I. Stranic et al. / Chemical Physics Letters 584 (2013) 18–23
19
decomposition pathway, the mole fraction of cyclohexene is
related to that of ethylene by the simple relation:
el. A comprehensive cyclohexane mechanism by Silke et al. [20]
was used as a basis for secondary reactions that may occur in the
shock tube. However, since this mechanism was not validated for
cyclohexene decomposition, the rate constants of several potential
secondary reactions were added and modified based on the latest
values suggested in the literature, as summarized in Table 1.
Though the rate constants for H-atom abstraction reactions from
cyclohexene by H-radicals were not modified, it was verified that
these reactions had reasonable rate estimates in the Silke et al.
[20] mechanism. The mechanism also indicates that H-radical gen-
eration is negligible at the conditions in this study, because kinetic
pathways that lead to H-radicals are at least two orders of magni-
tude slower compared to decomposition of cyclohexene via Reac-
tion 1. Therefore, since H-radical generating pathways are very
slow at the conditions in this study, simulations are not affected
by these reaction pathways and high-accuracy rate constant
estimates for cyclohexene + H reactions are not necessary.
xethylene ¼ xcyclohexene;initial—xcyclohexene
Therefore, since the mole fractions of cyclohexene, butadiene,
and ethylene are directly related, the ethylene mole fraction can
be explicitly calculated from the measured transmission via the
relations:
T ¼ expðꢀ
aÞ
a
nL ꢀ
r
cycxcyc;init
xeth
¼
reth
þ
rbut
ꢀ
rcyc
where T is the measured transmission,
a is the absorbance, n is the
total number density, L is the total pathlength through the shock
tube, and xi and ri are the mole fraction and absorption cross-sec-
tion of the absorbing species, respectively.
As expected, rate-of-production analysis indicates that virtually
all chemical processes occur via Reaction 1 at the conditions stud-
ied. The mechanism also confirms that 1,3-butadiene and ethylene
are equimolar at low conversion rates of cyclohexene because their
overall unimolecular decomposition rate constants are slower than
that of Reaction 1 by a factor of 300 at the conditions in this study.
This is explicitly confirmed in past studies by Tsang [3] and Heyne
et al. [21], the latter of which indicates that ethylene and 1,3-buta-
diene are equimolar even at 60% conversion rates of cyclohexene.
Simulations were performed with a rate constant estimate for
the reaction cyclohexene ? 1,3-cyclohexadiene + H2 nominally
equal to zero. Though the rate constant for this reaction was mea-
sured previously to be approximately one third of that for Reaction
1 near 500 K [13], several subsequent studies have concluded that
this pathway must be negligible at temperatures below 1200 K,
based on the observed pyrolysis products of cyclohexene decom-
position [3,5–7]. Therefore, past work suggests that this pathway
is approximately one to two orders of magnitude slower compared
to that of Reaction 1 below 1200 K, though an agreed upon reaction
rate constant in the literature does not exist. Brute force analysis
using an assumed rate constant for the reaction cyclohex-
ene ? 1,3-cyclohexadiene + H2 that is up to 10% of the value for
Reaction 1 does not perturb the experimentally inferred rate con-
stant for Reaction 1 by more than 2%. This is expected because
the decomposition of cyclohexene via alternative pathways does
not significantly perturb the absolute cyclohexene mole fraction
at low conversion rates where simulations were fit to experimental
data. Therefore, since the rate of ethylene formation via Reaction 1
is proportional to the concentration of cyclohexene, it remains
unperturbed by alternative cyclohexene decomposition pathways
at low conversion.
At a given post-reflected-shock condition, the rate constant for
Reaction 1 was inferred by adjusting its Arrhenius A-factor to
achieve a best-fit between simulations and measurements of eth-
ylene formation. Simulations were performed using a tempera-
ture-dependent rate constant for the title reaction in order to
account for small temperature changes which may occur through-
out the measurement time at high post-reflected-shock tempera-
tures, due to the endothermic decomposition of cyclohexene
(details are provided in following paragraphs). Data presented in
this study are the values of the rate constant for Reaction 1 at the
initial post-reflected-shock temperature, calculated using the fitted
Arrhenius A-factor and the Arrhenius activation energy from the
simulation. As a starting point, data was analyzed using a value
of the activation energy for Reaction 1 suggested by Tsang (1973)
[4]. Measurements of the rate constant as a function of tempera-
ture were then used to calculate a new activation energy, and
the above data analysis procedure was repeated. Values of the
measured reaction rate constant converged after a single iteration,
The absorption cross-section of ethylene at 10.532
ken from previous work [18], and the absorption cross-section of
cyclohexene, butadiene, and 1,3-cyclohexadiene at 10.532
lm was ta-
l
m
were measured behind reflected shock waves in this study. The
measured absorption cross-sections exhibited no pressure depen-
dence between 1.5 and 3.8 atm, and the results are summarized
in Figure 1. Since the absorption cross-section of cyclohexene is
over an order of magnitude lower than that of ethylene and 1,3-
butadiene, the above analysis which accounts for the variations
in absorbance caused by the reduction in the cyclohexene mole
fraction results in only a minor perturbation on the measurement
of the ethylene mole fraction. In addition, since the absorption
cross-section of 1,3-cyclohexadiene is low compared to that of eth-
ylene and 1,3-butadiene, and since the alternative cyclohexene
decomposition pathway to 1,3-cyclohexadiene and H2 (which does
not absorb 10.532 lm light) is at least an order of magnitude
slower than the primary decomposition pathway shown in Reac-
tion 1 (see discussion in the Kinetic Modeling Section), decomposi-
tion of cyclohexene via this alternative pathway would not perturb
the measured ethylene mole fraction by more than 2.5%.
3. Kinetic modeling
Simulations were performed using the CHEMKIN-PRO kinetics
solver assuming a constant volume, constant internal energy mod-
Cyclohexene
16
1,3-Butadiene
1,3-Cyclohexadiene
Ethylene
12
8
σ [m2mol-1] = 6.98 - 0.00131 T[K]
4
σ [m2mol-1] = 4.02 - 0.0049 T[K]
σ [m2mol-1] = 0.40
0
900
1000
1100
1200
1300
1400
T [K]
Figure 1. Absorption cross-sections of cyclohexene, 1,3-butadiene, 1,3-cyclohexa-
diene, and ethylene at 10.532 m. Cyclohexene, 1,3-butadiene, and 1,3-cyclohexa-
l
diene cross-sections measured in this study from 1.5 to 3.8 atm. Ethylene
cross-section taken from previous work and plotted for 2 atm [18].