A shock tube, laser-schlieren study of the pyrolysis of isobutene: Relaxation, incubation, and dissociation rates

Article abstract of DOI:10.1002/kin.10139

Dissociation, vibrational relaxation, and unimolecular incubation have all been observed in shock waves in isobutene with the laser-schlieren technique. Experiments covered a wide range of high-temperature conditions: 900-2300 K, and post-incident shock pressures from 7 to 400 torr in 2, 5, and 10% mixtures with krypton. The surprising observation is that of vibrational relaxation, well resolved over the full temperature range. The resolved process is completely exponential, with relaxation times in the range 20-120 ns atm. Relaxation and dissociation are clearly separated for T > 1850 K, with estimated incubation times near 200 ns atm. Incubation is essential for modeling of the very low-pressure decomposition. Modeling of gradients with a chain mechanism initiated by CH fission produces an excellent fit and accurate dissociation rates that show severe falloff. A restricted-rotor, Gorin-model RRKM analysis fits these rates quite well with the known bond-energy as barrier and 〈ΔE〉_down = 680 cm^-1. The extrapolated k_∞ is log k_∞ (s^-1) = 19.187-0.865 log T -87.337 (kcal/mol)/RT, in good agreement with previous work.

Full text of DOI:10.1002/kin.10139

A Shock Tube,
Laser-Schlieren Study of
the Pyrolysis of Isobutene:
Relaxation, Incubation, and
Dissociation Rates
S. SANTHANAM, J. H. KIEFER, R. S. TRANTER, N. K. SRINIVASAN
Department of Chemical Engineering, University of Illinois at Chicago, Chicago, Illinois 60607
Received 25 November 2002; accepted 2 April 2003
DOI 10.1002/kin.10139
ABSTRACT: Dissociation, vibrational relaxation, and unimolecular incubation have all been ob-
served in shock waves in isobutene with the laser-schlieren technique. Experiments covered a
wide range of high-temperature conditions: 900–2300 K, and post-incident shock pressures
from 7 to 400 torr in 2, 5, and 10% mixtures with krypton. The surprising observation is that of
vibrational relaxation, well resolved over the full temperature range. The resolved process is
completely exponential, with relaxation times in the range 20–120 ns atm. Relaxation and dis-
sociation are clearly separated for T > 1850 K, with estimated incubation times near 200 ns atm.
Incubation is essential for modeling of the very low-pressure decomposition. Modeling of gra-
dients with a chain mechanism initiated by CH fission produces an excellent fit and accurate
dissociation rates that show severe falloff. A restricted-rotor, Gorin-model RRKM analysis fits
these rates quite well with the known bond-energy as barrier and ꢀꢀEꢁdown = 680 cm−1. The
extrapolated k is log k (s−1) = 19.187–0.865 log T −87.337 (kcal/mol)/RT, in good agreement
∞
∞
with previous work. ꢂ 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 381–390, 2003
C
quickly followed by C H fission of this radical
INTRODUCTION
t-C4H9 → i-C4H8 + H
Isobutene is a principal product of the pyrolysis of
neopentane[1,2]. Theinitialdissociationinthisprocess
is clearly a C C fission leaving the tert-butyl radical,
as
Thus, the direct dissociation of neopentane, the process
that dominates its decomposition at high temperatures,
leads directly to isobutene.
The laser-schlieren (LS), shock tube investigation of
neopentane pyrolysis [1] was, as usual in LS studies,
confined to high temperatures (>1300 K) where di-
rect dissociation dominates over chain decomposition.
Thus, isobutene was a major product whose reactions
are very much needed in the development of a com-
plete decomposition model. Unfortunately, isobutene
C5H12 → CH3 + t-C4H9
Correspondence to: J. H. Kiefer; e-mail: kiefer@uic.edu.
Contract grant sponsor: U.S. Department of Energy, Division of
Basic Energy Sciences.
Contract grant number: DE-FG02-85ER13384.
2003 Wiley Periodicals, Inc.
c
ꢂ

382
SANTHANAM ET AL.
decomposition has never been studied above 1000 K,
so an essential part of this model was completely miss-
ing. To solve this problem we promptly began a par-
allel study of isobutene pyrolysis, again using the LS
technique and covering conditions that at least partly
overlap those of the neopentane work.
Previous work on the isobutene decomposition is
very limited; there are but two real studies of the disso-
ciation rate [3,4], one of which is quite dated [4]. The
sole dissociation channel is (other possible channels
are considered below)
were used, with uncertainties in composition of less
than 1%.
To produce the very weak shocks necessary for
observation of relaxation, incubation, and falloff in
isobutene, a slow flow of driver gas was achieved
by introducing various converging/diverging nozzles
of different throat diameters at the diaphragm. The
experiments all used Mylar diaphragms of 0.003 or
0.005 in. thickness, which were burst spontaneously
with helium. Molar refractivities used in the calcula-
tion for density gradient from measured angular de-
flection were 22.67 for isobutene [11] and 6.367 for
krypton. These were assumed constant throughout the
decomposition.
i-C4H8 → H + C4H7
(1)
Thermodynamic functions for i-C4H8 (Cp and
T
For high temperatures this will be quickly followed by
rapid dissociation of the 2-methyl-2-allyl (isobutenyl)
[5] as
H◦ − H◦298) and other species in the mechanism
were obtained from the NIST compilation of S. E. Stein
[12]. The C H bond energy, ꢀH◦ = 83.6 kcal/mol,
was calculated using ꢀf H◦ =0−4.1826, 52.103,
298
C4H7 → CH3 + C3H4
(2)
and 29 kcal/mol [13] for i-C4H8, H, and C4H7 re-
spectively, and H◦298 − H◦ = 4.0151 [14], 1.4811
0
There are also some examinations of other reactions
of the molecule such as abstraction/addition [6], the
effect of oxygen and hydrogen [6,7], and some prod-
uct dissociation [5], little of which is really helpful for
high-temperature modeling.
[15], and 4.239 kcal/mol (calculated from frequencies),
respectively, for these species.
RESULTS
Vibrational Relaxation
EXPERIMENTAL
Experimental records of voltages (raw data) taken from
some very low-pressure LS experiments are shown in
Fig. 1. These examples are also at temperatures too
low to exhibit decomposition in isobutene. The slight
bulge at the bottom right of the schlieren spike in the
upper example is then a consequence of very fast vi-
brational relaxation. For comparison, the lower figure
shows how an absence of resolved relaxation appears,
in this instance because the concentration of isobutene
is too high. The reason for the failure of resolution in
the latter is a simple consequence of the shock rela-
tions, not of an intrinsically faster process. The matter
is discussed more fully below.
Figure 2 shows semilog plots of density gradient
derived from relaxation experiments like the upper
example in Fig. 1, where the temperatures/pressures
are again too low for dissociation. Once past the shock
front signal, these profiles are clearly exponential,
and relaxation times have been obtained from these
and others like them, including the accurate Blythe
and Blackman corrections mentioned in the previous
section. The relaxation times derived from these are
presented in the Landau–Teller plot of Fig. 3. The
temperatures assigned to the experiments of both
Figs. 1 and 3 are vibrationally relaxed, chemically
The shock tube used in the experiments has a 4 ft long
driver section of 4 in. i.d. connected to a 10 ft driven
section of 2.5 in. i.d., an arrangement whose details
have been fully described [8]. Details of the LS di-
agnostics have also been given before [9]. The data
acquisition system for the LS experiment has recently
been upgraded, giving improved sensitivity and resolu-
tion, but again this has been fully described elsewhere
[1]. In addition to the improved hardware the control
and analysis software has also been updated. Among
other features the software now determines the (chem-
ically) frozen shock parameters and also calculates the
Blythe and Blackman corrections [10] used below in
the analysis of vibrational relaxation. As before [8],
velocities were set by interpolation of four intervals
calculated from measured times centered about the LS
beam. On the basis of extensive experience, the uncer-
tainty in velocity is estimated as 0.2%, corresponding
to a temperature error of < 0.5%, here approx. 10 K.
Isobutene was Matheson research (99.8%) grade,
and krypton Spectra Gases excimer grade. Mixtures
were prepared manometrically in a 50-L glass vessel
and stirred for 2 h using a Teflon-coated magnetic stir-
rer. Mixtures of 2, 5, and 10% isobutene in krypton

A SHOCK TUBE, LASER-SCHLIEREN STUDY OF THE PYROLYSIS OF ISOBUTENE
383
and again an “inverted” temperature dependence; in
all cases the observed times increase with temperature.
Thephenomenonhasbeendiscussedbrieflyinthework
on neopentane [1], and a more complete examination of
all of these molecules is in preparation [18]. Some fur-
ther comments are presented in the following section.
Dissociation
Relaxation is an important observation here, but exami-
nation of the dissociation remains our primary purpose.
Semilog plots of dissociation gradients derived from
experiments at both higher temperatures and pressures
that clearly show dissociation, but because of the high
pressure now evince no indication of relaxation, are
presented in Fig. 4. Also on these graphs are simu-
lations using the chain mechanism listed in Table I.
For this decomposition the modeling of the following
radical chain is rather more uncertain than usual, be-
cause there is almost no useful prior high-temperature
information available. The suggested mechanism cer-
tainly seems reasonable; it does consistently reproduce
the entire gradient variation in the experiments, and
it is in accord with the little available data. For ex-
ample, it produces as dominant species, CH4, C3H4
(allene/propyne), C2H6, C2H4, and H2. With one ex-
ception discussed below, this is what was found in the
few previous lower temperature studies [3,4,7]. Here
the important feature of the mechanism is its success
in fitting the profiles, because this allows for extrap-
olation of the gradients to t = 0, where unambiguous
initial conditions apply, or, equivalently, the derivation
of properties at all points following the shock-front sig-
nal. Then by producing a best fit, adjusting only the rate
of reaction (1), optimum dissociation rates can be ob-
tained. TheratesderivedfromthisroutineLSprocedure
are shown in the Arrhenius plot of Fig. 5. The “scatter”
in this plot results from the procedure of iterating a fit
to each experiment separately.
Figure 1 Two examples of raw LS voltage signals recorded
at low temperatures. The upper example shows a well-defined
exponential vibrational relaxation gradient in 5% C4H8–Kr,
the lower a complete absence of detectable relaxation in 30%
C4H8–Kr.
For short times the gradient is dominated by reac-
tions (1) and (2) in all cases, and these times are em-
phasized in the fit of the profile. The most important
of the remaining steps, again selecting those dominat-
ing the reaction for short times, are (3) through (7).
Although these steps have a significant and increasing
effect with time, they remain tied to the rate of (1), for
this is what initiates the chain. The rate of (2) is prob-
lematic at these high temperatures, but the only issue
is whether it is slow enough for (5) to contribute to
chain termination and exothermicity. Here the unusual
rate expression arises from a rough attempt to account
for falloff, and is chosen just large enough for a rapid
steady rate, and for minimal interference by (5). This
frozen values. With relaxation this fast, observation is
limited to close-to-equilibrium behavior, and this thus
seems the best assignment of conditions. This process
is but weakly temperature-dependent in any case.
The relaxation times in Fig. 3 are extremely short,
mostly less than 0.1 ꢀs atm. They are nonetheless very
long for the relaxation of a molecule with methyl ro-
tors, where typical room temperature values are in the
range of a few ns atm [16,17]. This surprising observa-
tion has now been repeated for neopentane, isobutane,
toluene, and propane, which show comparable times,

384
SANTHANAM ET AL.
Figure 2 Semilog plots of relaxation in low-temperature, low-pressure experiments for temperatures too low for evident
decomposition. The exponential relaxation zone is both fit and identified by the solid lines; preceding curved signals arise from
shock-front diffraction/refraction.
choice of rate is also fast enough to block the reverse
of reaction (1), a feature that appears to be necessary
for agreement with these gradient profiles. Reactions
(6) and (7), with their large heats of reaction, make a
significant contribution to the later gradient. Reaction
(12) gives late exothermicities. Fortunately their rates
are known for these conditions [15].
As noted, there is but little available information
on the detailed mechanism in isobutene; much of that
listed in Table I is but a crude and very uncertain esti-
mate. Except for the rate of (1), it is not recommended
for further application. For one thing there are many
likely processes and species missing. Examples are the
reactions of propene, allyl radical, and even butadiene.
The mechanism fits the LS profiles, but this is a very
Figure 3 Landau–Teller plot of vibrational relaxation times
weak criterion. There must be many other schemes that
would do this as well.
for 10% C H –Kr (ꢀ) and 5% C H –Kr [ ].
◦
4
8
4 8

A SHOCK TUBE, LASER-SCHLIEREN STUDY OF THE PYROLYSIS OF ISOBUTENE
385
Figure 4 Example dissociation density gradients in 2% C H –Kr ( ) and modeling of these (solid lines) for moderate to high
◦
4
8
pressures. Here temperatures and pressures are all vibrationally relaxed, chemically frozen, ideal incident shock values, values
assumed at the start of modeling (solid line). The tiny down signal at the start of the calculations is from C4H7 coming to
steady state; preceding experimental signals arise from shock-front diffraction/refraction. In the lower two, the absolute gradient
is plotted. The sharp downward cusp late in the process shows the onset of calculated negative gradient. The experimental
gradients are mixed.
Several much lower pressure dissociation experi-
ments are shown in Fig. 6. These are rather different
from those of Fig. 4; for one thing, they now clearly ex-
hibit both relaxation and dissociation. Again note that
relaxation actually slows with increasing T , and so the
Pτ derived from these are the largest as shown in Fig. 3.
Thus the dissociation is preceded here by a small but
significant incubation delay, as indicated by the vertical
lines in the examples of Fig. 6. Incubation times [20]
are estimated from the time of intersection of the steep
initial relaxation gradient and the more gradual sub-
sequent dissociation gradient, as shown in the figure.
Here this estimate is rendered particularly difficult by
the shortness of the delays and the large uncertainty in
time-origin (t = 0) location at very low pressures. At
the extremely low pressures of these experiments the
shock begins to become somewhat more curved and
the shock-front signal loses the initial negative spike,
a characteristic of diffraction [21], making the assign-
ment of this location increasingly difficult. Our best es-
timates of incubation time are shown in Fig. 7, where
as usual, the times are presented in ratio to the relax-
ation time. The magnitudes are much more constant,
all close to 200 ns atm.
In the present context the significant feature of the
above incubation delay is that it extracts the point of
completed relaxation with its unambiguous frozen re-
action conditions from the shock-front so that the dif-
ficulty in time-origin location is of much less conse-
quence. As shown in Fig. 6, the model calculation of
decomposition gradient has now been started at the
end of the incubation period, rather than at t = 0. The

386
SANTHANAM ET AL.
Table I Reaction Mechanism for Isobutene Pyrolysis
Reaction
log A (cgs)a
n
E (kcal/mol)
Source
(1) I-C4H8 = H + C4H7
9.939
7.970
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
3.160
0.000
−4.990
−2.100
0.000
1.500
4.000
0.000
2.530
−0.500
2.960
2.740
0.000
2.000
0.000
−7.490
0.000
0.000
0.000
0.000
0.000
0.000
0.840
0.000
41.890
25.000
0.000
8.843
0.000
62.300
70.400
90.820
8.756
14.674
40.003
0.318
8.000
7.411
8.280
98.157
12.240
0.000
8.436
9.418
0.000
6.000
0.000
45.540
0.000
0.000
63.000
0.000
0.000
78.460
59.810
0.000
See text
Estimated
See text
See text
Estimated
[15]
[15]
[15]
[19]
[15]
[15]
Estimated
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
[15]
(2) C4H7 = C3H4a + CH3
(3) I-C4H8 + H = H2 + C4H7
(4) I-C4H8 + CH3 = CH4 + C4H7
(5) H + C4H7 = CH4 + C3H4a
(6) C3H4a + M = C3H3 + H + M
(7) C3H4p + M = C3H3 + H + M
(8) M + CH4 → CH3 + H + M
(9) CH4 + H → CH3 + H2
13.600
11.459
13.800
16.690
17.540
17.655
3.610
13.500
33.601
17.044
14.000
9.060
−3.260
17.579
6.122
13.290
2.418
(10) CH3 + CH3 → C2H5 + H
(11) C2H5 + M → C2H4 + H + M
(12) 2CH3 → C2H6
(13) H + C2H5 → C2H4 + H2
(14) H + C2H6 → C2H5 + H2
(15) CH3 + C2H6 → CH4 + C2H5
(16) C2H4 + M → C2H3 + H + M
(17) C2H4 + H → C2H3 + H2
(18) CH3 + C2H5 → C2H4 + CH4
(19) CH3 + C2H4 → C2H3 + CH4
(20) CH3 + H2 → CH4 + H
(21) 2C3H3 = C6H6
3.836
12.410
6.700
(22) C3H4a + H = C3H3 + H2
(23) 2C3H3 = C6H6L
12.800
41.619
13.500
11.590
12.700
13.400
13.000
12.720
10.600
13.600
(24) C2H3 + M → C2H2 + H + M
(25) H + C2H3 → C2H2 + H2
(26) CH3 + C2H3 → C2H2 + CH4
(27) C3H4a + M = C3H4p + M
(28) C3H4a + H = C3H4p + H
(29) C3H3 + H = C3H2 + H2
(30) C3H3 = C3H2 + H
(31) C3H5 = C3H4a + H
(32) C3H5 + H = C3H4a + H2
[15]
ak = AT n exp(−E/RT ).
incubation delay is quite necessary; modeling actually
fails disastrously if it is not introduced. In Fig. 8 we
show several attempts to model the 1873 K example
of Fig. 6 without any such delay. As shown, there is
simply no choice of dissociation rate constant that can
fit these gradients without including the delay. Again,
the complete set of derived dissociation rate constants
for all pressures is presented in Fig. 5.
Also shown in Fig. 5 are the results of a sim-
ple restricted-rotor Gorin model RRKM calculation
[22,23]optimizedtofitthemeasuredrates. Thedetailed
parameters for the calculation are listed in Table II.
DISCUSSION AND CONCLUSIONS
Figure 5 Rate constants for C H fission in 2% C4H8–Kr
( ) 300–350 Torr, (ꢀ) 100–150 Torr; 5% C H –Kr (ꢁ) 300–
◦
4
8
A few features of the mechanism used herein are prob-
lematic and require further consideration. The first con-
cerns the possibility of other dissociation channels.
350 Torr; 10% C H –Kr [ ] 10–15 Torr. The RRKM model
ꢀ
4
8
fit is shown for infinite pressure, 300, 100, and 10 Torr by the
solid lines respectively.

A SHOCK TUBE, LASER-SCHLIEREN STUDY OF THE PYROLYSIS OF ISOBUTENE
387
Figure 6 Dissociation and preceding relaxation gradients ( ) in 10% C H –Kr at very low pressures. The steep straight lines at
◦
4
8
the outset are fits of the initial exponential relaxation, and the subsequent curves show modeling of the following decomposition
started after complete relaxation. Incubation times are bounded by the vertical dashed lines with delays marked ti. (Note the
caption of Fig. 4).
Some of these possibilities are
of the higher energy channel through interference by
the lower channel when energy transfer is nearly rate-
controlling [16]. The last two molecular channels will,
at least initially, produce high-energy diradicals. This,
together with the product analysis and the strong evi-
dence for chain reaction [3], would all suggest they are
not significantly involved.
˙
i-C4H8 → CH3 + CH3C CH2
i-C4H8 → CH4 + C3H4
i-C4H8 → C4H6 + H2
Another problem with the mechanism concerns the
possible role of the addition/substitution
The first step was actually proposed by Bradley and
West [25] as the dominant channel, but its heat of reac-
tion is estimated to be almost 17 kcal/mol higher than
that of C H fission and so its contribution should be
small. Of course, for very high temperatures, the larger
A-factor always associated with C C fission might be-
gin to make it more competitive. However, this is con-
sidered most unlikely here because of the strong falloff.
Such falloff will further act to reduce the contribution
H + i-C4H8 → tert-butyl → iso-butyl
→ CH3 + C3H6
Propene is a major product in the low-temperature py-
rolysis [3], so this step may well be important. Here

388
SANTHANAM ET AL.
In several ways, the dissociation rate results ob-
tained here are quite as expected. The RRKM model
fits the measured rates very well with the known bond
energy as barrier, ꢀH◦ = E0, and its other parame-
0
ters are routine. Over the 1600–2400 K range of the
experiments, a modified Arrhenius fit of the extrapo-
lated high-pressure-limit rate is
log k (s−1) = 19.187 − 0.865 log T
∞
− 87.337 (kcal/mol)/RT
A comparison of this expression with the two ear-
lier results [3,4], both at much lower temperatures so
they should closely approximate k , is presented in
∞
Fig. 9. Agreement is really excellent here considering
the length of the extrapolation. Because of the limited
range in 1/T of LS data, the most difficult determina-
tionisusuallythatofthebarrier, whereasthemagnitude
Figure 7 Incubation times in 10% C H –Kr ( ).
•
4
8
of k should be quite solid. Based on the length of the
∞
the prior isomerization to iso-butyl should be neces-
sary, as was suggested by Douhou et al. [3]. Tsang and
Walker [7] provide a rate constant over 1000–1180 K
for the overall process, which is just slightly less than
that of the abstraction (3). The difficulty with assess-
ing the contribution of this reaction lies in the high
temperatures and low pressures of the present study.
Here the activated adduct must be difficult to stabilize
and/or isomerize before rapid reversion to reactants. Of
course it is still possible there is some contribution from
substitution, but it should be small, and it is difficult to
estimate. This process is not included here.
extrapolation to k and the data scatter, the uncertainty
∞
in magnitude should be less than 50%.
The one unexpected feature of this study is the ob-
servation of vibrational relaxation, and at high tem-
peratures, a consequent unimolecular incubation delay.
Although there appear to be no room temperature ul-
trasonic results on relaxation in isobutene, the lowest
frequencies (see Table II) are near those of neopen-
tane where the room temperature relaxation time is ∼4
ns atm [17]. Isobutene may be assumed to be similar.
The probable cause of the considerable increase in re-
laxation times with T in this and other species with
methyl rotors and fast low-T relaxation must be the
Figure 8 Example illustrating the need for incubation de-
lay in modeling the low-pressure group of experiments. The
figure is a repetition of the 1873 K example in Fig. 6. The
solid (——), dotted (· · · · · ·), and dashed (-----) lines show
attempts to model the experiment without incubation using
a higher rate, the same rate (note the solid dark line), and a
lower rate. None of these is considered satisfactory.
Figure 9 Comparison of present derived k (1600–2300)
shown by the solid line. The data is extrapolated to compare
∞
with earlier literature rates from [ ] Ref. [3] and ( ) Ref. [4]
◦
ꢂ
by the dotted line.

A SHOCK TUBE, LASER-SCHLIEREN STUDY OF THE PYROLYSIS OF ISOBUTENE
389
Table II Restricted-Rotor Gorin Model RRKM Parameters for C4H8 → C4H7 + H
Frequencies (cm−1)a and degeneracies [24]
C4H8
3086(1), 2989(1), 2996(1), 2983(1), 2950(1), 2942(1), 2911(1), 2893(1), 1655(1),
1461(1), 1450(2), 1442(1), 1416(1), 1383(1), 1377(1), 1278(1), 1079(1), 1058(1),
1053(1), 988(1), 970(1), 887(1), 802(1), 700(1), 430(1), 431(1), 378(1),
196(1), 193(1)
C4H7
2989(1), 2983(1), 2996(1), 2950(1), 2942(1), 2911(1), 2893(1), 1400(1), 1461(1),
1450(1), 1442(1), 1416(1), 1383(1), 1377(1), 1200(1), 1079(1), 1058(1), 988(1),
970(1), 887(1), 1000(1), 700(2), 500(2), 378(1), 196(1)
Moments of inertia (10−40 g cm2)
Molecular active
Transition state activeb
η
91.837 [24]
91.837, 100.16, 181.88
1 − (0.0039) [present work]
Reaction path degeneracy
6
E0(=ꢀH◦0) (kcal/mol)
84.000
680.0 [present work]
ꢀꢀEꢁdown (cm−1
)
aState count used a grain size of 10 cm−1
bEstimated.
.
need to transfer much greater amounts of energy at
high temperatures. But this now occurs with a transi-
tion probability that is already near unity, so it cannot
further increase to compensate. This notion is (crudely
perhaps) embodied in the well-known “series model”
[26] of polyatomic relaxation, and this simple model
can actually account for the effect rather well. The ap-
plication of this model to isobutene and other related
systems will be published in Chemical Physics [18].
One unfortunate peculiarity of relaxation times that
decrease with lowering of the temperature is the dif-
ficulty of obtaining good low-temperature relaxation
times. In the present instance it is essentially impos-
sible to resolve the process much below 1000 K. A
related difficulty arises when one attempts to resolve
the process in higher concentrations of isobutene. Be-
cause of the much larger heat capacity of the isobutene
the shocks have to be much faster. Then the density
ratio across the shock also becomes large, produc-
ing increased time compression and loss of resolution.
This phenomenon is illustrated in the lower example
of Fig. 1, where the increased heat capacity requires
stronger shocks to reach the necessary high tempera-
tures, and these inevitably have larger velocities and
density ratios. Finally, we note that this study provides
another rather convincing example of the success of
“standard” RRKM models in treating high-temperature
falloff in large molecule unimolecular dissociation.
2. Baldwin, A. C.; Lewis, K. E.; Golden, D. M. Int J Chem
Kinet 1979, 11, 529–542.
3. Douhou, S.; Perrin, D.; Martin, R. J Chim Phys 1994,
91, 1597–1627.
4. Szwarc, M. J Chem Phys 1949, 17, 3, 292–295.
5. Tsang, W. Int J Chem Kinet 1973, 5, 929–946.
6. Tominaga, H.; Arai, H.; Moghul, K. A.; Takahasi, N.;
Kunugi, T. Kogyo Kagaku Zaashi 1971, 74(3), 371–
375.
7. Tsang, W.; Walker, J. A. Proc Combust Inst 1988, 22,
1015–1022.
8. Kiefer, J. H.; Manson, A. C. RevSci Instrum 1981, 52(9),
1392–1396.
9. Kiefer, J. H. In Shock Waves in Chemistry; Lifshitz,
A. (Ed.); Marcel Dekker: New York, 1981; pp. 219–
277.
10. Kiefer, J. H.; Kumaran, S. S.; Sundaram, S. J Chem Phys
1993, 99(5), 3531–3541. (Note: The Blythe correction
factor given here is incorrect. The correct expression
is µ = Cvib/Cα[1 − (m2(γα − 1)/(1 − m2))]. The cor-
rectexpressionwasusedtherein;thispapersimplyseems
to have a transcription error.)
11. Gardiner, W. C., Jr.; Hidaka, Y.; Tanzawa, T. Combust
Flame 1981, 40, 213–219.
12. Stein, S. E.; Rukkers, J. M.; Brown, R. L. NIST Stand.
Ref. Database 25, Thermochemical Data, 1991, Version
1.2, NIST, Gaithersburg, MD.
13. Burcat, A.; Mcbride, B. Ideal Gas Thermodynamic
Data for Combustion and Air-Pollution Use, Technion
Aerospace Engineering Report TAE 732, Technion,
Haifa, Israel, January, 1995.
14. Smith, B. J.; Radom, L. J Phys Chem A 1998, 102,
10787–10790.
15. Ikeda, E.; Tranter, R. S.; Kiefer, J. H.; Kern, R. D.; Singh,
H. J.; Zhang, Q. Proc Combust Inst 2000, 28, 1725–
1732.
BIBLIOGRAPHY
1. Srinivasan, N. K.; Kiefer J. H.; Tranter, R. S. J Phys
Chem 2003, 107, 1532–1539.
16. Just, Th. Proc Combust Inst 1994, 25, 687–704.

390
SANTHANAM ET AL.
17. Holmes, R.; Jones, G. R.; Lawrence, R. Trans Faraday
Soc 1965, 62, 46–53.
18. Gireesh, S. C.; Srinivasan, N. K.; Santhanam, S.; Kiefer,
J. H.; Tranter, R. S. Chem Phys (submitted).
19. Sutherland, J. W.; Su, M.C.; Michael, J. V. Int J Chem
Kinet 2001, 33, 669–684.
20. Tsang, W.; Kiefer, J. H. Advanced Series in Physical
Chemistry, Vol. 6 (Chemical Dynamics and Kinetics of
Small Radicals, Pt. 1), Liu, K.; Wagner, A. F. (Eds.);
World Scientific: Singapore, 1995; pp. 58–119.
21. Kiefer, J. H.; Al-Alami, M. Z.; Hajduk, J.-C. Appl Opt
1981, 20, 221–230.
22. Gorin, E. Acta Physicochim U.R.S.S. 1938, IX(5), 681–
696.
23. Baldwin, A. C.; Golden, D. M. J Phys Chem 1978, 82(6),
644–647.
24. Chhiba, M.; Vergoten, G. J Mol Struct 1994, 326(1–3),
35–58.
25. Bradley, J. N.; West, K. O. J Chem Soc, Faraday Trans
1 1976, 72(3), 558–567.
26. Cottrell, T. L.; McCoubrey, J. C. Molecular Energy
Transfer in Gases; Butterworths: London, 1961.