2762
The Journal of Physical Chemistry, Vol. 82,
No. 26, 1978
Trumbore et al.
Effects of Pulse Dose on Hydrated Electron Decay Kinetics in the Pulse Radiolysis of Water. A Computer Modeling Study Conrad N. Trumbore,*+ Davld R. Short,+ James E. Fanning, Jr.,+ and Jon H. Olson$ Departments of Chemistry and Chemical Engineering, University of Delaware, Newark, Delaware 1971I (Received May 15, 1978; Revised Manuscript Received August 8, 1978)
Results from a computer simulation of the pulse radiolysis of water using an improved spur model which includes a novel hydrated electron distribution and a spur overlap approximation are reported. Data for hydrated electron decay at nanosecond and subnanosecond times following pulse radiolysis of air-free water are fit within experimental error by adjustments in the initial spatial distribution of spur intermediates and the energy deposited per average spur. Using the same parameters which are successful in modeling the hydrated electron decay kinetics, pulse radiolysis data for hydroxyl radical decay are also fit within experimental error. Again using the same model parameters, the hydrated electron decay data for variable pulse dose were computed for times from s following the pulse. At a pulse dose of about 8000 rd the fit between computations and to experimental data for hydrated electron concentration is within experimental error at all times from 100 ps to 1 ps. At several kilorad pulse doses there is qualitative agreement but at very low pulse doses (below 200 rd) the fit between computer predictions and experimental hydrated electron decay data is not even qualitatively similar at times longer than s. The pulse-dose dependent deviations from our computer model predictions can be reconciled using Mozumder and Magee’s “blobs” and/or “short tracks”. The average spur density of these spatial regions is postulated to be on the order of that present in 8000-rd pulse-irradiated water.
Introduction A previous study on the effects of pulse dose on the decay kinetics of the hydrated electron in the pulse radiolysis of water has been interpreted as evidence for spur over1ap.l We further reported an empirical constant which related pulse dose to the time of the earliest, experimentally observable spur overlap. Based upon these experimental studies we have developed a simple computer spur overlap model2 which qualitatively agrees with experimental results. We have now extended the previously reported model2 into one which is fully equivalent to that used by Kup~ e r m a n nexcept ,~ for a novel initial hydrated electron distribution function, characterized by a hole in the center of the electron distribution, and a simple representation of spur overlap. We have tested our computer program with a set of parameters for a one radical model used by Kuppermann4 and have found agreement within roundoff error between the results of the two computer programs. In this paper the model has been used to match the previously reported kinetics of decay of hydrated e l e c t r ~ n s land , ~ hydroxyl radicals6generated by pulses of different doses of 14-MeV electrons. We believe the combined results of these computer studies and a reexamination of our pulse radiolysis datal give important information about spur and possibly track processes in aqueous radiation chemistry.
function of the hydrated electron and the other is the addition of a spur overlap approximation. The chemical reactions chosen to represent the expanding and overlapping spur, as well as rate constants for these reactions and diffusion coefficients for reactive species, are essentially those used by Kuppermann3 and Schwarz7 and are more fully elaborated in the supplementary material for this paper (Table 11, see paragraph at end of text regarding supplementary material). Spur reactions occur in a sphere of radius Po, which represents one-half the average interspur distance calculated from the equation
ro = 1.564 X 10-6[E/D]’/3 where E is the average spur energy in electronvolts per spur, pulse dose D is given in kilorads, and ro is in centimeters. We define C ~ ( P , T ) = c,’(p,T)/c,,d as the dimensionless concentration of reactant i at dimensionless radial position p r / r O and a t dimensionless time T t D r e f j r 2 . The scaling parameters cred and Dref(diffusivity) are those of the hydrated electron. Using a, = c,p as the modified concentration term in spherical coordinates, the conservation equations for the ith species are a set of partial differential equations of the general form aai
a2ai
- = pi-
ap2
Experimental Section All experimental data reported were determined in a manner previously described in ref 1.
where the additional parameters are defined as follows: T = t/O, dimensionless time; p i = D1/Drefr diffusivity ratio; O = ?-?IDref,diffusional time parameter; R, = dimensionless production rate of i from chemical reactions. This form is developed in greater detail below. The boundary conditions for a, are simple; the concentration of i a t the center of the sphere is finite and the concentration gradient a t the outer boundary of the sphere is zero. In terms of a, these conditions yield a t
Computer Studies (a) The Model. The computer simulation used to model pulse radiolysis data is the same application of diffusion processes coupled with chemical reaction as described by Kuppermann3 except for two modifications. One is a revision of the basic form of the probability distribution
a,=O
p = O
‘Department of Chemistry. Department of Chemical Engineering. 0022-3654/78/2082-2762$0 1.OO/O
+ Ri
p
C
=1
a a l / a p = a,
1978 American Chemical Society
The Journal of Physical Chemistry, Vol. 82, No. 26, 1978
Effects of Pulse Dose on Hydrated Electron Decay
(This latter equation is equivalent to ac,/ap = 0.) The initial distributions have three forms. The first is obvious; the concentration of scavengers and uniformly distributed reactants is c, = CLO (2) The initial concentrations of -OH, H+, and .H in dimensionless form are Gaussian, namely Cl
= G o exP[-(P/P,o)21
(3)
where plo = rlo/ro;rL0is the radial position for l / e reduction of the concentration in the spur; and clo is the concentration of species i at the center of the spur. The hydrated electron distribution is skewed away from the center of the spur; in dimensionless form the distribution is c, =
(;)
$+3/2]
exp
(-(;)I
cem is unity by virtue of the choice of the concentration scaying parameter. The term in square brackets [] is a constant. peo = (2/3)1/zpm,; pmaxis a dimensionless radial position corresponding to ce,, the maximum dimensionless concentration in the hydrated electron radial distribution. The average concentration of the ith species is the variable observed in experiments. The average concentration is given from integration in the sphere as
ci =
The reaction rate term R, is the sum of all reactions which consume or produce the ith species. a, is the dimensionless product c,p. For the hth second-order reaction involving the species 1 and m the contribution to R, is given as rik
=
TABLE I: Spur Parameters Used to Fit Pulse Radiolysis Data (from Ref 5 ) a Initial Yieldsb GoH . = 0.8’ Geaq-= 4.7‘ GoH i = 4.7‘ GoH, = 0.25‘ Go.OH = 6.0d
vikKkclarn
where Kk = hkC,,(O is the dimensionless second-order rate constant and V,k is the stoichiometric coefficient for the production of i from the hth reaction. The general term R, was partially linearized to yield the form R, = Slal + T , The coupled set of equations were solved using the Crank Nicholson finite difference algorithm. The values of S, and T, were evaluated by iteration. The solution increases the time step geometrically or under the control of max(aa,/ap) t o cover the time range from lo-’* to s. The solution accuracy is better than 1%relative error. Assumed initial yields of spur intermediates are listed in Table I along with values taken for other critical spur parameters. The initial G value for the hydrated electron, 4.7, was chosen to normalize calculations with reported G values of Jonah et aL5 A similar normalization to the G value reported for ,OH by Jonah and Miller6 yielded an initial G value of 6.0. The reported yields6 of OH radicals a t early times following the pulse are significantly higher than corresponding reported electron yields5s9under the same experimental conditions. Therefore, following the arguments of S ~ h w a r zwe , ~ have added to our computer calculations initial yields of hydrogen atoms and molecular hydrogen with the same Gaussian distribution function as that of H+ and .OH, which, along with the new hydrated electron distribution probability function, remain the same form as previously reportede2 (b) Tests of the Model. (1)Hydrated Electron and Hydroxyl Radical Decay Kinetics at Early Times. We
GoH , O , = 0
Initial Probability Distribution Function Parameters (1)l i e value is 30 A f for the .OH, H’,and H.distributions (Gaussian) (2) maximum of eaq- distribution is at 40 A f (skewed Gaussian, see text) The average energy per spur was 60 eV a Absolute rate constants, diffusion constants, and chemical reactions are essentially those of Kuppermann3 and Schwarz (available as supplementary material). Yields of molecules/100 eV at “ t = O”, before any spur Estimated from chemical reactions have taken place. Estimated from the work of the work of Jonah et aL5 Jonah and Millera6 e Arbitrary values, following treatment of Schwarz.’ No significant variation in hydrated electron decay kinetics was found by varying values of GoH from 0.4 to 1.0 (corresponding to changes in G’H, of from 0.45 to 0.15). Fits between experimental and computed values are quite sensitive to the last digit in these distribution parameters.
*
‘
U-J
1
w
pa
3
1
3pai dp
2763
“
w
> -
I-
a -J
4
I
I
t calcexp d a t a - - - 10
21:
-
9
L O G t (S)
Figure 1. Comparison of computed and experimental decay of eaqand .OH in air-free water following a short pulse of 14-MeV electrons. Experimental data are from ref 6 (OH) and 5 (eaq-)and computed curves are generated by a computer program described in the text with the fitting parameters listed in Table I.
have altered the following spur parameters to give the best fits of our computations with the experimental data of Jonah et al.5 for hydrated electron decay: average number of electronvolts per spur, width of .OH probability density distribution and radial position of the hydrated electron concentration maximum. The values listed in Table I are our current “best fit” parameters for high pulse dose hydrated electron decay kinetics and are those used for subsequent computations reported in this paper. Curve fitting of the hydrated electron decay was done primarily in the 10-lo-lO-s s region following the pulse. Figure 1 demonstrates the degree of fit achieved between computations and experimental data for the .OH radical6 and hydrated electron decay5 kinetics reported by Jonah and co-workers. The curves are within the combined limits of experimental error. We have curve fitted primarily the electron data, since there is a larger experimental uncertainty in the OH radical decay yields and kinetics.6 (2) Pulse Dose Studies. Using parameters obtained from the curve fitting procedure at early times (10-10-10-8s), the electron decay kinetics a t later times (10-8-10-6 s) were calculated and small adjustments were made in radial distribution parameters. These later times represent the period in which there is detectable spur overlap and, finally, homogenization of all spur intermediates in addition to chemical reaction. These computations are then further
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The Journal of Physical Chemistry, Vol. 82, No. 26, 7978
Trumbore et al. a CONCENTRATION US RADICIL POSITION
-
computed
exp. d a t a
0.
SEC
1 \0 . 3 9 x I O ' ' M
++**+**
(ref. 5 )
!i I \
-------
1.0
AT
( r e f . IO)
7.9 k r a d p u l s e
0
z 1 .o 0 0
1 .o W
L c
a
-1
w
1.0
LL
0
RCID
ms
1.0
b CONCENTRATION us RPIDICILPOSITIOP(AT
0
11
10
0
9 -LOG
t
7
i . ~ - e 7KC
6
6)
Flgure 2. Comparison of experimental and computed hydrated electron decay curves in the pulse radiolysis of air-free water using different pulse doses. Experimental data are taken from: (1) Jonah et al.5 for the period from 100 ps to 40 ns; (2) Fanning'' for the period from -40 ns to 1 ps. Parameters for the computer spur model are found in Table I. Arrows indicate times of overlap predicted by an empirical expression from ref 1. Curves are normalized at lO-''s to the value reported by Jonah et aL5 of Geac = 4.6 & 0.2.
tested against data taken as a function of initial pulse dose. In this manner the model is tested by demanding earlier significant spur overlap at the higher pulse doses. Figure 2 shows representative calculations and comparisons with the combined experimental data of Jonah et al.5 and of Fanning.'Jo The agreement between computer predictions and experiment is excellent at high pulse doses over four orders of magnitude of time. Good qualitative agreement is found a t doses in the kilorad range. However, a t very low doses there is no longer qualitative agreement. The nature of this disagreement a t low pulse doses is important, especially in view of the spatial plots generated by the computations. Figures 3a-3c illustrate representative spatial plots for several pulse doses. (More complete sets of radial distribution plots are presented in the supplementary material to this paper.) These plots demonstrate that, according to our model, a t relatively low pulse doses OH radicals are not homogeneously distributed at 1ps. Plots a t higher pulse dose (e.g., 2 krd) show that spur overlap does not occur until -W s and homogeneous distribution of OH radicals occurs some time between and s. (3) Oxygen Concentration Effects. Calculations of the effects of increasing concentrations of spur intermediate scavengers and variable pulse dose on hydrated electron decay kinetics are now in progress using the spur model outlined in this paper. Preliminary calculations of the effects of variable pulse dose and of relatively small concentrations of oxygen (up to 88 p M ) on the electron decay rate are being compared with the pulse radiolysis data of Fanningtofor the same oxygen concentrations. We find that for oxygen concentrations of 27 p M and 88 pM and a low pulse dose of 50 rd, as shown in Figure 4, the computed hydrated electron decay rates using the parameters listed in Table I agree within experimental error with experimentally determined rates.
q T N
R
I
1
0
1
I
RAD.
C
1.0
POS ,
CONCENTRATION US RFlDIAL POSITION FlT
LBE-ffi SEC
0.050 k r a d
40
P U ~ S B
i
WD
POS
10
Figure 3. Calculated radial concentration profiles for OH radicals as a function time following 50- and 7900-rd pulses. Spur parameters
employed are listed in Table I. Relative concentrations are scaled to the maximum concentrations of any species present. Values for this concentration maximum are shown. Radial distance is in the dimensionless parameter p ( p = r / r o , where r o is half the computed average distance between nearest neighbor spur centers). Spur overlap is indicated by a nonzero value at p = 1.0 and homogeneity of a spur intermediate is represented by a horizontal line.
Discussion T h e S p u r Overlap Approximation. First, we must emphasize that the spur overlap model employed in our calculations is only a first-order approximation to the very complex nature of the spur overlap process. Spur overlap in any real physical situation cannot be a discontinuous
The Journal of Physical Chemistry, Vol. 82, No. 26, 1978 2765
Effects of Pulse Dose on Hydrated Electron Decay
-50
0
200
400
600
Rad Pulses
800
loo0
1200
t Cns) Figure 4. Theoretical and experimental dependence of hydrated electron decay kinetics on oxygen concentration in the pulse radiolysis of water. Points are experimental data from ref 10. Solid lines are computed using the model described in the text with the parameters shown in Table I.
process but is probably instead a continuously occurring process from the earliest times following the pulse. Indeed there is undoubtedly a small amount of spur overlap during the pulse itself. Thus, it is a severe task to find a model which predicts the concentrations of reactive intermediates in the spur during the transition from the time domain when intraspur electron decay ceases to be dominant and interspur reaction becomes significant. Since spurs are randomly placed throughout the irradiated volume under our experimental conditions, the mathematical function describing the distribution of nearest-neighbor interspur distances1 exhibits a finite probability that a small number of spurs will already be “overlapping” a t times before chemical diffusion can set in. Thus, it may seem contradictory to choose an overlap approximation scheme based upon mean values of the probability distribution function for the distance between nearest neighbors. We offer the following points in defense of this model a t this stage of development: (1)The spherical overlap model chosen is mathematically the simplest first-order approximation possible. (2) The model for estimating the distribution of nearest neighbor spurs (Appendix 1 of ref 1) expresses the dependence of probability P on radius p as dP/dp = 3p2e-p3 and is based on the assumption that the spurs have initial sizes which are small in comparison with the average distance between spurs. If the spurs are considered to have an initial size of p = 0.1, then the probability of initial overlap is less than Thus, the initial overlap makes an unimportant contribution to the evaluation of the numerical parameter in the distribution function. Such an assumption has been a necessary foundation of all previous treatments of the “isolated” spur. However, with increasing time a rapidly accelerating number of spurs will overlap and contribute to interspur reaction until a t some time interspur hydrated electron reactions begin to dominate intraspur reactions. Under our pulse radiolysis conditions for all doses employed spurs should be randomly distributed throughout the irradiated sample. The average interspur distances are relatively large in comparison with the spur sizes. Therefore, there should be a finite period, which is dose dependent, in which the predominant (say up to
95%) part of the chemical reaction following an electron pulse can be attributed to intraspur reaction. We reflect this behavior in our model by approximating this early predominance of intraspur reaction as an induction period. ( 3 ) The analysis of our pulse radiolysis results1 strongly implies that under certain pulse radiolysis conditions there indeed appears to be a significant, measurable induction period before an experimentally detectable interspur contribution to chemical reactions of hydrated electrons. Our overlap test parameter is Q, the fractional electron decay rate ([-d(e, -)/(eaq-)]/dt]t,which measures the fraction of the total electron population decaying a t any particular time, t. Plots of Q vs. time for pulse doses from 37 to 364 rd are identical within experimental error up to 1ps following the pulse. This dose-independent behavior implies that at early times for low doses the contribution of interspur processes is far outweighed by intraspur processes, again justifying a significant delay time in our overlap approximation. This approximation is further justified by our plots1 of Q vs. the spherical geometry test parameter of Kenney and Walkerll [ ( d o ~ e ) l / ~ ( t i m ein )~/~] which there are a series of relatively abrupt changes from an essentially dose-independent (predominantly intraspur decay) to a strongly dose-dependent behavior of Q (increasing contribution from interspur reactions) a t a given time following the radiation pulse. (4) Finally, we believe the remarkably high degree of fit at high doses between experimental and computer curves for OH and ea; decay following high pulse doses over the time period from predominantly intraspur decay, through significant spur overlap, and on to complete homogenization is sufficient to keep this simple approximation. We believe the disagreement a t low doses arise for reasons other than the spur overlap approximation and treat this subject in the section below. Low Dose Effects. Figure 2 demonstrates that a t increasingly lower doses and between 5 X and lo4 s the predicted hydrated electron decay profile is quite different from that observed experimentally. Our model predicts very little electron decay during this late time period. Yet -25% of the hydrated electrons which have survived intraspur decay are lost to chemical reaction during this period. This implies either much higher local spur intermediate concentrations during these times or an experimental artifact which is only observed a t low doses. We have attempted to identify plausible experimental reasons for the relatively large deviations between experimental and computer-predicted electron decay rates a t low pulse doses. One possible explanation is the existence of a small, constant amount of electron scavenger which would become increasingly important in influencing the hydrated electron decay as the total concentration of spur intermediates is lowered. We have tried to curve fit our experimental results in Figure 2 a t low pulse doses by incorporating an adjustable concentration of an “impurity” electron scavenger and find that it is not possible to find a n y concentration of electron scavenger which even qualitatively fits the experimental decay pattern shown in the “oxygen-free’’solutions. This result, taken together with the ability to model the electron decays (within experimental error) a t several low oxygen concentrations (Figure 4), eliminates an electron scavenging impurity as a cause of the differences between computed and experimental values a t low pulse doses in Figure 2. Our air-free (H2 saturated), X-ray prepulsed solutions should have contained less than lo-’ M 02.12 The lower pulse doses were achieved experimentally by placing variable thicknesses of aluminum plates between
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The Journal of Physical Chemistry, Vol. 82, No. 26, 1978 I
Trumbore et al.
and/or short tracks are spaced randomly along the tracks and, therefore, are randomly distributed in three dimensions. As a crude qualitative estimate we assume that within t h e bulk of the blob or short track the density of spurs a t early times approximates the density of spurs found in -8000-rd pulse-irradiated water. Thus, at low doses we could consider two quite different regions of spur density, namely, the region within the short track and/or blob regions and the region outside these high spur density regions. As the pulse dose is increased by orders of magnitude, the average interspur distance of necessity decreases with a resulting increase in spur density. At the same time the spur density of blobs and short tracks may also increase. However, even allowing for spur penetration of blob and/or short track regions the average spur density of these high LET entities increases much more slowly than that of the spur-only regions. In some high dose region the spur densities of the spur-only region should approach the spur density of the blob and/or 1 I 1 I 1 1 I short track regions, thereby changing the kinetics to a more 100 200 300 400 t‘I2 d o s a 1 I a ( n s e c ” ‘ rod1l31 simple type. We believe the general features of Figure 5 can be explained by this qualitative model and are curFlgure 5. Test of spherically symmetric spur overlap according to the rently performing calculations which attempt to quantify model of Kenney and Walker“ for the pulse radiolysis of pure water. the behavior described above. This figure is an expanded version of Figure 4 of ref 1 and contains previously unpublished data beyond 140 ns. The relatively sharp breaks The curve fitting procedure employed has a number of at 110 ns1’2 were taken’ as an indication of experimentally critical, adjustable parameters: the three-dimensional detectable spur overlap. Data at times greater than 140 ns are inspacing of the hydrated electron and OH radical distriterpreted (see text) as indicating a change in symmetry at lower pulse bution functions and the average energy per spur. doses in agreement with trends noted in Figure 2. Quantitative fits have been found in a t least four tests of the accelerator and the sample. This would tend to scatter the computer model tried thus far: (1)eaq-decay during the beam more uniformly throughout the cell volume, but spur expansion, overlap, and homogenization at high pulse it would also lower the average energy of the pulsed dose; (2) .OH radical decay in the expanding spur; (3) ea; electrons and therefore increase the average LET of the decay with pulse dose variation over a factor of 2-3 in pulse electrons. This would lead to a somewhat higher perdose; (4) ea; decay with variation in oxygen concentration centage of the energy being deposited in short tracks and at low pulse dose. blobs, according to the calculations of Mozumder and The value used in our calculations of the average spur Magee.13 The change in the number of blobs and short energy parameter (60 eV/spur) is more consistent with the tracks caused by even such a drastic drop in pulsed theoretical predictions of Mozumder and Magee13than the electron energy from 14 to 2 MeV would cause the fracprevious adjusted value of K ~ p p e r m a n n .We ~ believe our tional contributions of short tracks to increase from -14 figure is in harmony with the concept of the bulk of the to -18% and of blobs from -8 to -9’70.~~ spurs consisting of a relatively small number of ionizations A reexamination of our pulse radiolysis data13l0points and/or dissociations, along with a small, and perhaps to a change in overlap kinetics at lower pulse doses. Figure significant, fraction of the spur energy being deposited in 5 shows an expanded version, with previously unpublished regions of more dense ionization, e.g., short tracks and/or data, of a plot of Q (see above) vs. [ ( d ~ s e ) ~ i ~ ( t i m e )the l ~ * ] , blobs. spherical geometry test parameter-ll It is clear from this The assumption of a qualitatively different hydrated plot that the data are qualitatively different after times electron distribution, with its small probability of the of 150 ns following the pulse from those,data taken hydrated electron being present initially in the same lopreceding this time. The relatively abrupt change from cation as the hydroxyl radical, is apparently successful in dose-independent to dose-dependent behavior is damped explaining the data we have examined thus far. Such a and a much longer limit to the period of dose independence hydrated electron distribution is supported by a number is observed than the previously noted constant value of of requests in the literature, e.g., Burns et al.,14Hunt,15 -110 ns1i2 rd1i3 between 60 and 150 ns. This strongly Stradowski and Hamill,16 and Pikaev,17for a similar type distribution function based on a number of different types implies that, a t lower doses, there is a slower than anof data and theoretical arguments. It is interesting to note ticipated “spur overlap” based upon extrapolations from that the data of Burns et al.14 from proton pulse radiolysis higher pulse doses. The lack of observable spur overlap at low pulse doses is also at odds with our predictions that has been explained qualitatively by a similar initial sepby 1 ys nearly complete electron homogenization has aration of the hydrated electron from other spur intermediates to prevent a rapid, early decay process. This occurred for a 50-rd pulse (see Figure 2c). We believe these apparently contradictory phenomena implies that a similar type hydrated electron distribution may be resolved by assuming a shortcoming of our model function to that employed in this paper also may be useful which is “washed out” by increasing the pulse dose. If we in calculations for higher LET radiations. assume a significant part of the pulsed electron energy, e.g., Acknowledgment. We are indebted to the University 25-5070, is deposited in blobs and/or short tracks, our of Delaware for financial support for these computations estimate of the average interspur distance of the spurs is and to Dr. Richard Murray, Dr. Charles Jonah, and Dr. on the low side because less energy is deposited in spurs. A. Mozumder for their comments and criticisms of our However, our assumption of random placement of spurs interpretation of our calculations. The USAEC supported holds even better since spurs should be spaced further the experimental portions of the work reported here. apart along the electron track. We assume that blobs I
I
/
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I
I
Gas Phase Elimination of Alkyl &Substituted Ethyl Chlorides
Supplementary Material Auailable: The chemical reactions chosen to represent the expanding and overlapping spur with the rate constants for these reactions and the diffusion coefficients for the reactive species (Table 11) as well as a more complete set of radial distribution plots (Figures 3d-31) (11pages). Ordering information is available on any current masthead page.
References and Notes (1) J. E. Fanning, Jr., C. N. Trumbore, P. G. Barkley, and J. H. Olson, J . Phys. Chem., 81, 1264 (1977). (2) J. E. Fanning, Jr., C. N. Trumbore, P. G. Barkley, D. R. Short, and J. H. Olson, J . Phys. Chem., 81, 1026 (1977). (3) A. Kuppermann in "Physical Mechanisms in Radiation Biology", Technical Information Center, Office of Information Services, US.
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Atomic Energy Commission, Washington, D.C., 1974, p 155. (4) A. Kuppermann and G. G. Belford, J. Chem. Phys., 36, 1428 (1962). (5) C. D. Jonah, M. S. Matheson, J. R. Miller, and E. J. Hart, J . Phys. Chem., 80, 1276 (1976). (6) C. D. Jonah and J. R. Miller, J . Phys. Chem., 81, 1974 (1977). (7) H. A. Schwarz, J . Phys. Chem., 73, 1928 (1969). (8) A. Kuppermann, Radiat. Res., Proc. Int. Congr., 3rd, 1966, 212 (1967). (9) J. W. Hunt et al., J . Phys. Chem., 77, 425 (1973). (IO) J. E. Fanning, Jr., Ph.D. Thesis, 1975, University of Delaware, Newark, Del. (1 1) G. A. Kenney and D. C. Walker, J . Chem. Phys., 50, 4047 (1969). (12) E. J. Hart and E. M. Fielden, Adv. Chem., 50, 253 (1965). (13) A. Mozumder and J. L. Magee, Radiat. Res., 28, 203 (1966). (14) W. G. Burns, R. May, G. V. Buxton, and G. S. Tough, Faraday Discuss., Chem. Soc., 63, 47 (1977). (15) J. W. Hunt, Adv. Radiat. Chem., 5, 303 (1976). (16) C. Stradowski and W. H. Hamill, J , Phys. Chem., 80, 1054 (1976). (17) A. K, Pikaev, High Energy Chem. (Engi. Transi.), 10, 95 (1976).
Unimolecular Gas Phase Elimination of Alkyl ,&Substituted Ethyl Chlorides and the Application of the Taft Equation Gabriel Chuchani," Jos6 A. Herndndez A,' and Irama Avila Centro de QGmica, Instituto Venezoiano de Investigaciones Cien$ficas, Apartado 1827, Caracas, Venezuela (Received June 2 1, 1978) Publication costs assisted by Instituto Venezoiano de Investigaciones Cient;'ficas
The kinetics of the gas-phase elimination of 1-chloro-3-methylbutane and l-chloro-3,3-dimethylbutane were studied in a static system over the temperature range of 418-470 "C and pressure range of 36-194 mmHg. The reactions in seasoned vessels, and in the presence of propene inhibitor, are homogeneous, unimolecular, and follow a first-order law. The rate constants are expressed by the following Arrhenius equation: for 1chloro-3-methylbutane, log h(s-l) = (14.12 f 0.05) - (235.3 f 0.7) kJ mol-l (2.303RT)-', and l-chloro-3,3dimethylbutane log k(s-l) = (13.08 f 0.19) - (218.8 f 2.5) kJ mol-' (2.303RT)-'. The relative rates of alkyl 0-substituted ethyl chlorides with respect to the unsubstituted compound when plotted against u* yield a straight line with p* = -1.81. However, polar ,!Isubstituents operating inductively with a -I effect give rise to an inflection point of the line at u*(CH3) = 0.0 into another approximate straight line with a slope of -0.42. These facts which are discussed provide further evidence of the heterolytic nature of the transition state for alkyl chlorides pyrolyses.
Introduction From the considerable number of works reported on the gas-phase pyrolyses of organic halides, only very few investigations have attempted to study compound series that may be correlated with a linear free energy relationship. This approach which may be useful to determine the nature of the transition state for these reactions has successfully been applied to the gas-phase elimination of substituted a-phenethyl chlorides' and a-substituted ethyl chloride^.^ In fact, the effect of substituents in the benzene ring remote to the reaction center in a-phenylethyl chloride gave a good linear relationship between log (hz/hojand u+ values. Electron-releasing substituents showed an increase in the rates, whereas electron-withdrawing substituents caused a decrease. The resulting p* value of -1.36 at 335 OC suggested a moderate degree of polar character in the transition state. With regard to a-substituted ethyl chlorides, the +I inductive release of the alkyl groups augment the reaction rate in the sequence t-Bu > i-Pr > Et > Me > H. This order expressed in terms g* constant by the Taft equation gave p* = -3.55 (360 "C) which favors the assumption that the elongation and polarization of the C-C1 bond in the sense C6+--C16-is the rate-determining step for these reactions. An inflection point a t a*(CH3j = 0.0 to give another slope of -0.51 is associated with 0022-3654/78/2082-2767$0 1.OO/O
electron-withdrawing substituents where a decrease in the decomposition rate is accord to the electronegativity differences, MeCO > C1 > F. This small negative p* implies that the partial positive carbon is being less developed a t the transition state. The formation of two slopes a t a*(CH3j = 0.0 was attributed to a small modification in the polar nature of the transition state due to changes of electronic relays at the carbon reaction center. Finally, other substituents with available 7~ or p electrons showed a dramatic enhancement in rate in the sequence Et0 > M e 0 > P h > CH2=CH. Since these substituents interact or delocalize their available electrons with the partial positive carbon their rate ratios relative to aphenethyl chloride were correlated with 0 values. These groups give a p+ value of -3.89 (360 "C). d e s e correlations which yield a negative reaction constant p further support the heterolytic nature of the gas-phase elimination of alkyl +
chloride^.^ In view of the results described above, it was thought to be of interest to examine the gas-phase pyrolysis of 1-chloro-3-methylbutane and l-chloro-3,3-dimethylbutane (reaction l j , and to find whether the series of alkyl psubstituted ethyl chlorides may be correlated by a linear free energy relationship. An additional purpose of the present work is to see how the few reported polar 0
0 1978 American Chemical Society
