An induction period in the pyrolysis of acetylene

Article abstract of DOI:10.1039/b103216j

Acetylene was pyrolysed in a flow system between 854 and 970 K, at pressures between 27 and 127 Torr and at residence times between 8 and 1520 ms. Both vinylacetylene and benzene were observed to be primary products, but secondary processes removed vinylacetylene and formed benzene. The orders for the steady-state rates of formation of vinylacetylene and benzene were measured to be 1.8 ± 0.1 and 2.4 ± 0.1, respectively. The corresponding rate constants were found to be, ln(kVA/L mol^-1 s^-1) = -(165 ± 11) kJ mol^-1/RT + (22.7 ± 1.5) and ln(k_B/L^1.4 mol^-1.4 s^-1) = -(100 ± 9) kJ mol^-1/RT + (15.6 ± 1.1). Induction periods were observed for the first time at these conditions, providing evidence that a free radical process dominates. The order of the initiation reaction was shown to be two. The temperature dependence of the product of the rate constants for the bimolecular, initiation reaction and the termination reaction was determined to be, ln(k_ik_t/L² mol^-2 s^-2) = -(261 ± 7) kJ mol^-1/RT + (53.1 ± 1.0).

Full text of DOI:10.1039/b103216j

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An induction period in the pyrolysis of acetylene
Xuejun Xu and Philip D. Pacey*
Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J3
Received 10th April 2001, Accepted 18th May 2001
First published as an Advance Article on the web 21st June 2001
Acetylene was pyrolysed in a Ñow system between 854 and 970 K, at pressures between 27 and 127 Torr and at
residence times between 8 and 1520 ms. Both vinylacetylene and benzene were observed to be primary
products, but secondary processes removed vinylacetylene and formed benzene. The orders for the steady-state
rates of formation of vinylacetylene and benzene were measured to be 1.8 ^ 0.1 and 2.4 ^ 0.1, respectively. The
corresponding rate constants were found to be, ln(k /L mol~1 s~1) \ [(165 ^ 11) kJ
VA
mol~1/RT ] (22.7 ^ 1.5) and ln(k /L1.4 mol~1.4 s~1) \ [(100 ^ 9) kJ mol~1/RT ] (15.6 ^ 1.1). Induction
B
periods were observed for the Ðrst time at these conditions, providing evidence that a free radical process
dominates. The order of the initiation reaction was shown to be two. The temperature dependence of the
product of the rate constants for the bimolecular, initiation reaction and the termination reaction was
determined to be, ln(k k /L2 mol~2 s~2) \ [(261 ^ 7) kJ mol~1/RT ] (53.1 ^ 1.0).
i t
Published experimental results are limited and are subject
to interference by secondary and even tertiary reactions, so
neither proposed mechanism could be eliminated. Study of the
pyrolysis of acetylene at low conversions should provide
crucial information regarding the mechanism.
1
. Introduction
Acetylene is believed to be a precursor of polycyclic aromatic
hydrocarbons (PAHs) and soot in the pyrolysis and com-
bustion of various hydrocarbons.1h5 The Ðrst experiment on
the pyrolysis of acetylene was performed by Berthelot in
When a free radical reaction starts, it takes a short time for
free radicals to be formed and to reach their steady concentra-
tion. This period of time is usually called the induction period.
Induction periods were observed in free radical poly-
merizations in the liquid phase using the viscosity method,31
the rotating-sector technique32 and the emulsion technique.33
A mathematical theory was proposed by Come34 for induc-
tion periods in the pyrolysis of hydrocarbons. Induction
periods have been observed in the pyrolysis of ethane,35 ethyl-
ene,36 neopentane,37,38 acetone39 and 1,2-dichloroethane.40
Such induction periods were usually observed in Ñow systems.
An equation was derived for the rate of formation of
methane in neopentane pyrolysis in a plug Ñow system.38 A
similar equation applies to other cases where the key radicals
are removed in a bimolecular, chain termination.
1
866.6 Various devices have been used to study this reaction,
including static reactors,7,8 Ñow reactors8,9 and shock
tubes.10h17
Several mechanisms have been proposed. The mechanism at
temperatures above 1500 K is believed to be a free radical
process.10,16 However, the mechanism below 1500 K is still
the subject of sharp controversy. Free radical mechanisms
were proposed18h21 because of observations of auto-
acceleration and because of the inhibition of the reaction by
nitric oxide, a known scavenger of free radicals. Several, di†er-
ent initiation reactions have been suggested. Minko†22 pro-
posed that one of the triple bonds in an acetylene molecule
could rupture to form a triplet, which then propagated a poly-
merization reaction. Back18 suggested that the initiation reac-
tion was a bimolecular disproportionation between two
acetylene molecules to form vinyl and ethynyl radicals. Other
workers10,19,21,23 suggested a bimolecular initiation reaction
forming C H and a hydrogen atom. Colket et al.20 suggested
[P]/t \ [(b /t)lnM[1 ] exp(a t)]/2N [ a b /2](1 [ c t) (E1)
P
P
P P
P
Here, [P] is the concentration of a product leaving the
4
3
reactor; t, the residence time of gases in the reactor; a b
that the reaction was initiated by acetone, an impurity in
acetylene.
P P
equals 2Rss where Rss is the steady-state rate of product for-
p
p
mation; a equals 4(R k )1@2 where R is the initiation rate; k ,
Because some free radical mechanisms predicted slower
rates of reaction than those observed experimentally, Duran et
al. (DAC)24 proposed a molecular mechanism involving vinyl-
P
i t
i
P
t
the termination rate constant; and c , a parameter associated
with secondary reactions. The relation between the induction
period, q, and the parameter, a , was derived as eqn. (E2),34
idene, H CC, providing three supporting arguments. Firstly,
p
2
assuming the termination step was second order.
ab initio calculations predicted that the heat of formation of
vinylidene was only 167 kJ mol~1 greater than that of acety-
lene.25,26 Secondly, their studies27 of the thermal reactions of
acetylene with benzene and toluene were interpreted to reveal
that the reactions were additions, instead of radical displace-
ments. Finally, vinylidene had previously been suggested to
participate in the high-temperature decomposition of methy-
lenecyclopropane.28 To interpret the observations of auto-
acceleration and the inhibition of the reaction by nitric oxide,
DACÏs molecular mechanism was further developed by Kiefer
and Von Drasek.29,30
q \ 1/(k k [C H ]n)1@2 \ 2 ln 2/a
i t 2 2
Here, k is the rate constant for the initiation reaction and n is
(E2)
p
i
the order of the initiation reaction.
Vinylidene was proposed to be a key intermediate in the
molecular mechanism. The induction period caused by the
delay in establishing the steady-state concentration of vinyl-
idene should be its lifetime, 3.5 ls, a recent experimental result
by Levin et al. using coulomb explosion imaging techniques.41
This is too fast to be observed in a Ñow system. Therefore, the
2836
Phys. Chem. Chem. Phys., 2001, 3, 2836È2844
This journal is ( The Owner Societies 2001
DOI: 10.1039/b103216j

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observation of an induction period at low temperatures would
be an excellent method to distinguish between a free radical
mechanism and a molecular mechanism.
In the present work, we will search for an induction period
of a few milliseconds at very low conversions.
2. Experimental
Acetylene was pyrolysed in a Ñow system, described else-
where.42 Cylindrical quartz tubes (Quartz ScientiÐc, Inc.) of 28
cm length and 0.969 mm, 1.96 mm and 3.96 mm internal
diameters were used as reactors. Acetylene (Canox, \30 000
ppm acetone) was passed through an isopropanol/dry ice trap,
which reduced the mole fraction of impurities to less than 120
ppm of acetone, less than 270 ppm of ethane, less than 250
ppm of propane and less than 80 ppm of propylene. But-1-ene
Fig. 1 Dependence of the rates of formation of vinylacetylene and
benzene on the residence time at 27 Torr and 935 K in a 4 mm id
reactor; (=) vinylacetylene; (+) benzene; solid curve, non-linear least-
squares Ðt of eqn. (E1) to the data for vinylacetylene; dotted curve,
non-linear least-squares Ðt for benzene.
(
Matheson, C. P.), acetone (Fisher, A. R.) and benzene (Fisher,
A. R.) were used to prepare calibration mixtures to determine
the concentrations of products and acetone. Here, but-1-ene
was used to calibrate vinylacetylene (VA) due to the lack of
suppliers of vinylacetylene. A gas chromatograph (Tracor 550)
with a Hayesep D column (3.1 m, Alltech) and a Ñame ioniza-
tion detector was used to analyze products at a temperature of
time, the rates of formation of vinylacetylene and benzene
were only 24% and 21%, respectively, of their values at 0.4 s.
This behavior is characteristic of an induction period. The
increases in the rates of formation for vinylacetylene and
benzene were almost parallel to each other; indicating that
their induction periods were similar.
Fig. 2 shows typical induction periods observed at 68 Torr
and 936 K in a 1.96 mm id reactor. The rate of formation of
vinylacetylene increased with increasing residence time to a
maximum value, and then gradually fell o†. On the other
hand, the rate of formation of benzene increased with the
residence time to a shoulder value, and then continued to
increase more gradually.
210 ¡C. Nitrogen (extra dry, Praxair) was used as carrier gas.
To estimate the systematic error caused by calibration, GC
sensitivities of but-1-ene and buta-1,3-diene were compared;
the former sensitivity was 6% higher than the latter value.
Therefore, the systematic error resulting from the replacement
of vinylacetylene by but-1-ene for calibration should be very
small.
All reactors were immersed in concentrated HNO over-
3
night to remove organic and inorganic impurities. Then, the
reactors were washed with a 25% HF solution, rinsed with
distilled water and dried. Carbon deposited in the reactor was
burned o† between injections by Ñowing puriÐed air through
the reactor at 200 Torr. Injections were made when the acety-
lene had Ñowed for only 5 min, so as to limit any build-up of
carbon, which had been found to inhibit the gas phase reac-
tion in a previous study.42
3.2. Results of Ðtting the induction periods for vinylacetylene
and benzene
Eqn. (E1) was Ðtted to the data for vinylacetylene and benzene
by non-linear least squares.43 Fig. 1 and 2 show examples of
the Ðtted curves. Table 1 lists the values of the parameters
obtained from the Ðts. Quoted uncertainties are standard
deviations. The values of the induction period, q, obtained
from the vinylacetylene data and from the benzene data
agreed within 9% in most cases. There were di†erences in a
few cases at low pressures because of the larger errors in the
benzene data, associated with the much smaller peaks for
benzene. The steady state rates obtained for vinylacetylene
were greater than those obtained for benzene. The parameters,
c, obtained from the secondary processes for vinylacetylene
and for benzene were similar in absolute magnitude, but
opposite in sign.
3. Results
3
.1. Observation of induction periods for the formation of
vinylacetylene and benzene
Acetylene was pyrolysed in a Ñow system between 854 and
970 K, at pressures between 27 and 127 Torr and at residence
times between 8 and 1520 ms. Only vinylacetylene and
benzene were observed as products in these conditions. The
Ñow rates of acetylene into the reactors and the diameters of
the reactors were varied to attempt to detect an induction
period in the formation of vinylacetylene and benzene. The
residence time of gas in the reactor was calculated from the
reactor temperature and volume, and from the gas pressure
and Ñow rate. The average rates of formation of vinylacetylene
(
R
) and benzene (R ) were calculated by dividing their con-
VA
B
centrations at the reactor exit by the residence times. Conver-
sions were calculated to be in a range between 0.0022% and
1.4%. Reactors with smaller inner diameters were used at high
pressures or high temperatures.
Fig. 1 shows the average rates observed for vinylacetylene
and benzene at 27 Torr and 935 K in a 3.96 mm id reactor at
residence times between 0.027 and 0.39 s. At residence times
greater than 0.2 s, the rates of formation of vinylacetylene and
benzene were almost independent of the reaction time; this
behavior would be characteristic of a primary reaction
occurring with the concentrations of intermediates at their
steady-state values. At shorter residence times, the rates of
product formation were much less. At the shortest residence
Fig. 2 Dependence of the rates of formation of vinylacetylene and
benzene on the residence time at 68 Torr and 936 K in a 2 mm id
reactor; (=) vinylacetylene; (>) benzene; solid lines, non-linear least-
square Ðts of eqn. (E1) to the data.
Phys. Chem. Chem. Phys., 2001, 3, 2836È2844
2837

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Table 1 Parameters of the progress curves for vinylacetylene and benzene obtained by nonlinear least-squares Ðts of eqn. (E1) to experimental
data
T /
K
P/
Torr
Reactor
id/mm
q
VA/
q /
B
Rss /
Rss/
c
/
c /
B
VA
B
VA
s~1
s
s
10~7 mol L~1 s~1
10~7 mol L~1 s~1
s~1
9
9
9
9
9
9
9
8
8
70
53
36
126
69
52
34
27
60
120
1.96
0.969
0.969
1.96
3.96
3.96
3.96
3.96
3.96
0.035 ^ 0.002
0.049 ^ 0.005
a
0.045 ^ 0.003
0.056 ^ 0.007
0.096 ^ 0.012
0.121 ^ 0.005
0.118 ^ 0.008
0.121 ^ 0.003
0.038 ^ 0.006
0.086 ^ 0.018
a
0.041 ^ 0.008
0.057 ^ 0.006
0.072 ^ 0.006
0.151 ^ 0.014
0.105 ^ 0.003
0.121 ^ 0.009
67.5 ^ 1.5
30.1 ^ 1.1
195 ^ 8
8.5 ^ 0.5
4.03 ^ 0.25
65 ^ 5
0.44 ^ 0.04
[1.03 ^ 0.16
70
38
36
34
34
35
95
54
a
a
a
a
63 ^ 3
12.8 ^ 1.1
7.0 ^ 0.3
0.30 ^ 0.09
0.34 ^ 0.06
0.36 ^ 0.07
[0.55 ^ 0.27
40.6 ^ 1.7
20.8 ^ 1.3
11.5 ^ 0.2
22.7 ^ 0.8
28.1 ^ 2.0
[0.37 ^ 0.07
2.33 ^ 0.10
1.76 ^ 0.07
6.9 ^ 0.1
[0.60 ^ 0.09
a
a
a
a
0.20 ^ 0.04
16.9 ^ 0.4
0.090 ^ 0.001
a There was insufficient data to reliably obtain the missing parameters.
The orders of the parameters were calculated from their
pressure dependences at 934È936 K. Fig. 3 shows an order
Arrhenius plots for k (\Rss /[C H ]2), and k (\Rss/
VA VA 2 2
B
VA
B
[C H ]2.4) are shown in Fig. 6. Here the order for Rss was
2
2
plot for the induction period, q. The order for q
VA
1.09 ^ 0.07. The order for q was [1.2 ^ 0.3, and the order
was
rounded to 2, but the order for Rss was kept as a fraction.
B
[
Eqns. (E6) and (E7) were obtained from the data on vinyl-
B
for the combination of q and q was [1.1 ^ 0.1. In deter-
acetylene and benzene, respectively.
VA
B
mining these orders, individual points were given weights pro-
portional to the inverse squares of their fractional standard
deviations. All these values are consistent with an order of
[
1, indicating that the value of n (the order of the initiation
reaction) in eqn. (E2) is 2. Fig. 4 shows that the order for the
formation of vinylacetylene, Rss , was 1.8 ^ 0.1, and that the
VA
order for the formation of benzene, Rss, was 2.4 ^ 0.1. The
B
parameters, c and c , were found to be almost independent
VA
B
of the pressure.
Arrhenius plots for k k (\(q[C H ])~2 from eqn. (E2)) are
i t
2 2
shown in Fig. 5. Similar parameters (E3)È(E5) were derived
from di†erent sets of data.
ln(k k /L2 mol~2 s~2)
\
i t
VA
[(268 ^ 8)kJ mol~1/RT ] (54.1 ^ 1.1) (E3)
ln(k k /L2 mol~2 s~2) \
i t
B
[
(231 ^ 34)kJ mol~1/RT ] (49.2 ^ 4.4) (E4)
ln(k k /L2 mol~2 s~2)
\
i t
VA`B
[(261 ^ 7)kJ mol~1/RT ] (53.1 ^ 1.0) (E5)
Fig. 4 Dependence of the steady-state rates, Rss, on the acetylene
concentration at 934È936 K; (=) vinylacetylene; (>) benzene.
Here, eqn. (E5) was obtained from the data for both vinyl-
acetylene and benzene.
Fig. 3 Dependence of the induction period, q, on the acetylene con-
centration at 934È936 K; (=) vinylacetylene; (|) benzene; solid line,
weighted least-squares Ðt to the data for both vinylacetylene and
benzene.
Fig. 5 Arrhenius plot of k k ; (=) vinylacetylene; (|) benzene; solid
i t
line, weighted least-squares Ðt to the data for both vinylacetylene and
benzene.
2838
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4.1. Effect of incomplete radial heat transfer
In a conventional Ñow reactor, it is often assumed that gas is
instantly warmed to the reactor temperature. However, when
gas Ñows through the reactor too fast, i.e. when the residence
time of gas in the reactor is too short, an error may be intro-
duced because of the delay in warming up the gas. The gas
temperature on the axis at the inlet of the reactor would be
lower than that near the wall. Mulcahy and Pethard44 derived
an equation,
k
/k \ 1 [ (r2/(3.658it))[0.577 ] lnM0.82E (T [ T )/(RT 2)N]
app
A w
i
w
(
E10)
Here, k is the apparent Ðrst-order rate constant when radial
app
heat transfer is incomplete; k, the true Ðrst-order rate con-
stant; r, the radius of the reactor; i, the coefficient of thermal
di†usivity; t, the residence time; E , the activation energy;
Fig. 6 Arrhenius plots for k/Ln mol~n s~1 (n \ 1 for vinylacetylene,
and 1.4 for benzene), the e†ective rate constants in the steady-state
regime; (=) vinylacetylene; (>) benzene.
A
T , the temperature of the reactor wall; and T , the tem-
w
i
perature of the entering reactant.
Thermal properties of acetylene were obtained from ref. 45.
Using the activation energies and the reactor radii, residence
times and temperatures from the present work, the maximum
reduction in k
because of incomplete radial heat transfer
ln(k /L mol~1 s~1) \
app
VA
was calculated to be 4%. This may be compared to the experi-
mental reductions in rates of between 60% and 80% observed
in Fig. 1 and 2. We conclude that the induction periods
observed were not caused by incomplete radial heat transfer.
[(165 ^ 11)kJ mol~1/RT ] (22.7 ^ 1.5) (E6)
ln(k /L1.4 mol~1.4 s~1) \
B
B
[(100 ^ 9)kJ mol~1/RT ] (15.6 ^ 1.1) (E7)
4.2. Pressure drop, axial di†usion and volume contraction
Fig. 7 shows the Arrhenius plots for the parameters, c
The Reynolds number was estimated to be in the range
between 0.20 and 24, so laminar Ñow was established in the
present work. A gas Ñowing through a reactor can cause a
pressure drop along the reactor, because there is friction
between the reactor wall and the moving gas, especially at
high Ñow rates. The magnitude of the pressure drop, which
can be measured readily by measuring pressures at the
entrance and the exit of a reactor, mainly depends on the tem-
perature, the pressure, the Ñow rate, and the dimensions of the
reactor. The pressure drop in the present work was minimized
by using short reactors. Measured pressure drops were always
less than 10%, so the e†ect of pressure drop was negligible.
It is generally assumed that all the gas molecules spend the
same length of time in the reactor. Actually, the occurrence of
the reaction causes a concentration gradient of the reactant in
the reactor, which in turn causes axial di†usion of the reactant
toward the exit. The residence time for the reactant would be
shorter than the calculated value. On the other hand, the
parabolic velocity proÐle in the reactor could cause radial dif-
fusion of the reactant. Furue and Pacey46 investigated the
e†ect of mass transfer in the pyrolysis of cyclopropane in
cylindrical Ñow reactors and found that the apparent Ðrst
order rate constant was reduced by 10% only at conversions
of 83% or more. Hence, the e†ect of mass transfer was not
signiÐcant at the low conversions of less than 1.4% in the
present work. The Peclet number was calculated to be
between 4 and 1800, also indicating that di†usion was insig-
niÐcant compared to convection.
VA
and c . The following equations were derived,
B
ln(c /s~1) \ [(95.4 ^ 9.3)kJ mol~1/RT ] (11.1 ^ 1.2)
VA
(E8)
ln([c /s~1) \ [(67.0 ^ 14.1)kJ mol~1/RT ] (8.2 ^ 1.8)
B
(E9)
4
. Discussion
We will start by considering whether there may be systematic
errors interfering with the results reported. We will consider
Ðrst various physical interferences, such as heat, momentum
and mass transfer, and then various chemical processes, such
as surface reactions and possible parallel processes. We will
then consider the lessons to be drawn from these experiments,
and compare the results with theoretical predictions and with
the results of earlier experiments, where appropriate.
When a reaction occurs in a reactor, the total number of
moles of gas in the reactor may change. A decrease in the
number of moles would result in a volume contraction. In this
case, the molecules in the reactor would leave the reactor
more slowly. Thus, the actual residence time of molecules in
the reactor would be longer than the value calculated from the
Ñow rate, pressure, and temperature in the reactor. The low
conversions in this work should not have resulted in a signiÐ-
cant volume contraction.
4.3. Surface reaction and the e†ect of impurities
Fig. 7 Arrhenius plots for the absolute values of the parameters, c,
for secondary reactions; (=) vinylacetylene; (>) benzene.
A possible source of error is a surface reaction, which would
vary in importance in reactors with di†erent diameters. A
Phys. Chem. Chem. Phys., 2001, 3, 2836È2844
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carbon deposit on the surface was found in previous work42
to inhibit the formation of gaseous products by a hetero-
geneous termination process. Washing the reactor with HF
and burning o† the carbon deposit almost eliminated this
inhibition. These procedures were followed in the present
work.
Table 2 shows the ratio, d/Rss, of the rate of a possible molec-
ular process to the full steady-state rate, obtained by Ðtting
eqn. (E11) to the data for vinylacetylene and for benzene. The
uncertainties in the parameters a, b and c, increased by factors
between 2 and 5. Uncertainties greater than 50% in most
cases, and negative values in some cases, were obtained for the
Eqn. (E1) applies to a mechanism with a bimolecular termi-
nation process. It has been shown elsewhere47 that, if termina-
tion occurs by a unimolecular, surface process, the induction
parameter, d. The average value of d /Rss , expressed as a
VA VA
percentage, was (2.6 ^ 7.7)%. Therefore, the contribution from
a molecular mechanism to the formation of vinylacetylene
period is inversely proportional to k . If a surface reaction is
limited by the Ðrst-order rate of reaction of radicals at the
(d /Rss ) was negligible. At 934È936 K, the maximum contri-
t
VA VA
butions from a molecular mechanism to the formation of
surface, the induction period will be independent of [C H ]. If
benzene (d /Rss) were about 30%. The average value of d /Rss
2
2
B
B
B
B
a surface reaction is limited by di†usion, the induction period
will be proportional to the gas pressure. Neither of these
hypotheses would predict the inverse proportionality between
q and [C H ] observed in Fig. 3. We conclude that chain ter-
in the table was (15 ^ 15)%. This leaves open the possibility of
a minor, molecular pathway leading to the formation of
benzene.
It is necessary to distinguish the present induction period
from another period of time, the auto-acceleration period,
which has sometimes been called an induction period in pre-
vious work. When signiÐcant amounts of products have been
formed, one or more of these products could introduce new
sources of free radicals. Therefore, the entire reaction could be
accelerated. Auto-acceleration has been observed at higher
conversions in the pyrolysis of acetylene by some previous
workers. Frank-Kamenetzky53 found an auto-acceleration
period of 12 s at 192 Torr and 877 K in a Ñow system. He
found the auto-acceleration period was proportional to the
inverse square of [C H ] at temperatures above 773 K.
2
2
mination in the present system occurs in the gas phase. If the
termination occurs by bimolecular removal of two interme-
diates, eqn. (E1) and (E2) in the Introduction are appropriate.
If termination occurs by a collision between the key interme-
diate and acetylene, the induction period would be equal to
(
k [C H ])~1.47 This possibility also agrees with the observed
t
2 2
order in Fig. 3, and will be considered further in the next two
sections.
The results at the highest concentrations in Table 1 and Fig.
3
and 4 were obtained using reactors of di†erent diameters.
These results agreed very well with the trends established at
lower concentrations in the large reactor.
2
2
Minko† et al.54 observed an auto-acceleration period of 48 s
at 236 Torr and 773 K in a static reactor. Cullis and
Franklin8 observed an auto-acceleration period between 10
and 20 s at pressures from 270 to 370 Torr over the tem-
perature range 828È938 K. These auto-acceleration periods
were two or three orders of magnitude longer than the induc-
tion periods observed in the present work, and represent a
distinct chemical phenomenon. The rates at short residence
times in Fig. 1 and 2 in the present work appeared to
approach zero, whereas a Ðnite rate was observed at short
residence times in the previous studies. Auto-acceleration was
observed for benzene in the present work. If the data at
residence times less than 0.2 s were deleted from Fig. 2, we
would have a similar situation to that reported by the earlier
workers.8,53,54 The rate of benzene formation would increase
with increasing residence time, but, without the Ðrst few data
points, there would appear to be a Ðnite initial rate. Benson21
interpreted auto-acceleration as the result of the build-up of
vinylacetylene concentration in the system.
The main impurity in acetylene was acetone, which is a
source of free radicals at high temperatures. It was previously
found that acetone had no signiÐcant e†ect on the pyrolysis of
acetylene when its mole fraction was less than 400 ppm.48 In
the present work, its mole fraction was controlled to be less
than 120 ppm. The rates of initiation reactions from acetone,
propylene, propane and ethane impurities in the puriÐed
acetylene were estimated from the concentrations in Section 2
and from rate constants in the literature39,49h51 to be
5
.9 ] 10~9, 4.7 ] 10~16, 1.4 ] 10~9 and 2.3 ] 10~11 mol L~1
s~1, respectively. The value for initiation by acetone was the
largest of these, so initiation by propylene, propane and
ethane should also be negligible.
4.4. Mechanism of the reaction
As mentioned in the Introduction, molecular mechanisms
involving vinylidene and free radical mechanisms have both
been proposed to interpret the pyrolysis of acetylene. The life-
time for vinylidene in a vacuum was determined to be 3.5 ls
by Levin et al.41 A multiple barrier recrossing between vibra-
tionally excited acetylene and vinylidene was simulated by
Hayes et al. using ab initio molecular dynamics methods.52 At
the gas pressures used in the present work, the lifetime of
vinylidene would be determined by its deactivation by colli-
sion with other molecules. Assuming deactivation on every
collision, the lifetime is estimated to be 1È5 ns in our system,
seven orders of magnitude shorter than the induction periods
observed.
In the present work, both vinylacetylene and benzene were
found to be primary products. The induction periods in Table
1
were between 35 and 150 ms. These are seven orders of mag-
nitude slower than the relaxation time for vinylidene, and nine
orders of magnitude slower than the lifetime for propar-
gylmethylene. They are one or two orders of magnitude
slower than radial heat transfer. They are two or three orders
of magnitude faster than auto-acceleration.8,53,54 They are
Table 2 Estimated fractional rates of formation of vinylacetylene
and benzene from a possible, parallel, molecular pathway obtained by
nonlinear least-squares Ðts of eqn. (E11) to the experimental dataa
The lifetime of the propargylmethylene intermediate,
CH CCHCH, proposed by Kiefer and Von Drasek,29 was
2
T /K
P/ Torr
d
/Rss
d /Rss
estimated to be between 10~11 and 10~12 s at 854È970 K,
VA VA
B
B
using the rate constant for its conversion to vinylacetylene
suggested by Benson.21
The contribution of a molecular mechanism should be inde-
pendent of the residence times used in the present work. When
a term, d, representing the contribution of a molecular mecha-
nism is added into eqn. (E1), we obtain,
970
970
53
36
69
34
27
60
120
0.059 ^ 0.082
0.18 ^ 0.09
0.10 ^ 0.02
0.30 ^ 0.08
0.27 ^ 0.05
0.070 ^ 0.071
0.13 ^ 0.07
9
9
9
8
8
36
34
35
95
54
[0.087 ^ 0.006
[0.0008 ^ 0.0312
0.066 ^ 0.116
[0.019 ^ 0.004
[0.072 ^ 0.126
0.30 ^ 0.48
[0.053 ^ 0.181
[
P]/t \ d ] [(b /t)lnM[1 ] exp(a t)]/2N [ a b /2](1 [ c t)
a Non-linear least-squares Ðts did not converge at 938 K and 126
Torr, and at 934 K and 52 Torr.
P
P
P P
P
(E11)
2840
Phys. Chem. Chem. Phys., 2001, 3, 2836È2844

View Article Online
similar to the induction periods caused by the establishment
of free radical concentrations in other pyrolysis systems.35h39
This is crucial evidence for a free radical mechanism in the
pyrolysis of acetylene. Molecular mechanisms involving
vinylidene24,29 do not appear to play a dominant role in the
present work. However, we cannot rule out a minor contribu-
tion from a molecular mechanism to the formation of benzene.
The similarity of the induction periods for vinylacetylene
and for benzene indicates that both vinylacetylene and
benzene were formed from the same free radicals or from free
radicals which could rapidly interconvert.
alpies of formation of the latter species and of acetylene,58 the
activation energy for reaction (3) could be calculated to be 273
kJ mol~1. This value is very close to that determined from the
data for vinylacetylene in the present work.
The rate constant of this initiation reaction has also been
measured experimentally. One of the possible products of the
initiation reaction, C H , was observed in a shock tube at
1600È2400 K by Gay et al.10 They assumed that the rate of
the initiation reaction was equal to the rate of formation of
diacetylene, for which an induction period was observed in
their system. The Arrhenius expression for initiation was cal-
culated to be 2.95 ] 1010 L mol~1 s~1 exp([162 kJ mol~1/
RT ). Frank and Just13 observed another possible product of
the initiation reaction, H, in a shock tube at 1850È3000 K.
The concentration of H built up to a steady-state value fol-
lowing an induction period. They Ðrst assumed that the only
source of H atoms was reaction (2), but the Arrhenius curve
for this reaction was found to bend up at their lowest tem-
peratures, 1850È2000 K, indicating that there was an addi-
tional source of H atoms, which was suggested to be reaction
4
3
4.5. Properties of the initiation and termination reactions
The order of the initiation reaction may be estimated using
eqn. (E2). It is twice the absolute value of the slope of a graph
of log q vs. log [C H ], as shown in Fig. 3. The order of
1
0
10 2 2
the initiation reaction can be calculated to be 2.18 ^ 0.14 from
the vinylacetylene data, 2.4 ^ 0.6 from the benzene data, and
2
.2 ^ 0.2 from the data for both vinylacetylene and benzene. A
second-order initiation reaction was supported.
(
3). However, they did not propose an Arrhenius expression
Most radical recombination reactions have rates which are
almost independent of temperature. Sometimes there is a
dependence on T 1@2 or T ~1@2, corresponding to an activation
energy of ^0.5 RT , or ^4 kJ mol~1 at the temperatures of
this work. Therefore, the temperature dependence of the
for this initiation reaction because of the narrow range of tem-
peratures. They found that their rate constant was 12 times
slower than that reported by Gay et al.,10 and suggested that
a chain reaction might have been involved in the earlier
experiments.
Dimitrijevic et al.48 obtained an Arrhenius expression of
1012.7B0.9 L mol~1 s~1 exp([253 ^ 15 kJ mol~1/RT ) for a
bimolecular, initiation reaction, assuming a Ðrst-order, surface
termination, by studying the acceleration of the pyrolysis of
acetylene by acetone at 914È1039 K.
product, k k , in eqn. (E3) to (E5) must be almost entirely
i t
associated with k . The activation energy for the initiation
i
reaction may be derived to be 268 ^ 12 kJ mol~1 from the
data for vinylacetylene, 231 ^ 38 kJ mol~1 from the data for
benzene and 261 ^ 11 kJ mol~1 from the combined data.
The singletÈtriplet gap for acetylene was experimentally
determined to be 346 kJ mol~1,55 which is much higher than
the activation energy for initiation in the present paper.
Therefore, Minko†Ïs triplet-initiation mechanism can be ruled
out.
A C H triplet, H ~CCCC~H , was calculated using ab
4 4
2
2
initio MO methods57 to be 224.7 kJ mol~1 more stable than
C H plus H. Using the ab initio enthalpy of C H above,56
4 3
4 3
the enthalpy change for the formation of C H triplet from
4 4
acetylene would be only 6 ^ 15 kJ mol~1. The original
BackÏs initiation reaction,18
authors57 did not suggest this triplet would participate in
acetylene pyrolysis, but it is energetically accessible, so it must
be considered further.
2
C H ] C H ] C H
(1)
2
2
2
2 3
can be ruled out, because its activation energy was calculated
using ab initio methods24 to be 370 kJ mol~1, which is again
much higher than the activation energy determined in the
present work.
If the triplet, C H , was the main chain carrier, net removal
4
4
of the triplet species could occur by three possible pathways,
i.e. unimolecular intersystem crossing to a singlet, bimolecular
quenching to a singlet, or bimolecular tripletÈtriplet annihi-
lation. The Ðrst, unimolecular process would lead to an induc-
tion period independent of [C H ], contrary to the
experimental observations. Bimolecular quenching and
tripletÈtriplet annihilation would agree with the observed con-
centration dependence.
Unimolecular initiation by the rupture of a CÈH bond in
acetylene,
2
2
C H ] M ] C H ] H ] M
(2)
2
2
2
was important at much higher temperatures. The activation
energy for this reaction was calculated to be 508 kJ mol~1 at
In the case of bimolecular quenching between a triplet and
an acetylene molecule, the expression for the induction period
could be derived as,
1000 K, using recent experimental results reported by Kruse
and Roth17 at 2580 to 4650 K. This energy is almost twice as
great as our activation energy, so unimolecular initiation was
not important in this work.
q \ 1/(k [C H ])
(E12)
q
2 2
The rate constant for an initiation reaction involving the
formation of C H and H,
Here, k is the rate constant of bimolecular quenching. To
agree with the experiments, this quenching process would
q
4
3
need to have a pre-exponential factor equal to the square root
of 1023.1B0.4 L2 mol~2 s~2, i.e. 3.6 ] 1011 L mol~1 s~1, and
an activation energy of 130 ^ 4 kJ mol~1. The Arrhenius
2
C H ] C H * ] C H ] H
(3)
2
2
4 4
4 3
has been estimated by some previous workers using thermo-
chemical methods. Tanzawa and Gardiner19 suggested a rate
constant of 2 ] 109 L mol~1 s~1 exp([192 kJ mol~1/RT ).
Wu and co-workers15 estimated an expression of 2 ] 1010 L
mol~1 s~1 exp([186 kJ mol~1/RT ). Kiefer et al.16 predicted
an expression of 1.5 ] 1011 L mol~1 s~1 exp([234 kJ mol~1/
RT ). Melius et al.56 calculated an activation energy of
parameters for k could be estimated from the parameters for
q
similar processes. The pre-exponential factor and the activa-
tion energy for the quenching of triplet acetophenone by
singlet acetophenone were reported to be 2.5 ] 108 L mol~1
s~1 and 1.3 kJ mol~1 in the gas phase, and 6.3 ] 106 L mol~1
s~1 and 2.1 kJ mol~1 in solution, respectively.59 Typical pre-
exponential factors for quenching of various triplet species in
solution were determined to lie between 106 and 1010 L
mol~1 s~1.60 We can Ðnd no precedent for an activation
energy for quenching as high as 130 kJ mol~1, nor for a pre-
exponential factor as high as 3.6 ] 1011 L mol~1 s~1 for this
spin-forbidden process. Therefore, we can rule out bimolecular
2
31 ^ 15 kJ mol~1 for this reaction by ab initio methods. The
values estimated by Kiefer et al. and by Melius et al. are very
close to the value determined from the benzene data in this
work. The lowest energy form of C H plus H was calculated
to be 179.7 kJ mol~1 more stable than C(3P) plus allene using
ab initio MO methods.57 Combining this result with the enth-
4
3
Phys. Chem. Chem. Phys., 2001, 3, 2836È2844
2841

View Article Online
quenching of a triplet as the process responsible for the
observed induction periods.
In the case of tripletÈtriplet annihilation, by analogy with
eqn. (E1) an expression for the induction period could be
derived, as follows:
product, the order for the decomposition of acetylene would
approximately equal the order for the formation of vinyl-
acetylene. The order for the decomposition of acetylene was
measured by many previous workers, and the results were
reviewed by Colket et al.20 Most orders were found to be
between 1.5 and 2.0. Most workers favored an order of two.
The second-order rate constant for the formation of vinyl-
acetylene has been measured by several groups. Arrhenius
parameters are also summarized in Table 3. The large varia-
tions in these parameters may be caused by the presence of
auto-acceleration in experiments at higher conversions and by
the presence of surface reactions in earlier work in static and
Ñow reactors. In shock tube studies, the dominant initiation
reaction may be reaction (2). The absolute rate constants are
compared in Fig. 8. The rate constants from the present work
lie between the results of Dimitrijevic et al.48 and those of
Duran et al.62 It should be pointed out that the rate constant
determined in the present work may have a small systematic
error, because but-1-ene was used to calibrate the GC peaks
for vinylacetylene.
Benzene was also found to be a primary product in the
pyrolysis of acetylene at 1273 K by Becker and Huttinger.63
The order for the formation of benzene was suggested to be a
combination of Ðrst and third order, depending on the
residence time. The rate of formation of benzene could be cal-
culated from their results to be 8.60 ] 10~5 mol L~1 s~1 at
60 Torr and 1273 K. This is Ðve times faster than the value
calculated using our eqn. (E7). The third-order rate constant
for the formation of benzene was reported to be 1011.6B0.9 L2
mol~2 s~1 exp([164 ^ 17 kJ mol~1/RT ) by Dimitrijevic et
al.48
q \ 1/(k k [C H ]2)0.5
(E13)
SS TT 2 2
Here, k is the rate constant for the formation of C H triplet
from two singlet acetylene molecules, and k is the rate con-
stant for the tripletÈtriplet annihilation. To agree with the
SS
4 4
TT
constant term in eqn. (E5), these processes would need to have
the product of their pre-exponential factors equal to
1023.1B0.4 L2 mol~2 s~2. The pre-exponential factor for the
bimolecular interaction of singlet methylene and singlet acety-
lene to form triplet methylene and singlet acetylene in the gas
phase was reported to be 4.8 ] 1010 L mol~1 s~1.61 The pre-
exponential factor for the bimolecular removal of two triplet
methylenes in the gas phase was reported to be 1.2 ] 1010 L
mol~1 s~1.61 The product of these two numbers is 5.8 ] 1020
L2 mol~2 s~2, more than two orders of magnitude slower
than the value determined in the present work. Slow pre-
exponential factors from 108 to 1010 L mol~1 s~1 were also
found for deactivation of large organic triplets by triplet
oxygen in solution.60
Furthermore, the deactivation of C H
triplet,
4
4
H ~CCCC~H , should produce butatriene, which was not
2
2
observed experimentally. Ab initio calculation showed that
butatriene was only 26.7 kJ mol~1 less stable than vinyl-
acetylene, and that there was a high barrier, 320 kJ mol~1, for
the conversion of butatriene to vinylacetylene.56 The conver-
sion from butatriene to vinylacetylene should not be signiÐ-
cant in the present work. Therefore, no signiÐcant amount of
C H triplet, H ~CCCC~H , could have been formed in the
In the present work, expression (E7) has an order of 2.4,
instead of an integer. There are various interpretations of the
fractional factor. One explanation could be that benzene was
formed by two parallel pathways with di†erent orders. Di†er-
ent free radicals might have been involved. Therefore, the
order observed would be a combination of the two orders of
the pathways. According to the polymerization mechanism
4
4
2
2
present work.
In view of the foregoing, the only initiation reaction which
is consistent with the order, activation energy and product
distribution observed in the present work is reaction (3).
Recent workers56 suggest this reaction occurs by the isomer-
ization of an acetylene molecule to vinylidene, which adds to
another acetylene to give a vibrationally excited, singlet C H
4
4
complex, which decomposes to C H and H. These two rad-
4
3
icals would then add to acetylene, producing further radicals
which would participate in the main chain reaction.
The constant term in eqn. (E5) corresponds to a product of
the pre-exponential factors, A A , for initiation and termina-
i t
tion of 1023.1B0.4 L2 mol~2 s~2. Vinylidene, with three rota-
tional degrees of freedom, would be expected to have a higher
entropy than acetylene, which has only two rotational degrees
of freedom. Provided the attack of vinylidene on acetylene
and the radical recombination occur with pre-exponential
factors near the collision limit, the magnitude of the product,
A A , above can be explained.
i t
4.6. Properties of the steady-state rates
The order for the formation of vinylacetylene was determined
by some previous workers; results are summarized in Table 3.
Ogura12 found an order of 2.35 while most other workers
reported an order of two. When vinylacetylene was the main
Fig. 8 Arrhenius plot for k /L mol~1 s~1; (…) Bradley and Kistia-
VA
kowsky;70 (>) Ogura;12 (>) Kiefer et al.;71 (@) Duran et al.;62 (+)
Dimitrijevic et al.;48 (K) this work.
Table 3 Orders and Arrhenius parameters measured for the formation of vinylacetylene
Ref.
Apparatus
T /K
log(A/Ln~1 mol1~n s~1)
E /kJ mol~1
Order
A
7
1
7
6
4
0
2
1
2
8
shock tube
shock tube
shock tube
static reactor
Ñow reactor
Ñow reactor
1800È2700
1000È1670
1700È2400
770È980
914È1039
854È970
11.56
185
2
13.74 ^ 1.05
201 ^ 6
2.35 ^ 0.15
10.77
187
2
2
2
9.74 ^ 0.20
11.8 ^ 0.7
9.86 ^ 0.65
155
208 ^ 13
This work
165 ^ 11
1.8 ^ 0.1
2842
Phys. Chem. Chem. Phys., 2001, 3, 2836È2844

View Article Online
conversion to benzene and the continuous addition of C
suggested by Benson,21 a series of free radicals of di†erent
lengths could be formed. A second explanation could be that
benzene was limited by di†erent, consecutive steps in a mecha-
nism, e.g., the rate-determining step for the formation of
benzene could be
2
units to form C and higher species.
8
Vinylacetylene was reported to be a reactive species at high
temperatures.67 The Ðrst-order rate constant for the total
removal of vinylacetylene in the pyrolysis of pure vinyl-
acetylene in a shock tube68 was reported to be 6.1 ] 1013 s~1
exp([334 kJ mol~1/RT ). This is about four orders of magni-
C H ] C H ] C H
2 3 4 5
(4)
2
2
at high pressures and
tude smaller than the value of c from eqn. (E8) at 970 K in
VA
the present work. The activation energy reported was three
C H ] C H ] C H
(5)
times greater than the value measured in the present work.
This indicates that the main secondary reaction of vinyl-
acetylene in the present work was not the unimolecular
decomposition of vinylacetylene.
2
2
4 5 6 7
at low pressures. The combination of these two cases would
lead to an order between 2 and 3. A third possibility is that
two or more free radicals might be involved in termination
reactions, which would also lead to a fractional order.
The rate of vinylacetylene removal in the pyrolysis of an
equimolar mixture of acetylene and vinylacetylene in a static
vessel at 723 K69 was shown to be 2.6 ] 10~6 mol L~1 s~1.
This rate is about half the value calculated using eqn. (E8).
This agreement within a factor of two indicates that the main
secondary reaction of vinylacetylene in the present work is a
bimolecular reaction between vinylacetylene and a radical
whose concentration is almost independent of the pressure of
acetylene. According to eqn. (E15) this radical is not the main,
chain-terminating radical. The radical removing vinyl-
acetylene is probably a smaller radical, such as a hydrogen
atom.
4.7. The parameters, b
Using eqn. (E2) and the deÐnitions following eqn. (E1), it may
be readily shown that the parameter b equals Rssq/2. This
parameter may be obtained by multiplying the parameters
listed in the fourth and sixth columns of Table 1. An expres-
sion for ln(b/[C H ])
2
2 VA can be derived from eqn. (E3) and (E6)
as,
ln(b/[C H ]) \ [(31 ^ 12)kJ mol~1/RT [ (5.0 ^ 1.6)
2 VA
2
(E14)
Now we know that both the initiation and termination
reactions are bimolecular, it is possible to obtain an expres-
sion for the steady-state concentration of the radical, X,
removed in the termination step.
5. Conclusion
Induction periods for the formation of vinylacetylene and
benzene have been observed between 854 and 970 K. This is
the Ðrst observation of an induction period, distinct from an
auto-acceleration period, in acetylene pyrolysis below 1600 K.
This is crucial evidence for a free radical mechanism. Any con-
tribution from a parallel, molecular mechanism was too small
to be reliably established. The initiation reaction was shown
to involve two acetylene molecules. The termination reaction
is a bimolecular, gas phase, radical combination. The product
of the rate constants for the initiation and termination steps
was determined from the induction periods. The initiation
reaction was shown to have an activation energy of approx-
imately 260 kJ mol~1. The orders and the rate constants for
the formation of vinylacetylene and benzene were determined.
Vinylacetylene was formed from a reaction or series of reac-
tions involving the main, chain-terminating radical, X, and an
additional molecule of acetylene. These reactions have an
overall activation energy of 31 ^ 12 kJ mol~1. Benzene has an
overall order of formation of 2.4. Its overall activation energy
of formation is only 100 ^ 9 kJ mol~1, indicating it is formed
from intermediates with a lower enthalpy than the main,
chain-terminating radical.
[
X] \ (k [C H ]2/k )1@2
(E15)
ss
i
2 2
t
The case where there is more than one termination step has
been considered by Come.64 [X] depends on the Ðrst power
ss
of [C H ], whereas Rss has been shown to be approximately
2
2
VA
proportional to [C H ]2. So Rss can be related to [X] as
2
2
VA
ss
follows:
Rss \ k [X] [C H ]
(E16)
VA
p
ss 2 2
Here, k is an e†ective rate constant for propagation. It may
be that X does not lead to vinylacetylene in one step but by
p
several steps involving the rapid interconversion of radicals.
Combining eqn. (E2), (E15) and (E16), we Ðnd the quotient in
eqn. (E14) is related to k and k .
p
t
b
/[C H ] \ k /(2k )
(E17)
VA 2 2
p
t
Again the termination rate constant, k , is likely to have
t
only a weak temperature dependence, so the activation
energy, 31 ^ 12 kJ mol~1, in eqn. (E14) must be similar to the
activation energy for k . The constant term, [5.0 ^ 1.6, indi-
To obtain more information regarding the mechanism of
the pyrolysis of acetylene, more experiments will be performed
to study the rate constant for the initiation reaction by investi-
gating the acceleration of the reaction by additives, and to
search for products heavier than benzene.
p
cates that k has a pre-exponential factor lower than that for
p
k by about two orders of magnitude.
The activation energy for reaction (4) has been estimated to
t
be 25 kJ mol~1 using a thermochemical method65 and 36 kJ
mol~1 from an ab initio calculation.66 These values are within
the range of uncertainties in eqn. (E14).
Because of the greater uncertainties in the benzene data, it
is not possible to perform a similar analysis.
Acknowledgement
We wish to thank the Natural Sciences and Engineering
Research Council of Canada for a grant in support of this
work, S. Dimitrijevic and S. Paterson for preliminary experi-
ments,72 and H. Furue for assistance with the experiments.
4.8. The parameters, c
Auto-acceleration was observed in the formation of benzene
in the present timescale. (The parameter c was always posi-
B
tive.) This process might involve secondary reactions of vinyl-
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