Pyrolysis of furan at low pressures: Vibrational relaxation, unimolecular dissociation, and incubation times

Article abstract of DOI:10.1021/jp9823042

Vibrational relaxation, incubation times, and unimolecular dissociation of C₄H₄O have been investigated over the extended temperature range 500-3000 K in 2-5% furan-krypton mixtures, 2% furan-neon mixtures, and in pure furan. The experiments were performed in shock waves using laser-schlieren (LS) densitometry and time-of-flight (TOF) mass spectrometry. At low temperatures and low pressures, only vibrational relaxation was observed using the LS technique. This relaxation is unexpectedly slow and shows a strong nonexponential time dependence. Unimolecular dissociation is observed in TOF experiments between 1300 and 1700 K in a pressure range of 175-250 Torr as well as LS experiments between 1700 and 3000 K for pressures between 100 and 600 Torr. The TOF experiments show that under the given conditions two molecular dissociation channels leading to C₂H₂ + CH₂CO or to C₃H₄ + CO are dominant. The branching ratio between these channels has been determined between 1300 and 1700 K. At low temperatures, the molecular channel leading to C₃H₄ and CO is preferred, but a channel switching was observed around 1700 K. The domination of these molecular channels is consistent with the shape of the LS profiles, and these have been successfully modeled with just these two reactions. The overall unimolecular rate constant is in the falloff regime close to the low-pressure limit. By use of statistical reaction rate theory, the total unimolecular rate constant could be modeled over an extended temperature and pressure range using a value of 〈ΔE〉_all = 50 cm^-1 for the furan dissociation. In a small range of conditions at low pressures and high temperatures, both the vibrational relaxation and dissociation were resolved and incubation times estimated.

Full text of DOI:10.1021/jp9823042

7480
J. Phys. Chem. A 1998, 102, 7480-7486
Pyrolysis of Furan at Low Pressures: Vibrational Relaxation, Unimolecular Dissociation,
and Incubation Times
D. Fulle, A. Dib, and J. H. Kiefer
Department of Chemical Engineering, UniVersity of Illinois at Chicago, Chicago, IL 60607
†
Q. Zhang, J. Yao, and R. D. Kern*
Department of Chemistry, UniVersity of New Orleans, New Orleans, Louisiana 70148
ReceiVed: May 19, 1998; In Final Form: July 7, 1998
4 4
Vibrational relaxation, incubation times, and unimolecular dissociation of C H O have been investigated over
the extended temperature range 500-3000 K in 2-5% furan-krypton mixtures, 2% furan-neon mixtures,
and in pure furan. The experiments were performed in shock waves using laser-schlieren (LS) densitometry
and time-of-flight (TOF) mass spectrometry. At low temperatures and low pressures, only vibrational relaxation
was observed using the LS technique. This relaxation is unexpectedly slow and shows a strong nonexponential
time dependence. Unimolecular dissociation is observed in TOF experiments between 1300 and 1700 K in
a pressure range of 175-250 Torr as well as LS experiments between 1700 and 3000 K for pressures between
1
00 and 600 Torr. The TOF experiments show that under the given conditions two molecular dissociation
channels leading to C + CH CO or to C + CO are dominant. The branching ratio between these
channels has been determined between 1300 and 1700 K. At low temperatures, the molecular channel leading
to C and CO is preferred, but a channel switching was observed around 1700 K. The domination of these
2
H
2
2
3 4
H
3 4
H
molecular channels is consistent with the shape of the LS profiles, and these have been successfully modeled
with just these two reactions. The overall unimolecular rate constant is in the falloff regime close to the
low-pressure limit. By use of statistical reaction rate theory, the total unimolecular rate constant could be
-
1
modeled over an extended temperature and pressure range using a value of 〈∆E〉all ) 50 cm for the furan
dissociation. In a small range of conditions at low pressures and high temperatures, both the vibrational
relaxation and dissociation were resolved and incubation times estimated.
Introduction
performed very low pressure pyrolysis experiments and identi-
fied C3H4 and CO as the products of the unimolecular
The unimolecular dissociation of large molecules is of
considerable importance in many combustion processes. Aro-
matic heterocycles such as furan are emitted by combustion of
dissociation using mass spectrometry. The higher temperature
6
,8
single-pulse shock-tube (SPST) experiments and the time-
resolved infrared absorption measurements of furan disappear-
1
2
fuels and biomass and have been identified as air pollutants.
8
ance draw a more complicated picture of the pyrolysis
Additionally, furan appears to be an excellent molecule to study
the fundamentals of the unimolecular dissociation of large
molecules over a wide range of conditions, covering vibrational
relaxation, unimolecular dissociation, and perhaps incubation.
This study describes laser-schlieren and time-of-flight experi-
ments behind shock waves at pressures below 600 Torr that
were performed over a wide temperature range. At low
temperatures, only vibrational relaxation of furan was observed
in diluted krypton mixtures and in the pure gas. At higher
temperatures, the unimolecular dissociation becomes important.
At very low pressures (<100 Torr) and higher temperatures,
both processes were observed during a single experiment. From
these experiments the incubation time, the delay until a steady
state for the unimolecular dissociation has been achieved, could
mechanism. Propyne, CO, C2H2, CH2CO, allene, C4H6, C2H4,
CH4, C4H4, C4H2, and benzene have been identified by gas
chromatography/mass spectrometry (GC/MS) analysis. Lifshitz
6
8
et al., as well as Organ and Mackie suggested that the initial
and rate-determining step of furan dissociation is a ring-opening
process, a cleavage of the C-O bond. The resulting L-furan
then reacts rapidly to form several products. This mechanism
suggests that the overall rate constant for furan loss can be
treated by unimolecular reaction rate theory as a rate-controlling
single-channel reaction leading to L-C4H4O. The branching ratio
between the different product channels will then depend on the
energy and structure of multiple transition states. In detail, their
suggested dissociation mechanism can be written as
3
4
be estimated. Besides N2O and norbornene C7H10, furan is
the only polyatomic molecule for which vibrational relaxation,
unimolecular dissociation, and incubation times have been
experimentally observed.
C H O f L-C H O
4
4
4
4
f C H + CO
∆Hr,298 ) 110 kJ/mol
∆Hr,298 ) 214 kJ/mol (1b)
∆Hr,298 ) 422 kJ/mol (1c)
(1a)
3
4
f CH CO + C H
2
2
2
Previously, the dissociation of furan had been investigated
5
-8
5
for temperatures between 960 and 1700 K.
Grela et al.
f HCO + C H
3 3
†
However, reaction 1c should be negligible because of its high
heat of reaction compared to the other two channels. Its possible
Permanent address: Department of Physics and Engineering, Xavier
University of Louisiana, New Orleans, LA 70125.
S1089-5639(98)02304-4 CCC: $15.00 © 1998 American Chemical Society
Published on Web 09/02/1998

Pyrolysis of Furan at Low Pressures
J. Phys. Chem. A, Vol. 102, No. 38, 1998 7481
contribution to the initiation of a radical chain mechanism is
discussed below. It should be noticed that the heat of formation
for the biradical L-furan has not been determined experimentally.
8
Organ and Mackie estimated a value of ∆Hf,298 K ) 297 kJ/
mol for L-furan and a heat of reaction of ∆Hr,298 ) 332 kJ/mol
for the initial dissociation step using group additivity techniques
described in ref 9. This value is in good agreement with the
experimental activation energies at high pressures of 324 or 327
8
kJ/mol obtained in SPST experiments. The overall heats of
reaction for the formation of final products are very well
established. Because of the large variety of products, they
concluded that the pyrolysis must include some contribution
from a chain mechanism, which may be started by reaction 1c
or by the unimolecular dissociation of either of the products
C3H4 and CH2CO.
The SPST studies were performed at total pressures of around
and 20 bar. One would then expect that the unimolecular
26
8
Figure 1. LS profile showing vibrational relaxation in a 2% furan/
krypton mixture at P ) 68 Torr and T ) 1168 K. The dashed line
represents the exponential fit to the final decay.
dissociation rate constant of a molecule the size of furan is close
to the high-pressure limit. Consistent with this, there are no
significant differences in the rate constants from the study at 2
bar and the study at 20 bar. The rate constant of the 2 bar
study of Lifshitz et al. is even a little higher than the data from
the 20 bar study of Organ and Mackie, but within experimental
error they agree with each other.
shock velocity was measured by interpolation of intervals from
five pressure transducers spaced about the observation window
at 120 mm apart. Using thermodynamic properties of the
reactants, the diluent, and the reaction products, postshock
temperatures without relaxation and for fully relaxed conditions
were calculated with an accuracy of (10 K.
6
While the high-pressure limiting rate constant k1,∞ for the
unimolecular furan dissociation seems to be well established,
there is no information regarding falloff behavior or the low-
pressure limiting rate constant. In addition, the temperature
dependence of the branching ratio between the two dominant
molecular channels 1a and 1b is still uncertain. Therefore, time-
resolved kinetic measurements in shock waves combining the
time-of-flight (TOF) and the laser-schlieren (LS) techniques are
indeed helpful to improve the understanding of the pyrolysis
mechanism of furan. The first low-pressure measurements of
the rate constant for the initial rate-determining step (the C-O
bond cleavage) and the real time measurements of major product
formation are presented, giving a new measure of the branching
ratio between the dissociation channels. Additionally, accurate
rates at low pressures will be provided, allowing the observation
of falloff effects in this reaction. Furthermore, the vibrational
relaxation and incubation time measurements represent a unique
opportunity to improve the understanding of collisional energy
transfer and dissociation in polyatomic molecules.
Time-of-Flight. A 2% furan-98% Ne mixture was prepared
from reagents obtained from the following sources: furan from
Aldrich (purity >99%) and research grade neon from Matheson
(99.999%). Furan was introduced into the gas-handling system
by vaporization of the liquid sample, condensed by LN2, and
doubly distilled. The middle fraction was retained for the
mixture. Mass spectrometric analysis of the pure furan and of
the 2% furan/neon mixture revealed an absence of impurities
within the detection limit of TOF, ca. 300 ppm. The following
mixtures, all with neon diluent, were prepared to determine the
mass spectrometric sensitivity factors: 2% C2H2, 2% CO, 2%
allene, 2% propyne, and 2% diketene. The calibration experi-
ments were performed at nonreacting temperatures. For the
diketene mixture, the dissociation of diketene at 1050 K occurred
shortly after shock front arrival; the mass peak due to ketene,
m/e 42, was constant during the observation period. The
sensitivity factors for allene and propyne were found to be
identical.
The temperature and pressure ranges covered by the TOF
experiments are 1300-1700 K and 175-250 Torr. The mass
balance is ∼100%.
Experimental Section
The details of the experimental setup for both shock tubes
including the LS and TOF detection techniques have been
described in previous publications.
10,11
Results and Discussion
Therefore, only relevant
details of the furan dissociation experiments will be mentioned
here.
Vibrational Relaxation. At temperatures below 1200 K and
pressures below 100 Torr, the density gradients in the gas are
solely due to vibrational relaxation. The typical semilog laser-
schlieren profile of Figure 1 shows a markedly slow and
nonexponential time dependence of the density gradient for
mixtures of furan in krypton. The density gradients increase
during the first 2 µs, reach a maximum, and then decrease
exponentially after about 3 µs. In a small temperature range
(503-620 K) and for total pressures around 10 Torr, we were
able to resolve vibrational relaxation in pure furan (Figure 2).
The vibrational relaxation is faster than that in furan/Kr mixtures,
but the nonexponential time dependence of the laser-schlieren
profile remains (see Table 1). Final decay times were extracted
by fitting the exponential decay well after the maximum in the
semilogarithmic plot. These times were corrected to Bethe-
Laser Schlieren. Furan was obtained from Aldrich (purity
>
99%) and was vacuum degassed using the middle fraction
for the experiments. For the experiments in pure furan, the
shock tube was directly filled with the purified vapor. Diluted
mixtures of 5% and 2% furan in Kr were also prepared
manometrically in a 50 L glass bulb with excimer grade krypton
(Spectra gases, >99.997%). The molar refractivity of the gases
was taken as a constant 6.367 for krypton and 18.432 for furan.
To produce the combination of low postshock pressures and
temperatures necessary for vibrational relaxation or incubation
studies, various Laval nozzles were used to slow the shock wave.
These nozzles are made from brass and inserted in the driven
section of the shock tube close to the diaphragm. The incident

7482 J. Phys. Chem. A, Vol. 102, No. 38, 1998
Fulle et al.
Figure 3. Landau-Teller plot for relaxation of pure furan and furan
in krypton. O, 2% furan in krypton; 4, 5% furan in krypton; 9, pure
furan. The solid line represents the best fit to the 2% data, the dotted
line represents the best fit to the 5% data, and the dashed line represents
the best fit to the pure furan data.
Figure 2. LS profile showing vibrational relaxation in pure furan at P
)
7 Torr and T ) 620 K. The dashed line represents the exponential
fit to the final decay.
TABLE 1: Relaxation Times for Pure Furan and Furan/Kr
Mixtures
empirical biexponential expression
mixture
T/K
Pτ/atm µs
dF
dx
t
τa
t
τb
)
A exp -
- B exp -
(3)
2
% furan in Kr
746
0.812
0.739
1.012
0.438
0.517
0.504
0.462
0.457
0.476
0.357
0.299
0.179
1.330
1.351
1.177
1.087
0.194
0.250
0.173
0.190
0.201
0.227
0.163
0.169
0.165
0.144
(
)
(
)
7
7
8
8
9
9
9
034
102
168
294
512
59
65
40
74
09
46
82
and integrated the density gradients as
∞
dF
dx
∆
F ) u1
∫
dt
(4)
0
(
)
1
1
1
1
The experimental density change, which was obtained by
integrating the LS profile, can then be compared to the
theoretical value of ∆F. This theoretical value is calculated from
thermodynamic properties as the difference between the equili-
brated density and the density for the hypothetical initial state
of frozen vibration but equilibrated rotation and translation. The
mean absolute percent deviation is 14% compared to the
experimental value. The fit of the 2% furan and the pure furan
LS profiles with eq 3 was poor, and these were not integrated.
Instead, we fit a single-exponential expression to the late density
gradients. Using the cited temperature functions we extrapolated
the PτKr to 300 K to compare our LS data with results from
ultrasonic measurements. We thus obtained the average
number of collisions necessary for a molecule to lose or take
up one vibrational quantum for furan, Z10 ) 760. The value of
Z10 can be correlated (Lambert-Slater plot ) to the lowest
vibrational mode of the molecule. For furan, the frequency of
5
% furan in Kr
5
6
6
25
30
37
pure furan
503
5
5
5
5
5
5
5
6
6
26
43
49
69
77
86
87
19
20
1
4
1
4
Teller12 energy relaxation times using the specification of
1
3
Blythe. In Figure 3 the temperature dependence of these
relaxation times for diluted and pure furan is presented in a
Landau-Teller plot. The measurements of Pτ in pure furan,
Pτfuran, give
-1 15
this lowest vibrational mode is νmin ) 603 cm . Lambert
14
and Slater give values between Z10 ) 100 and Z10 ) 200 for
a molecule with two or more hydrogen atoms and a lowest
-1
vibrational frequency of 600 cm .
The complex relaxation exhibited here by furan and by other
large molecules (see, for example, ref 16), can only be
understood by a detailed master-equation analysis, which will
be presented together with more examples in upcoming papers.
Unimolecular Dissociation. Whereas both of the earlier
single-pulse shock-tube experiments identified several py-
rolysis products as mentioned in the Introduction, the TOF
experiments reported herein detected only major products, which
result directly from reactions 1a and 1b. Example concentration
profiles for the products and reactants are displayed in Figure
4. No other products were detected during the observation
period of ∼800 µs. The branching ratio for reaction 1b/1a was
determined by measuring the ratio [C2H2]/[CO] at the end of
-
1/3
log(Pτfuran/atm s) ) -8.42 + 13.9T
(2a)
From the dilute gases we are now able to calculate the PτKr for
furan infinitely diluted in Kr using a linear mixing rule. The
temperature dependence can be described by
6
,8
-1/3
log(Pτ /atm s) ) -8.78 + 24.4T
(2b)
Kr
As the LS technique monitors the density change associated
with the vibrational relaxation of furan, we compared the
theoretical density change ∆F with the experiments. To do this,
we described LS profiles for the 5% furan experiments by the

Pyrolysis of Furan at Low Pressures
J. Phys. Chem. A, Vol. 102, No. 38, 1998 7483
Figure 4. TOF concentration profiles in 2% C
4
4
H O/98% Ne at 1533 K and 198 Torr. The solid lines are calculated from the model using reactions
1
a and 1b only.
the observation period. The temperature dependence of the
branching ratio is shown in Figure 5. The data can be fitted by
the following expression:
-9
2.5
[
C H ]/[CO] ) (5.5 × 10 )T
(5)
2
2
Some earlier points in the temperature range 1060-1260 K6
were also included in this fit.
The second set of laser-schlieren experiments, with higher
temperatures, now show density gradients due to the unimo-
lecular dissociation of furan. These LS experiments cover a
wide range of experimental conditions: 1700-2500 K at
pressures between 100 and 600 Torr. Similar to the TOF
experiments, these LS profiles can accurately be modeled with
just the initial reaction 1a and 1b. Figure 6 shows two examples
of laser-schlieren time profiles together with this model calcula-
tion. For this model, the heats of formation, vibrational
frequencies, and moments of inertia for product species were
Figure 5. The branching ratio k1b/k1a, [C2H2]/[CO], vs temperature:
3 4
b, TOF results; O, SPST results. [C ]/[C H ] is in the range 1060-
taken from the literature.1
7,18
For furan, vibrational frequencies
2
H
2
6
and the molecular geometry needed to calculate the moments
of inertia were taken from an ab initio calculation by Montero
1260 K. Solid line represents an empirical fit to the data.
1
5
et al., whose calculated molecular parameters agree very well
obtained from LS experiments are shown in an Arrhenius
representation (Figure 7).
19
with earlier experimental results.
The rate constants k1

7484 J. Phys. Chem. A, Vol. 102, No. 38, 1998
Fulle et al.
preceding steady-state dissociation. In some laser-schlieren
signals we were able to resolve both vibrational relaxation and
unimolecular dissociation, which allows the estimation of an
incubation time. However, in most of the dissociation experi-
ments the signal generated by the vibrational relaxation of furan
is hidden under the shock front signal. The incubation times
will be discussed later; for now we will concentrate on the steady
unimolecular reaction rate for furan dissociation.
6
While Lifshitz et al. found almost no temperature dependence
to the branching ratio between reactions 1 at temperatures below
1
300 K, the TOF experiments from this study show a weak
temperature dependence of this branching ratio for temperatures
above 1400 K. The TOF branching ratio, given in eq 5, was
used to model the laser-schlieren profiles at high temperatures.
It was suggested that furan dissociation occurs via a biradical
6
,8
mechanism.
The initial and rate-determining step of the
Figure 6. LS profiles showing unimolecular dissociation of 2% furan
in krypton at P ) 596 Torr and T ) 1834 K (left trace) and at P )
unimolecular dissociation of furan is then a cleavage of the C-O
bond leading to a stabilized biradical, L-furan. This biradical
further fissions either to C2H2 + CH2CO or to C3H4 + CO,
where the latter requires an H atom shift. While the overall
rate constant k1 depends only on the rate-determining initial step,
the temperature dependence of the branching ratio strongly
depends on the threshold energies and the properties of the
transition states between L-furan and the final products. One
can also imagine an alternative reaction pathway starting with
an H atom shift from C1 to C2 in furan followed by direct
dissociation into the products propyne, ketene, acetylene, and
2
61 Torr and T ) 1963 K including an incubation time of 0.6 µs (right
trace). The solid lines represent the kinetic model using reactions 1a
and 1b.
2
1
CO, as proposed by Higgins et al. In this mechanism, no
biradical is formed intermediately, but the A-factor of the high-
pressure limit A∞ for an H atom shift should be on the order of
1
3
14 -1
1
0 -10 s . Both single-pulse shock-tube experiments,
which have been performed close to the high-pressure limit for
the unimolecular dissociation of furan, derive an A-factor of
1
5
-1
2
.5 × 10 s . This A-factor is thus consistent with the rate-
controlling formation of a biradical intermediate from an initial
CO bond cleavage. The high-pressure activation energy EA,∞
observed in both SPST studies, which is in good agreement
with the CO bond energy for the ring opening, strongly supports
this notion of a biradical mechanism.
Figure 7. Arrhenius representation of the unimolecular rate constant
k derived from LS experiments without chain reaction: 0, 100 Torr;
1
b, 150 Torr; 3, 250 Torr; [, 550 Torr. The lines represent the falloff
model (eq 6) with k1,0, k1,∞, and F1,cent from eqs 7-9.
For modeling of the LS profiles, we interpret the experimental
rate constant as determined by the initial CO bond cleavage.
The following procedure has then been used to construct an
RRKM model of this process. The overall rate constant k1
derived from the two SPST studies, which agree very well with
each other, was taken as the high-pressure limiting rate constant
k1,∞. The low-pressure limiting rate constant k1,0 was calculated
6
As already mentioned, Lifshitz et al. as well as Organ and
8
Mackie found several products clearly indicating a chain
reaction under their experimental conditions. The LS experi-
2
2
ments are performed on a 10 µs time scale, while the reaction
following Troe.
As the low-pressure limit k0 for strong
8
6
times for the SPST experiments are ca. 300 µs or even 2 ms.
collisions does not depend on properties of the products and
only slightly depends on the chosen structure of the transition
state, the calculation is straightforward using the well-
Therefore, under our conditions, the LS profiles are only weakly
sensitive to chain reaction when compared to the SPST studies;
the chain does not have time to develop.
1
5,19
established
molecular properties of furan. We used a value
-
1
The source of radicals needed for the chain so evident in
of 27 400 cm (327 kJ/mol) as the threshold energy for the
CO bond cleavage, which is consistent with the apparent
activation energy at high-pressure Ea,∞ from refs 6 and 8. This
value for ꢀ0 is also consistent with estimations of the heat of
formation for L-furan using group additivity techniques. The
collision efficiency âc was derived from a fixed -〈∆E〉all, and
this was adjusted to fit the experimental data from the LS
experiments. We found good agreement using a temperature-
8
single-pulse experiments is not clear. Organ and Mackie
suggested reaction 1c, but this has serious problems, especially
at low temperatures. To reach HCO and propargyl from the
L-furan intermediate requires a prior 1,2 shift to either OdCH-
CHdCdCH2 or OdCH-CH2-CtCH, quite stable species not
easily dissociated or detected in the single-pulse studies. At
high temperatures, dissociation of the dominant products C3H4
and CH2CO is a likely possibility. At the lowest temperatures
impurity initiation should at least be considered.
-
1 20
independent and rather routine value of -〈∆E〉all ) 50 cm .
This value corresponds to a collision efficiency of âc ) 0.039
-
1
-3
Under special conditions of very low pressure, the density
gradient could only be modeled by introducing an incubation
time ti (see refs 4 and 20). This incubation is the delay
and 〈∆E〉down ) 250 cm at 1000 K and âc ) 3.5 × 10 and
-1
〈∆E〉down ) 820 cm at 3000 K. These values were used to
calculate broadening factors Fcent, modeling the falloff behavior

Pyrolysis of Furan at Low Pressures
J. Phys. Chem. A, Vol. 102, No. 38, 1998 7485
Figure 9. LS profiles showing relaxation and unimolecular dissociation
of furan. The dashed lines represent the exponential fit to the density
gradients due to vibrational relaxation. The solid lines represent the
kinetic model using the unimolecular dissociation reaction 1a,b.
Figure 8. Arrhenius representation of the unimolecular rate constant
k
1
with 0, 100 Torr (LS); b, 150 Torr (LS); 3, 250 Torr (LS); [, 550
wider temperature regime. While the SPST data are close to
the high-pressure limit, a strong falloff of the LS rate constants
at low pressures and high temperatures was observed. Whereas
the high-temperature rates are close to this falloff model and
the LS results, at the lowest temperatures the TOF rates are
above the model prediction. Since the falloff model can describe
the LS profiles with a reasonable value of -〈∆E〉all ) 50 cm
as well as the high-pressure data from refs 6 and 8, we have no
explanation for this low-temperature discrepancy.
Incubation Times. Under special conditions, both vibra-
tional relaxation and unimolecular dissociation can be seen in
the LS profiles and incubation times can then be estimated. Two
LS profiles, which appear to show both processes, are given in
Figure 9. The first exponential decay is due to the vibrational
relaxation; after a few microseconds the slope changes as the
unimolecular dissociation begins. Such profiles, which show
both processes, were not used to evaluate dissociation rate
constants because of the great uncertainty in time origin, but
the rate constants derived from these experiments are fully
consistent with the profiles showing only dissociation.
The experimental conditions under which both relaxation and
dissociation can be resolved are very narrow. The pressure has
to be low enough so the vibrational relaxation time is on the
order of a few microseconds. But low pressure decreases the
rate of the dissociation process, which is then close to the low-
pressure limit. Therefore, the temperature has to be increased
to compensate. As a result, we were only able to resolve both
processes at pressures below 100 Torr and temperatures above
Torr (LS); *, 150-250 Torr (TOF) from this work and -O-, ref 6;
-
9-, ref 8; -+-, ref 7. The lines represent the falloff model (eq 6)
with k1,0, k1,∞, and F1,cent from eqs 7-9.
of the unimolecular dissociation as described in ref 22. The
adjusted -〈∆E〉all value strongly depends on the chosen
threshold energy, because a change in the threshold energy
directly affects the strong collision low-pressure limiting rate
constant. Nonetheless, a consistent model to describe the
pressure and temperature dependence of the furan dissociation
rate constant has been developed. This model will need to be
refined, when more details about the potential-energy surface,
especially the energetics of the intermediate, L-furan, are
available. From the LS data, the pressure dependence of the
rate constant k1 ) k1a + k1b at fixed temperature can be described
-
1
23
by
k [M]
1
,0
k1 )
×
1
+ k [M]/k
1,0 1,∞
2
-1
log(k [M]/k1,∞)
1
,0
F 1 +
(6)
(
(
) )
N - 0.14(log(k [M]/k1,∞) + c)
1,0
where c ) -0.4 - 0.67 log F1,cent and N ) 0.75-1.27 log F1,cent.
Using the following temperature dependencies for the pa-
rameters k1,∞, k1,0, and F1,cent,
1
5
-1
k1,∞ ) 2 × 10 exp(-39 632K/T) s
(7)
2000 K. As mentioned previously, incubation times could also
be estimated from the experiments where the schlieren profile
shows dissociation only. Vibrational relaxation is very fast, so
the density gradients from this are covered by the shock-front
signal and are not seen. Nonetheless, to accurately model the
experiments, a short incubation time has to be introduced to
reproduce the measured density gradients (see Table 2).
All measured incubation times are plotted as the ratio ti/τ vs
temperature in Figure 10. The relaxation time τ was extrapo-
lated from measurements at low temperatures using the Lan-
dau-Teller expression given before. The ratio is about 5 around
1700 K and rises slightly to 8 at 2500 K. These ratios are little
higher than what has been observed for the norbornene
5
9
-11.9
k /[Kr] ) 2.8 × 10 (T/K)
×
1,0
exp(-39 380K/T) cm mol s-1 (8)
3
-1
F1,cent ) exp(-5208 K/T) + exp(-T/594K) (9)
the rate constant can be well described over an extended
temperature and pressure range. In Figure 7, the rate constants
from the LS experiments alone are presented divided into four
narrow groups according to the postshock pressure. The lines
represent the RRKM rate constants at constant pressures of 100,
1
50, 250, and 550 Torr, respectively, as described by eq 6 with
4
the temperature dependence of k1,∞, k1,0, and Fcent from eqs 7-9.
In Figure 8 the TOF and LS experimental rate constants are
presented in an Arrhenius representation together with the
dissociation, where ratios between 2.5 and 5 have been
extracted from laser-schlieren experiments.
Incubation times have also been estimated from N2O dis-
5
,6-8
3
modeled falloff behavior and the literature results
over a
sociation experiments using the LS technique. While vibra-

7486 J. Phys. Chem. A, Vol. 102, No. 38, 1998
Fulle et al.
Acknowledgment. This research was supported by the U.S.
Department of Energy, Office of Basic Energy Science, under
Contracts DE-FG02-85ER13384 (J.H.K.) and DE-FG05-
8
5ER13400 (R.D.K.). D.F. thanks the Deutsche Forschungs-
gemeinschaft for a postdoctoral fellowship.
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(Induction Times Are in Laboratory Time)
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4
-1
T
2
/K
P
2
/Torr
k
1
/10 s
k
1a/k1b
i
t /µs
(
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
700
773
791
834
854
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892
922
934
977
963
991
021
035
070
096
174
189
276
346
529
578
306
182
280
596
283
591
276
564
270
533
262
159
243
282
240
510
234
152
94
1.07
1.96
2.61
5.66
3.31
8.02
3.76
9.82
5.98
12.9
5.92
5.90
10.1
9.28
9.48
31.0
9.34
12.9
13.6
18.4
20.1
24.5
1.41
1.17
1.12
1.58
0.95
0.63
0.85
0.63
0.78
0.63
0.72
0.71
0.62
0.59
0.53
0.63
0.40
0.40
0.32
0.20
0.20
0.20
0
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0.6
0
0
0
0.5
0
0.6
0
0.6
1.0
0.4
0.5
0.7
0
0.6
1.0
1.1
1.0
1.4
1.3
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(
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2
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7
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tional relaxation and unimolecular dissociation are observed in
a single LS profile in the furan and norbornene experiments,
the N2O incubation times could only be estimated, because the
incubation period was shorter than 1 µs and, therefore, hidden
behind the shock-front signal.
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(