 3% decay in hydrated electron concentration, which they observe in their electron pulsed water from 100 to 350 ps, is probably within the experimental error of the measurements of Wolff et ala6 However, both Wolff et aL6 and Jonah et al.7 state, for different reasons, that their hydrated electron decay (or lack thereof) differs by amounts greater than their estiThe Journal of Physical Chemistry, Vol. 81, No. 10, 1977
mated experimental error from the spur decay calculations based upon parameters used by Schwarz5 and Kupperman,2 respectively. Most quantitative pulse radiolysis studies have concentrated on either one of two time periods following delivery of the pulse, either the period of “isolated spur decay” or a much later time period when all reactive intermediates are homogeneously distributed. We have completed an experimental pulse radiolysis study of the effects of pulse dose on hydrated electron decay rates in pure water using 20-11s pulses of 14-MeV electrons.8 In order to interpret the results of this study, we have postulated spur overlap as being responsible for the relatively abrupt alterations in the kinetics of electron decay observed as functions of pulse dose and of time following the pulse. A simple model’ for the relaxation of the concentration distribution in the spurs suggests that the critical length parameter is proportional to dose’I3 and the critical (diffusional) time parameter should be scaled as time’/2. The data were analyzed to yield an estimate of the time (in nanoseconds) of spur expansion following a 20-11s electron pulse to reach experimentally observable spur overlap (to):
to =
1.2 x 104 [ d ~ s e ( r a d s ) ] * ns ’~
The time to reach observable spur overlap suggested by these relations is earlier than those predicted by Kenney and Walker.’ Furthermore, these data suggest that spur overlap needs to be taken into account in spur modeling studies, especially when using large pulse doses and/or relatively low energy pulsed electrons as radiation sources. As a result of the above experimental results, we have initiated a computer modeling study to attempt to fit a diffusion model incorporating spur overlap features to pulse radiolysis hydrated electron decay data between lo-’’ and lo-’ s. In this relatively crude model we have included a smooth transition through the time regions of predominantly intraspur electron decay, spur overlap (with spherical symmetry), and, finally, homogeneous reactions of the hydrated electron. This model has given surprisingly good qualitative overall fits to these experimental data over this wide time region and especially good fits to very early electron decay data. We wish to report on these preliminary results at this time because the nature of the initial hydrated electron distribution employed differs qualitatively from those used heretofore. Previously published computer modeling ~ t u d i e s have ~-~ employed concentration probability distribution functions for intermediates created by the ionizing radiation centered about the spur origin with a maximum value at the origin for all intermediates contained in the spur. Such functions appeared to us to be inherently in conflict with at least some of the experimental data of picosecond pulse radiolysis experiments showing the lack of or very small amount of decay between and lo-’ s. They also appeared to be in conflict with the basic ideas of Lea” and Platzman,” namely, that ejected electrons would be hydrated or thermalized at some distance from the parent positive ion. The Gaussian distribution for hydrogen atoms was originally chosen by Samuel and Magee3a(a) for mathematical tractability and (b) since the ejected “electron cannot go very far without suffering wide deflections resulting from s~attering”.~‘We believe that electrons formed in the ionization event may very well be able to travel fairly large distances from their positive ion N
1027
Communications to the Editor
The model is the numerical solution to three partial differential equations of the form
aci/at= Div2Ci- ri
(1)
where Ci is the concentration of eaq-.,H+, or OH.; Di is the translational diffusivity of the species (values were taken from ref 2); and pi is the rate of consumption of the ith species. Equation 1is formulated in spherical coordinates; the two boundary conditions are:
aCi(t, 0 ) p r = 0 bounded concentration a t spur 00
0 2
0 4
P Figure 1. Probability density functions chosen for hydrated electron, hydroxyl radical, and hydrogen ion in the overlapping spur model. The ordinate represents the probability of finding the reactive species at the radial distance ( p = r / r o where r,, is half the average distance between nearest neighbor spur centers). These curves are constructed in the computer program to make the integrated concentration between p = 0 and p = 1 proportional to the initial Gvalues of the reactive species. p = 1 represents the radius of the sphere inside which the spur (whose center is located at p = 0) expands until overlapping with the spherically symmetrical average of all other spurs overlapping with that designated spur. Spur overlap in this figure occurs when the concentration of any reactive intermediate is a significantly nonzero value at p = 1 .O. Parameters for these figures include the Gvalues: Geaq-= 4.6, GOH= 4.6, G+ , = 4.6. The maximum in the hydrated electron distribution function illustrated is at 40 A from the spur center, whereas the average interspur distance (2r0) is approximately 900 A (corresponding to a pulse dose of 2400 rads). The l / e value for the -OH and H+ concentrations is 25 A from the spur center. A value of 60 eV/spur is employed in these calculations
partner without significant scattering, perhaps by means of “conduction bands’’ formed from the transient water organization. As Samuel and Magee originally suggested3” their model is a classical picture and a quantum mechanical model is probably needed for a more accurate representation of very early electronic phenomena at times during and immediately following ionization. Some indirect evidence for separate distributions of electrons and positive ions or .OH can be seen in the work of Fhitsimring et a1.l’ in their study of the detailed track structure of irradiated frozen aqueous acids. In our model, we have assumed identical Gaussian initial distributions centered at the origin of the spur for both H+ and .OH and a skewed Gaussian for the hydrated electron distribution, with zero probability of finding the hydrated electron in the center of the spur. Plots of the distributions tested are shown in Figure 1. The forms are chosen to separate initially most of the hydrated electrons from other reactants and consequently produce a negligible initial rate of reaction for hydrated electrons. The computer simulation used to model an overlapping spur is a straightforward application of diffusional processes coupled with chemical reaction. The simplest set of reactions which can be expected to represent hydrated electron decay at early times (less than 1ks after the pulse) is comprised of the following reactions, using the rate constants quoted in ref 2: ea
