Kinetics of the reaction between vinyl radical and ethylene

Article abstract of DOI:10.1016/j.cplett.2005.04.057

The C₂H₃ + C₂H₄ reaction was studied using the laser photolysis/photoionization mass spectrometry technique at T = 625-950 K and bath gas (helium) densities of (6-12) × 10 ¹⁶ atom cm^-3. Reaction rate constants can be described by the expression k₁ = 10^{-11.69 ± 0.44} exp (-(2830 ± 790) K/T) cm³ molecule^-1 s^-1. C ₄H₆ and C₄H₇ were detected as primary products; thermal stability of C₄H₇ at 950 K indicates that it is a delocalized radical. The experimental results are compared with predictions obtained in master equation modeling based on the potential energy surface of Miller (J. Phys. Chem. A 108 (2004) 2268).

Full text of DOI:10.1016/j.cplett.2005.04.057

Chemical Physics Letters 408 (2005) 339–343
www.elsevier.com/locate/cplett
Kinetics of the reaction between vinyl radical and ethylene
1
Alexander A. Shestov , Konstantin V. Popov , Irene R. Slagle, Vadim D. Knyazev
2
*
Research Center for Chemical Kinetics, Department of Chemistry, The Catholic University of America, Washington, DC 20064, United States
Received 25 February 2005; in final form 14 April 2005
Available online 13 May 2005
Abstract
The C2H3 + C2H4 reaction was studied using the laser photolysis/photoionization mass spectrometry technique at T = 625–950 K
and bath gas (helium) densities of (6–12) · 1016 atom cmꢀ3. Reaction rate constants can be described by the expression
k1 = 10ꢀ11.69 0.44 exp(ꢀ(2830 790) K/T) cm3 moleculeꢀ1 sꢀ1. C4H6 and C4H7 were detected as primary products; thermal
stability of C4H7 at 950 K indicates that it is a delocalized radical. The experimental results are compared with predictions obtained
in master equation modeling based on the potential energy surface of Miller (J. Phys. Chem. A 108 (2004) 2268).
ꢀ 2005 Elsevier B.V. All rights reserved.
C2H3 þ C2H4 ! CH2CHCH2CH2
! 1; 3-C4H6 þ H
ð1aÞ
ð1bÞ
ð1cÞ
1. Introduction
Numerous efforts have concentrated on the elucida-
tion of chemical pathways in the combustion of
hydrocarbons that lead to molecular mass growth
and the formation of polycyclic aromatic hydrocar-
bons and soot. Most of the proposed chemical routes
resulting in the formation of aromatics are based on
reactions involving delocalized radicals such as prop-
argyl (C3H3), allyl (C3H5), and cyclopentadienyl
(c-C5H5) or on reactions of highly active radicals of
vinylic type, which are capable of adding to unsatu-
rated hydrocarbons (e.g., see review in [1]). In the cur-
rent work, we continue our experimental studies of the
kinetic of a series of relevant reactions [2–5] with an
investigation of the reaction between vinyl radicals
and ethylene:
! CH2CHCHCH3
There have been no direct determinations of the rate
constant of this reaction; however, values obtained from
two indirect sources are available in the literature [6,7].
A theoretical study of the potential energy surface
(PES) of reaction 1 was recently performed by Miller
[8] as a part of a larger study of the dissociation and iso-
merizations routes of several C4H7 isomers. In the cur-
rent work, we present the first direct experimental
investigation of the reaction between the vinyl radical
and ethylene.
2. Experimental study and results
Reaction 1 was studied by the laser photolysis/photo-
ionization mass spectrometry (LP/PIMS) technique in
the temperature range 650–950 K and bath gas densities
[He] + [C2H4] = (6–12) · 1016 molecule cmꢀ3. Details of
the experimental apparatus [9] and technique [2,3] have
been described previously. Vinyl radicals were created in
pulsed 248-nm laser photolysis of vinyl bromide and
*
Corresponding author. Fax: +1 202 319 5381.
E-mail address: knyazev@cua.edu (V.D. Knyazev).
1
Present address: Center for Magnetic Resonance Research, Uni-
versity of Minnesota, Minneapolis, MN 55455, United States.
2
On leave from the Higher Chemical College of the Russian
Academy of Sciences, Miusskaya sq, 9, Moscow 125190, Russia.
0009-2614/$ - see front matter ꢀ 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2005.04.057

340
A.A. Shestov et al. / Chemical Physics Letters 408 (2005) 339–343
their kinetics were monitored in real time by photoioni-
zation mass spectrometry. The tubular heatable quartz
reactor (1.05 cm i.d.) was coated with boron oxide [10].
Experiments were conducted under pseudo-first-order
conditions with the concentrations of C2H4 ((4.6–
107) · 1014 molecule cmꢀ3) in large excess over vinyl
([C2H3]0 6 (2.8–22) · 1010 molecule cmꢀ3). Low initial
concentrations of vinyl radicals ensured that radical–
radical reactions had negligible rates compared to that
of the reaction of C2H3 with C2H4. The observed expo-
nential decay of the C2H3 radical (with pseudo-first-order
rate constant k0) was attributed to reaction 1 and heter-
ogeneous loss:
There are potential complications that could affect
the values of k1 obtained in this study. The first is the
possibility of formation of reactive species in the photol-
ysis of ethylene; the second is the possible regeneration
of vinyl radical via the reactions of H atoms produced
in reaction channel (1b) with ethylene:
H þ C2H4 ! C2H3 þ H2
ð3Þ
Vinyl radicals formed in the 248-nm photolysis of C2H4
were observed in preliminary experiments. Accordingly,
in all experiments the photolyzing laser intensity was
kept to a low level so that the contribution of the ethyl-
ene photolysis was less than 10% of the concentrations
of C2H3 produced in the photolysis of vinyl bromide.
The rate constants of reaction (3) are in the
(0.6–49) · 10ꢀ15 cm3 moleculeꢀ1 sꢀ1 range [11] at the
temperatures used in the current experiments, yielding
a 7–100 sꢀ1 range for the pseudo-first-order rates
k00 = k3[C2H4] at the highest ethylene concentrations used
in individual experiments. In order to assess the influence
of reaction (3) on the kinetics of vinyl radicals, experi-
ments were conducted where allene (CH2CCH2) was
added to the gas flow through the reactor in concentra-
tions of up to 1014 molecule cmꢀ3 and the decay profiles
of C2H3 in the presence and in the absence of allene were
compared. The H + CH2CCH2 ! CH2CHCH2 reaction
is fast under the experimental conditions used, with
the rate constant expected to be in the (1.5–4.6) ·
10ꢀ12 cm3 moleculeꢀ1 sꢀ1 range (a combination of data
in [12–15]); it should effectively compete with reaction (3).
The results of the experiments performed at both the
low and the high ends of the experimental temperature
range demonstrated that addition of allene had no influ-
ence on the C2H3 decay due to reaction 1 and that no
production of CH2CHCH2 was observed upon addition
of CH2CCH2. These results lead to the conclusion that
any H atoms produced in reaction channel (1b) quickly
decay on the wall of the reactor, as was also observed in
our earlier LP/PIMS experiments [2,4] on the reactions
of C2H3 and CH3 radicals with acetylene under similar
conditions.
C2H3 ! heterogeneous loss
ð2Þ
In a typical experiment to determine k1, the kinetics
of the decay of C2H3 radicals was recorded as a function
of the concentration of ethylene; the values of k2 were
determined in the absence of C2H4. Values of k1 were
obtained from the slopes of the linear k0 vs. [C2H4]
dependences (k0 = k1[C2H4] + k2) (Fig. 1). Experiments
were performed to establish that the decay constants
did not depend on the initial C2H3 concentration, the
concentration of C2H3Br, or the photolyzing laser
intensity.
(a)
+
C2H3
400
200
0
-10
0
10
t / msec
(b)
The rate constants of reaction 1 obtained in the
experimental study are presented in Table 1 and in
Fig. 2. The results yield the Arrhenius expression
+
+
C4H6
C4H7
k1 ¼ 10ꢀ11.69ꢁ0.44
ꢂ expðꢀð2830 ꢁ 790ÞK=TÞ cm3 moleculeꢀ1 sꢀ1: ðIÞ
-10
0
10
t / msec
Error limits in expression I are 2r and represent statisti-
cal uncertainties of the fit only.
0
5
10
15
20
[C2H4] / 1014 molecule cm-3
C4H6 (m/z = 54) and C4H7 (m/z = 55) were identified
as primary products of reaction 1 with characteristic
growth times matching those of the C2H3 decay (Fig.
1). Both C4H6 and C4H7 were observed at the lowest
(625 K) and at the highest (950 K) temperatures of the
experimental study.
Fig. 1. Pseudo-first-order C2H3 decay rate k0 vs. [C2H4]. T = 950 K,
[He] + [C2H4] = 6.0 · 1016 molecule cmꢀ3. The insets show the recorded
profiles of (a) C2H3 and (b) C4H6 and C4H7 for the conditions of the open
circle: [C2H4] = 2.11 · 1015 molecule cmꢀ3 (k0 = 483 29 sꢀ1 from
C2H3 decay and k0 = 445 24 sꢀ1 from C4H6 growth).

A.A. Shestov et al. / Chemical Physics Letters 408 (2005) 339–343
341
Table 1
Conditions and results of experiments to determine the rate constants k1 of the reaction between vinyl radical and ethylene
[M]a
[C2H3Br]b
[C2H3]0
[C2H4]c
Id
k2
(sꢀ1
k1
b
e
T
(K)
)
625
650
700
750
800
850
850
900
900
950
a
12.0
12.1
12.2
12.2
12.2
12.1
12.1
12.2
12.2
6.0
1820
1610
121
88
1.0
1.0
41.3–107
18.3–84.5
15.2–35.2
4.97–26.0
6.03–21.1
5.74–25.6
5.46–23.0
5.76–21.2
5.73–24.7
4.56–21.1
20
129.3
130.1
69.0
1.77 0.37
3.77 0.31
3.08 0.57
4.16 1.09
6.90 1.13
7.12 0.72
7.36 1.29
6.85 1.66
7.46 0.77
13.70 2.61
15
92
0.50
0.41
1.1
74
92
80.6
87.5
137
83
1.1
133
34
111.1
94.1
92.2
83
92
0.28
1.2
120
74
97
1010
0.79
2.2
80.1
181.4f
18
Concentration of the bath gas ([M] = [He] + [C2H4]) in units of 1016 molecule cmꢀ3
In units of 1011 molecule cmꢀ3. The values of [C2H3]0 represent an upper limit estimated assuming 100% yield of C2H3 in the photolysis of
C2H3Br. Actual C2H3 yields can be expected to be smaller by approximately a factor of two [23].
.
b
c
In units of 1014 molecule cmꢀ3
Laser intensity in mJ pulseꢀ1 cmꢀ2
In units of 10ꢀ14 cm3 moleculeꢀ1 sꢀ1. Error limits represent a sum of 2r statistical uncertainty and estimated systematic uncertainty.
Includes contribution from thermal decomposition.
.
d
e
f
.
formed by Benson and Haugen [6] and Fahr and Stein
[7]. The authors of [6] derived the rate expression for
k1(T) from kinetic modeling of the product analysis
study of the pyrolysis of ethylene performed by Skinner
and Sokoloski [16]. The resultant k1(T) dependence
(dash-dotted line in Fig. 2) is a factor of 5–10 lower than
the results of the current work. Most of the current
models of hydrocarbon combustion use the k1(T)
expression of [6]; the new higher rate constants values
are likely to increase the importance of reaction 1 in
combustion mechanisms.
20
10
5
2
1
The only prior experimental work in which reaction 1
was specifically targeted for study is that of Fahr and
Stein [7] who used a very-low-pressure pyrolysis (VLPP)
reactor at 1023–1273 K and pressures 1–10 mTorr with
mass spectrometric final product analysis. These authors
determined the rate constants of reaction 1 relative to
reaction (4), that of self-reaction of vinyl radicals pro-
ducing C4H4 and either H2 or two H atoms:
k
0.5
0.2
0.8
1.0
1.2
1.4
1.6
1000 K / T
C2H3 þ C2H3 ! C4H4 þ 2Hðor H2Þ
ð4Þ
Fig. 2. Temperature dependence of the rate constant of reaction 1.
Circles: experimental results of the current study; open square: value of
k1 reported in [7]; filled square: the same value adjusted using a new
rate constant of the reference reaction (4) (see text). Heavy solid line:
Arrhenius fit of Eq. I. Thin lines represent the k1(T) dependences
obtained in master equation modeling based on the PES of Miller [8]:
long-dashed line: the original model; short-dashed line: ÔentranceÕ
barrier increased by 1.3 kcal moleculeꢀ1; dotted line: the two lowest
vibrational frequencies of the ÔentranceÕ transition state increased by a
factor of two. Heavy dash-dotted line: k1(T) dependence of [6].
In order to obtain k1 values from the results of [7], val-
ues of the rate constants of reaction (4) (which repre-
sents an unknown fraction of the overall vinyl radical
self-reaction rate) are required. Having assumed
k4 = 3.3 · 10ꢀ11 cm3 moleculeꢀ1 sꢀ1
, Fahr and Stein
obtained k1 = (2.3 0.3) · 10ꢀ13 cm3 moleculeꢀ1 sꢀ1 at
1100 K (open square on the plot in Fig. 2, values of k1
at other temperatures are not given in [7] in a numerical
format but are only presented graphically). In our
earlier study of the reaction of C2H3 with acetylene [2],
we derived the value of k4 = 1.3 · 10ꢀ11 cm3 mole-
culeꢀ1 sꢀ1 for the experimental conditions of Fahr and
Stein by comparing the rate constants of the
C2H3 + C2H2 reaction reported by these authors (also
determined using reaction (4) as the reference reaction)
3. Discussion
The current study provides the first direct determina-
tion of the rate constants of the reaction of vinyl radical
with ethylene. Two earlier indirect studies were per-

342
A.A. Shestov et al. / Chemical Physics Letters 408 (2005) 339–343
and those obtained in our direct time-resolved LP/PIMS
experiments. If this value of k4 is used together with the
relative-rates results of Fahr and Stein, one obtains
k1 = 1.44 · 10ꢀ13 cm3 moleculeꢀ1 sꢀ1 at 1100 K (filled
square on the plot in Fig. 2), which is in general agree-
ment with the results of the current study.
presented in Fig. 2 by the long-dash dashed line, which
lies approximately a factor of two higher than the exper-
imental values. The differences between the calculations
and the experiment are not unexpected since the accu-
racy of methods such as G3, generally, does not exceed
1–2 kcal moleculeꢀ1. Variations of the model parame-
ters within reasonable ranges can bring the calculated
rates into better agreement with experiment. For exam-
ple, increasing the calculated energy of the transition
state for the C2H3 + C2H4 addition by 1.3 kcal mole-
culeꢀ1 (short-dash dashed line) or increasing the two
lowest vibrational frequencies of the same transition
state by a factor of two (dotted line) result in better
matches between the calculated and the experimental
rate constant values.
The C4H6 species, whose formation was observed in
the experiments, is likely to be the expected 1,3-butadiene
product of the chemically activated decomposition of the
vibrationally excited CH2CHCH2CH2 adduct. The
isomeric structure of the second observed product,
C4H7, cannot be determined on the basis of experimental
information alone. It can be asserted, however, that at
least some fraction of the C4H7 products of reaction 1
is thermally stable at temperatures up to 950 K and bath
gas density of 6 · 1016 molecule cmꢀ3 and, therefore, is
most likely a delocalized radical. These results are in
agreement with the conclusions following from the
computational study of Miller [8], which predicts a
relatively low barrier for the isomerizations of the
CH2CHCH2CH2 radical adduct to the delocalized 1-
methylallyl isomer (Fig. 3). Master equation modeling
indicates that ꢃ40% of reaction 1 at T = 600–1000 K
and [He] = 12 · 1016 molecule cmꢀ3 proceeds to the for-
mation of 1-methylallyl radical. Calculations also predict
that, at 600 K and the same bath gas density, a fraction
(36%) of the CH2CHCH2CH2 adduct gets stabilized by
the collisions with the bath gas. Thus, the C4H7 signal
observed in the experiments is likely to represent a sum
Recently, Miller [8] used the G3/B3LYP quantum
chemical method [17] to study the PES of several
C4H7 isomers and their reactions of decomposition
and isomerizations. This PES incorporates, as a subsys-
tem, that of reaction 1 (Fig. 3), including the routes of
addition of C2H3 to C2H4 forming the CH2CHCH2CH2
radical adduct, its subsequent chemically activated
decomposition to H + 1,3-C4H6 (reaction channel
(1b)), reversible isomerizations to the relatively unstable
CHCHCH2CH3 and to the delocalized CH2CHCHCH3
(1-methylallyl, product of the reaction channel (1c))
structures, and decomposition of 1-methylallyl to
H + 1,3-C4H6 (also contributing to the reaction channel
(1b)). Here, we use the results of the quantum chemical
study of Miller to calculate the temperature dependence
of the rate constant of the reaction of C2H3 with C2H4.
In these calculations, master equation modeling using
the ChemRate [18] program was employed (see [19] for
the details of the modeling procedures). The PES infor-
mation of Miller was supplemented with additional
quantum chemical calculations (using GAUSSIAN 98
[20]) providing the values of barrier widths [11,21,22]
needed to evaluate tunneling effects. The resultant values
of the barrier widths (in amu1/2 A) are 1.65 and 1.34 for
˚
the isomerizations of CH2CHCH2CH2 to 1-methylallyl
and CHCHCH2CH3 and 1.61 for the decomposition
of CH2CHCH2CH2 to H + 1,3-C4H6. The value of the
average energy transferred per deactivating collision
with He bath gas was taken as equal for all C4H7 spe-
cies: ÆDEædown = 0.52 · T cmꢀ1 Kꢀ1 [19].
The results of the rate constant calculations
performed for the conditions of the experiments are
89.2
85.6
86.5
84.9
82.0
81.6
81.8
C2H3+ C2H4
80
H + CH2CHCHCH2
62.8
60
CHCHCH2CH3
52.8
CH2CHCH2CH2
40
36.7
CH2CHCHCH3
Reaction Coordinate
Fig. 3. PES of reaction 1 (DH0f ;0K values of Miller [8]) used in master equation calculations.

A.A. Shestov et al. / Chemical Physics Letters 408 (2005) 339–343
343
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26 (1996) 513.
of the signals of the CH2CHCH2CH2 and the
CH2CHCHCH3 isomers at the lowest temperature used
(625 K) and that of CH2CHCHCH3 at the highest tem-
perature (950 K).
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[4] M.N. Kislitsyn, I.R. Slagle, V.D. Knyazev, Proc. Combust. Inst.
29 (2002) 1237.
The results of the current experimental work and
master equation modeling of reaction 1 provide support
for the computational PES study of Miller [8]. They also
indicate that, in mechanisms of molecular mass growth
under combustion conditions, reaction 1 serves not only
as a route of formation of C4 compounds (1,3-butadiene)
from C2 species, but also as a source of delocalized rad-
icals (1-methylallyl). The latter can be expected to accu-
mulate in combustion systems in large amounts due to
their stability and low reactivity and thus contribute to
the formation of larger unsaturated hydrocarbons
through recombination.
[5] E.V. Shafir, I.R. Slagle, V.D. Knyazev, J. Phys. Chem. A 107
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Acknowledgement
[16] G.B. Skinner, E.M. Sokoloski, J. Phys. Chem. 64 (1960) 1028.
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Chem. Phys. 110 (1999) 7650.
This research was supported by US Department of
Energy under grant no. DE/FG02-98ER14463. The
authors thank Drs J.L. Miller and L.J. Butler for sharing
quantum chemical data prior to publication and
Drs A. Fahr and C.A. Taatjes for stimulating discussions.
[18] V. Mokrushin, V. Bedanov, W. Tsang, M.R. Zachariah, V.D.
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