Modeling the decomposition of nitromethane, induced by shock heating

Article abstract of DOI:10.1021/jp970716p

The decomposition of nitromethane was studied over the temperature range 1000-1100 K in reflected shock waves. CH₃NO₂ and the reaction products were analyzed by gas chromatography. The derived gross rate constant and activation energy for the disappearance of CH₃NO₂ is consistent with that of Gl?nzer and Troe. A reaction mechanism consisting of 99 chemical reactions was developed to simulate the experimental data of the present study and that of Hsu and Lin. Good agreement between experiments and simulations was achieved. It appears that significant amounts of CH₃NO₂ are destroyed through secondary reactions that involved highly reactive free radicals (H, OH, and CH₃), suggesting the need for redeterming the true unimolecular decay rate constant for CH₃NO₂. For improvement of the performance of the model, several other rate constants also need to be determined. The final section is a preliminary report on a spectrophotometric technique for measuring the loss of nitromethane due to pyrolysis by recording its absorption of UV radiation, directed axially along a small diameter shock tube. Although only semiquantitative data were obtained, this novel procedure merits discussion.

Full text of DOI:10.1021/jp970716p

J. Phys. Chem. B 1997, 101, 8717-8726
8717
Modeling the Decomposition of Nitromethane, Induced by Shock Heating
Yi-Xue Zhang and S. H. Bauer*
Department of Chemistry, Baker Chemical Laboratory, Cornell UniVersity, Ithaca, New York 14853
X
ReceiVed: February 26, 1997; In Final Form: April 15, 1997
The decomposition of nitromethane was studied over the temperature range 1000-1100 K in reflected shock
waves. CH NO and the reaction products were analyzed by gas chromatography. The derived gross rate
constant and activation energy for the disappearance of CH NO is consistent with that of Gl a¨ nzer and Troe.
3
2
3
2
A reaction mechanism consisting of 99 chemical reactions was developed to simulate the experimental data
of the present study and that of Hsu and Lin. Good agreement between experiments and simulations was
achieved. It appears that significant amounts of CH
involved highly reactive free radicals (H, OH, and CH
unimolecular decay rate constant for CH NO . For improvement of the performance of the model, several
3
NO
2
are destroyed through secondary reactions that
3
), suggesting the need for redeterming the true
3
2
other rate constants also need to be determined. The final section is a preliminary report on a spectrophotometric
technique for measuring the loss of nitromethane due to pyrolysis by recording its absorption of UV radiation,
directed axially along a small diameter shock tube. Although only semiquantitative data were obtained, this
novel procedure merits discussion.
I. Introduction
(clearly secondary) products: CO, NO, CH4, H2, C2H6, CH3-
OH, HCN, CO2, CH2O, H2O, and N2. The time dependent
The gas phase kinetics and mechanism of the thermal
concentrations were accounted for by a proposed mechanism
of 28 reactions. Their numerical simulations matched the
experimental data.
decomposition of organic-nitro compounds have been inves-
tigated by numerous authors.1
-5
These compounds are highly
6
energetic and are commonly used as explosives and propellants.
Kinetic and mechanistic information on their decomposition
pathways are critical for understanding their physical and
chemical properties and particularly the environmental conse-
quences of their extremely complex reactions in the atmosphere.
The first kinetic investigation of the decomposition of highly
1
0
Hsu and Lin followed the pyrolysis of CH3NO2 over the
temperature range 940-1520 K in a shock tube, over the
pressure range of 0.4-2 atm, and monitored the appearance
only of NO and CO in the reflected shock region with a
frequency stabilized continuous wave (cw) CO laser. They
suggested a mechanism of 37 reactions that was an extension
diluted CH3NO2 in the gas phase Via shock heating was carried
9
out by Gl a¨ nzer and Troe.7 The reaction was studied over the
of the mechanism of Perche and Lucquin. A large body of
kinetic data could thus be fitted reasonably well, proVided that
temperature range 900-1400 K by following concentration
changes of CH3NO2 and NO2, spectrophotometrically; other
products were not determined. They assumed that the pyrolysis
could be adequately described by the following three reactions.
1
2
3
a rate constant of 1.2 × 10 cm /(mol‚s) was chosen for the
reaction between CH4 and CH2O. However, this value, together
with the previously determined rate constants at lower temper-
1
1
atures, leads to an Arrhenius plot that very sharply curves
upward above 1000 K. Whereas a nonlinear shape was later
indicated by the experimental data of Choudhury et al.,12 the
magnitude of curvature was much smaller. At 1050 K, the
measured rate constant is 30-fold smaller than that predicted
CH NO f CH + NO
2
(1)
(2)
3
2
3
CH NO + M f CH + NO + M
3
2
3
2
1
0
CH + NO f CH O + NO
(12)
by the earlier mechanism of Hsu and Lin.
3
2
3
Here we report on the decomposition of CH3NO2 developed
in reflected shock waves. Our attention was focused on the
rate of disappearance of CH3NO2 and on the production rates
of several light hydrocarbons over the temperature range 1000-
The rate constants of reactions 1 and 2 were determined from
first order decay curves for CH3NO2, over a range of temper-
atures and initial nitromethane and argon concentrations. They
found that the reaction was in the fall-off region. The derived
limiting low- and high-pressure rate constants are
1
100 K. To account fully for the totality of available data, a
reaction mechanism of 99 reactions is proposed. Simulations
based on this mechanism account very well for the kinetic data
3
17.1
k /(cm /(mol‚s)) ) 10 [Ar] exp{(-42 kcal/mol)/RT}
10
0
we derived and for the results reported by Hsu and Lin, by
7
8,9
Gl a¨ nzer and Troe, and Perche et al.
-
1
16.25
k /s ) 10
exp{(-58.5 ( 10.5 kcal/mol)/RT}
∞
II. Experimental Section
1
3
3
For reaction 12 the value 1.3 × 10 cm /(mol‚s) was found
We used a stainless steel, heatable shock tube, 1 in. i.d. The
lengths of the driver and driven sections are 120 and 170 cm
long, respectively. A damp tank is located on the driven section
side next to the diaphragm holder. Shocks were generated by
increasing the pressure of the He driver until the mylar
diaphragm broke. Typical pressures on the driver (He) and
driven sides are 80 psig and 300-400 Torr of ∼0.6% CH3NO2
in Ar, respectively. Two piezoelectric pressure sensors are
by fitting the recorded [NO2] vs time curves to the above
reactions.
Perche, et al.8,9 investigated the pyrolysis of CH3NO2 over
the temperature range of 676-771 K, in a static reaction vessel.
The content of the reactor was sampled periodically and
analyzed by gas chromatography. They found numerous
X
Abstract published in AdVance ACS Abstracts, October 1, 1997.
S1089-5647(97)00716-5 CCC: $14.00 © 1997 American Chemical Society

8718 J. Phys. Chem. B, Vol. 101, No. 43, 1997
Zhang and Bauer
Figure 2. Arrhenius plots for reaction 1. Symbols are derived from
7
our experiments. Lines 1, 2, and 4 are from Gl a¨ nzer and Troe; Ar
-
3
-2
-2
concentrations are 1.5 × 10 , 1.0 × 10 , and 8.0 × 10 M,
respectively. Line 3 is the least squares fit to our data; values from
line 5 were used for reaction 2 in Table 1 for simulating the
experimental results in Figure 1.
Figure 1. Experimental (symbols) and simulation (lines) for the
decomposition of CH NO over the temperature range 1000-1100 K.
Conditions: [CH NO
) 3.7 × 10 M; [Ar] ) 0.055 M; heating
time, 1500 µs. Symbols: (O) CH NO ; (b) CH ; (4) C ; (1) C
0) C . The rate constant of reaction 2 was from line 5 of Figure 2,
and k , and k were chosen to be 0 in the simulations.
in combustion chemistry, the roles they play in the pyrolysis of
CH3NO2 may be critical for understanding this complex system.
3
2
-
4
3
2 0
]
To compare our experimental data with those of Gl a¨ nzer and
3
2
4
2
H
6
2 4
H ;
7
Troe, an Arrhenius plot based on our data is presented for
(
2 2
H
1
, k
3
4
comparison with plots of Gl a¨ nzer and Troe in Figure 2. The
vertical axis is the logarithm of the observed pseudo-first-order
decay rate constant of CH3NO2 divided by the concentration of
the bath gas. In the figure lines 1, 2, and 4 are from Gl a¨ nzer
stationed 10 cm apart at the end of the driven section. Their
combined signal was recorded and digitized through Biomation
7
8100 and Northern Tracor Signal Analyzer and stored in an
and Troe, line 3 is the least squares fit to our experimental
IBM AT computer. The effective heating time was defined as
the elapsed time from the beginning of the reflected shock wave
to the point where the pressure signal was 80% of that of the
reflected shock region. The storage tank, gas handling line,
and the shocked tube were maintained at ∼100 °C throughout
the experiments. Nitromethane from Aldrich was used without
further purification. High-purity helium and argon were the
driving and carrier gases. Research grade methane, ethane,
ethylene, and acetylene gases, used for GC calibration were from
Matheson.
Immediately after each shock, a 16 mL sample was collected
through the sampling valve located at the end of the driven
section and analyzed via a Nicolet GC/9630 (Nicolet/IBM
Instrument Inc.) with a flame ionization detector. The packed
GC column Carbograph I (from Alltech) separated the hydro-
carbons. Injector and detector temperatures were typically set
at 250 °C, and the initial column temperature was 45 °C for
the first 3 min. That temperature was increased at a rate of 20
values, and line 5 is the rate constant for reaction 2 used in our
simulations. The justification for using line 5 instead of the
experimentally measured values (line 3) will be made clear
below. The Arrhenius line for the experimental data is given
1
2
-1
by 1.977 × 10 exp{[-(38 ( 3) kcal/mol]/RT} (s ). The
activation energy is a few kilocalories smaller than that of
7
Gl a¨ nzer and Troe. The reason for the discrepancy may be due
to the relatively large scatter of our data. [We have not found
a suitable reference reaction to add to our system without
disturbing the overall reaction kinetics.] Over the temperature
range shown in Figure 2 the rate constant is in the fall-off
range: the low- and high-pressure limiting rate constants were
7
derived by Gl a¨ nzer and Troe on the basis of their extensive
experimental data. However, a unified expression that takes
into account the entire fall-off behavior has not been reported.
Mechanism of the Reaction. The reaction mechanism we
used to simulate the experimental data is compiled in Table 1.
14
The NIST Chemical Kinetics Database was the primary
°
C/min until it reached the final temperature of 275 °C. The
reference for the inserted rate expressions. The full mechanism
was used to simulate all of the experimental results. Then the
mechanism was simplified with the aid of a sensitivity analysis,
after all the experimental results were satisfactorily explained.
The rate constant of reaction 34, which is identified as a critical
reaction in Hsu and Lin’s mechanism to reproduce the experi-
mentally determined CO production rate, was updated from the
chromatograms were recorded with a Hewlett-Packard 3396A
integrator. The following species were detected and well-
separated: CH3NO2, CH4, C2H6, C2H4, and C2H2. Radical
scavengers were not introduced because we wish to determine
the evolution of the overall pyrolysis, including secondary
reactions.
1
2
3
original 1.2 × 10 cm /(mol‚s) to the experimentally deter-
III. Results and Discussions
-
12.05 7.4
3
mined values of 10 exp(483/T) (cm /(mol‚s), a 30-fold
T
The percentage conversion of CH3NO2 and the products
decrease at temperatures above 1000 K. In our mechanism,
several other routes for CO production were identified. The
most important appears to be the unimolecular decomposition
of CH2O, the rate constant of which was determined experi-
distribution from GC analysis are plotted in Figure 1. The
production of CH4 and C2H6 has been reported,8,13 but that of
C2H4 and C2H2 has not been mentioned. When the temperature
was increased, more CH4, C2H4, and C2H2 were generated,
whereas C2H6 passed through a maximum and then decreased.
Since the interactions among these four species and their radicals
comprise the most important and exhaustively studied reactions
1
5
mentally by Miyauchi et al.
CH O + M f H + CO + M
(95)
2
2

Modeling the Decomposition of Nitromethane
J. Phys. Chem. B, Vol. 101, No. 43, 1997 8719
TABLE 1: CH
3
NO
2
Decomposition Mechanisma
no.
reaction
A
n
E
a
/R
ref
1
1
1
1
6
4
0
4
1
2
3
4
5
6
7
8
9
CH
CH
CH
CH
CH
3
3
3
3
3
NO
NO
2
f CH
+ M f CH
2
2
2
3
+ NO
2
1.78 × 10
1.26 × 10
2.07 × 10
3.59 × 10
0
0
29 439
21 137
0
7
7
2
3
+ NO
2
+ M
+ M
+ NO
+ NO
+ NO
f CH
+ M f CH
f CH ONO
O + NO
ONO + M f CH O + NO + M
O + NO f CH ONO
ONO f CH O + HNO
ONO + M f CH O + HNO + M
3
NO
2
-0.6
-6
24
24
25
26
27
28
29
30
10
7
3
NO
2
0
0
7
3
7 × 10
0
0
0
0
0
0
0
0
1
1
1
1
0
0
5
3
0
3
9
8
CH3ONO f CH
3
6.31 × 10
2.29 × 10
1.21 × 10
3.98 × 10
4.63 × 10
2.40 × 10
20 733
15 298
0
19 374
0
4 529
0
329
1 390
10 820
0
CH
CH
CH
CH
CH
CH
CH
CH
3
3
3
3
3
3
3
3
3
3
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
2
NO
2
+ CH
2
3
f CH
3
4
+ CH
O + NO
2
NO
2
1
0
+ NO
+ CH
+ CH
f CH
1.3 × 10
1
1
1
8
b
b
3
f C
+ M f C
f CH + C
f N
+ M f N
2
H
6
1.09 × 10
-1.18
-7.03
0
-1.1
-3.8
-1.1
-3.8
0.73
0
-5.24
1.4
0
0
0
0
0
0
0
3.1
3.2
3.1
7.4
0
16
16
10
32
32
32
32
33
34
10
36
10
37
56
38
10
40
41
43
43
43
12
44
45
46
31
33
31
31
31
47
43
43
31
48
40
43
31
33
43
49
31
50
31
51
52
53
52
10
31
31
31
31
31
3
2
H
6
+ M
1.28 × 10
1
1
C
2
H
6
+ CH
3
4
2
H
5
5.5 × 10
8
NO
NO
2
+ NO
+ NO
2
O
2 4
5 × 10
8
1
1
8
2
2
2
O
4
+ M
5.08 × 10
7.69 × 10
7.76 × 10
6.17 × 10
0
5
5
N
N
2
O
O
4
f 2NO
2
6 460
6 460
10 530
0
1 902
0
2
4
+ M f 2NO
f NO + NO
+ NO f 2NO
+ NO + M f CH
+ NO f N
O f CH
2
+ M
NO
NO
2
+ NO
2
3
9
3
2
8 × 10
1
9
2
3
CH
NO
3
3
NO + M
8.89 × 10
4.66 × 10
2
2 3
O
1
0
CH
CH
CH
CH
CH
CH
3
3
3
3
3
3
O + CH
3
3
OH + CH
2
O
1.1 × 10
0
0
0
7
1
O + NO
2
f CH
+ M f CH
O + NO
3
ONO
2
1.21 × 10
3.27 × 10
O + NO
2
3
O NO
2
+ M
1
3
ONO
2
f CH
f CH
3
2
1 × 10
16 802
0
11 372
0
3 490
3609
8 166
-483
15 097
8
O + NO
OH + NO
f H
2
2
O + HNO
2
2
4.0 × 10
9
2
f CH
OH + HNO
2
2 × 10
2
5
6
6
3
2HNO
2
2
O + NO + NO
2
5.71 × 10
6.75 × 10
2.64 × 10
1.01 × 10
1.82 × 10
CH
CH
CH
CH
CH
3
3
2
3
4
OH + CH
OH + CH
OH + CH
3
3
4
f CH
f CH
f CH
4
4
3
+ CH
+ CH
3
O
2
OH
OH + CH
3
+ CH
+ NO
+ HNO
O + NO
O + CH
+ NO f NO + NO + O
HCO + CH
2
O f CH
f CH + HNO
f NO + HNO
f HCO + HNO
f CH OH + CH
4
+ HCO
1
0
2
3
2
1.2 × 10
-
8
2
NO
2
2
3
6.03 × 10
2.95 × 10
1.57 × 10
1.63 × 10
8.18 × 10
1.21 × 10
1.81 × 10
CH
CH
2
2
2
0
0
0
2.85
0
0
0
0
0
0
0
0
2.9
0.5
0
0
0
0
0
0
0
5.64
0
0
0
0
4.14
2.81
-0.5
0
0
0
1.5
-7.5
0
0
0
6 470
4 450
13 147
11 330
0
8
3
4
3
3
9
NO
2
2
2
7
4
f CH
3
4
3
+ CH
+ CO
CHO
2
O
1
1
1
CH
CH
CH
3
3
3
+ HCO f CH
+ HCO f CH
CHO f CH
0
0
15
3
+ HCO
OH f CO + CH
OH f CH O + CH
2 × 10
39 811
0
1
1
1
8
1
1
0
HCO + CH
HCO + CH
2
3
OH
1.21 × 10
1.81 × 10
2.41 × 10
3.12 × 10
2
2
2
O
0
0
CH
CH
CH
CH
3
3
3
3
+ CH
CHO + NO
OH + NO
OH + HCO f CH
3
O f CH
4
+ CH
2
O
2
f HNO
2
+ CH
+ CH OH
O + CH OH
3
CO
13 632
11 372
6 596
1 007
1 000
0
8
2
f HNO
2
2
2 × 10
8
2
2
1.45 × 10
9
HCO + NO f CO + HNO
HCO + HNO f NO + CH
3.453 × 10
8
2
O
6.03 × 10
1
0
CH
CH
CH
CH
CH
CH
CH
CH
CH
3
3
3
3
3
3
3
3
3
O + CH
O + CH
O + HCO f CH
O + HNO f CH
O + CH O f CH
+ HNO f CH + NO
+ CH
+ CH
+ CH
2
OH f CH
3
OH + CH
OH + CH
2
O
2.41 × 10
6
3
CHO f CH
3
3
CO
5 × 10
0
0
0
1
1
8
0
3
OH + CO
3
9.04 × 10
3.16 × 10
1.02 × 10
0
OH + NO
2
3
OH + HCO
1 500
0
1 240
16 566
6 800
13 387
0
6 322
2 950
0
3 570
7 922
10 052
3 730
11 370
0
9
4
2 × 10
5
1
3
3
3
CHO f CH
f C
f C
4
+ CH
2
CHO
1.79 × 10
1
3
2
H
H
4
+ H
+ H
2
1.0 × 10
0
0
2
5
3.01 × 10
1
1
C
2
C
2
C
2
C
2
C
2
C
2
H
H
H
H
H
H
5
5
5
5
5
6
f C
2
H
4
+ H
O f CH
f C
4.7 × 10
1
6
7
9
8
+ CH
+ CH
+ CH
+ CH
+ CH
3
4
2
3
3
2
O + C
+ CH
+ HCO
+ C
OH + C
+ HNO
+ NO
2
H
6
2.41 × 10
1.51 × 10
4.93 × 10
1.13 × 10
2.41 × 10
2
H
2
6
3
O f C
f CH
O f CH
H
6
4
2
H
4
3
H
2 5
1
1
2
4
CH
CH
3
NO
+ HNO
f H
2
+ H f CH
f CH
3
2
3.176 × 10
this work
this work
3
2
4
2
2.142 × 10
9
H + C
2
H
6
2
+ C
O + H + M
2
H
5
7.43 × 10
52
10
10
10
10
10
10
10
1
9
CH
CH
CH
3
3
3
O + M f CH
2
1.11 × 10
9
O + NO f CH
2
O + HNO
O + H
3.2 × 10
1
1
9
1
0
O + OH f CH
2
2
O
3.2 × 10
2.9 × 10
8.0 × 10
2.0 × 10
0
1
NO
2
+ H f NO + OH
407.6
CH
CH
CH
3
3
3
+ OH f CH
+ OH f CH
2
O + H
2
0
0
1.27
0
13 790
1 329
3
3
O + H
9
NO
2
+ H f CH
2
NO
2
+ H
2
3.469 × 10

8
720 J. Phys. Chem. B, Vol. 101, No. 43, 1997
Zhang and Bauer
ref
TABLE 1 (Continued)
no.
reaction
A
n
a
E /R
7
7
7
7
8
8
8
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
9
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
CH
CH
CH
CH
CH
CH
3
2
3
3
2
2
NO
NO
2
+ OH f CH
2
NO
2
+ H
2
O
2.325 × 10
2.48
0
0
-6.85
1.27
2.65
0
-1 218
18 120
19 780
24 360
1 329
-956.2
24 560
3 271
10 970
26 320
7 398
0
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
15
36
31
31
52
1
9
3
2
f CH
2
O + NO
1.0 × 10
7.9 × 10
NO f HCN + H
NO + M f CH
O + H f HCO + H
O + OH f HCO + H
2
O
2
1
0
0
2
8
3
+ NO + M
8.447 × 10
3.469 × 10
2.486 × 10
2
2
O
1
1
1
3
0
1
HNO + M f H + NO + M
2.9 × 10
5.2 × 10
2.2 × 10
H
H
HNO
2
+ OH f H
O + H f H
2
O + H
+ OH
0
0
2
2
1
8
7
2
+ M f NO + OH + M
5.068 × 10
-3.86
0
0
1.3
0
0
0
0
0
0
0
2.53
2.63
0
1
1
1
1
HCO + M f CO + H + M
HCO + NO f HNO + CO
CO + OH f H + CO
1.6 × 10
1.0 × 10
2
2
2
1.037 × 10
-385
14 750
1 812
0
9
CO + NO
2
f NO + CO
2
1.9 × 10
1
1
9
1
1
0
C
2
C
2
C
2
H
H
H
6
5
4
+ OH f H
+ NO
+ OH f CH
2
O + C
2
H
5
6.3 × 10
1.3 × 10
5.0 × 10
3.2 × 10
2.1 × 10
0
2
f CH
3
+ CH
2
O + NO
3
2
O + CH
0
0
3
CH
CH
4
+ OH f CH
3
+ H
2
O
2 516
17 620
2 456
6 160
4 298
20 000
2
O + M f CO + H
2
+ M
16
N
2
O
3
f NO + NO
+ H f C
+ H f C
f C + H
2
4.577 × 10
9
C
2
C
2
C
2
H
H
H
4
3
3
2
H
3
+ H
4
2
2.41 × 10
7
2
2
H
+ H
9.71 × 10
1
4
H
2 2
2.0 × 10
a
n
/RT). The unit of rate constant is M-(m-1) s-1, where m is the order of the
a
Rate expression in the mechanism is in the form of A(T/298) exp(E
reaction.
b
Fcent ) 0.381 exp(-T/73.2) + 0.619 exp(-T/1180).
Because of its importance in combustion chemistry, the
recombination reaction of CH3 radicals has been studied
extensively; the most reliable rate constant seems to be that of
Slagle et al. Rate constants for the branching reactions have
been debated. However, since they are only important at much
higher temperatures, these reactions are not critical under our
experimental conditions.
that it accounts for about 70% of the reaction. We assumed
that it is also important over the temperature range covered in
1
2
this work and chose the expression 3.18 × 10 exp(-7922/T)
for the best fit of our experimental data. The rate constant for
the reaction between CH3 and HNO2 has not been reported,
1
6
14
-1 -1
We choose k68 ) 2.142 × 10 exp(-10052/T) (M s ), which
is comparable to rate constants for several analogous reactions.
To account for the production rates of CO and NO, Hsu and
Lin10 used values of k2, given by line 1 in Figure 2, which was
suitable for the density of gases in their experiments. Simulation
of the data of Hsu and Lin with the reactions in Table 1 are
shown in Figure 3. Our mechanism correctly simulates the
measured CO production rate using the rate constant for [CH3
+ CH2O], which is about 30-fold smaller than that of Hsu and
Lin. Because of the larger rate constant, their mechanism
predicts a larger production of CH4 than that observed (Figure
1). The major discrepancy between simulation and experiment
is the production of NO at low temperatures (∼1050), where
the predictions are noticeably smaller than the measured values.
This is partially inherited form the mechanism of Hsu and Lin.10
Since the major portion of NO is formed at early times from
the reaction of [CH3 + NO2 f CH3O + NO], the reliability of
this rate constant is critical for successfully modeling the NO
kinetics.
To derive the consequences of the mechanism listed in Table
1
, we used the program Livermore-solver for ordinary dif-
ferential equations (LSODE) developed by Alan C. Hindmarsh.
-
3
A relative error tolerance of 10 was found to be sufficient to
give accurate results from the integrator. We first integrated
the differential equations that express the mechanism at the
measured reflected shock temperatures up to the measured
effective heating times and then lowered the reaction temper-
ature to ∼100 °C (temperature of the heated shock tube) and
continued the integration for one more minute. The second part
of the integration reflects the contribution from reactions of
unquenched radicals during the cooling wave. These calcula-
tions indicated that the added effects are negligible. Therefore,
for most of the calculations presented in this work only the first
part of the integrations was performed. Since a unified
expression for the fall-off curve for the unimolecular CH3NO2
decomposition is not available, the experimental values from
line 3 of Figure 2 were used initially for k2 in place of reactions
Figure 4 shows the kinetic behaviors of all chemical species
-
4
1
-4, to fit the experimental data in Figure 1. It was soon
in the reaction at 1090 K, for [CH3NO2]0 ) 3.7 × 10 M. The
major chemical species are CH3NO2, CO, NO, CH4, C2H6, C2H4,
C2H2, CH2O, NO2, HCN, H2O, and CO2. Of particular interest
are the [CH3NO2] and [NO2] Vs time curves. Gl a¨ nzer and Troe7
followed the changes of these two species and derived rate
constants of reactions 1, 2 and 12 by assuming that the reaction
occurred mainly through these three steps; i.e., the disappearance
of CH3NO2 was unimolecular. We have shown that the decay
of CH3NO2 is complicated by direct reactions between the free
radicals formed during the pyrolysis and the remaining CH3-
NO2. Since this effect is sufficiently large, we questioned the
reliability of the rate constants they determined. However, the
[CH3NO2] Vs time curve from simulations does remain close
to a first-order decay process, as shown in Figure 5 a, where
the dotted line are the least squares fit to the logarithm of the
CH3NO2 concentration. Comparison of the NO2 profile derived
from the mechanism of Table 1, and that due only to reactions
discovered, however, that this value for k2 leads to much greater
extents of reaction than those measured. The decay of CH3-
NO2 is not really a unimolecular process. In fact about 40%
of the CH3NO2 is lost to secondary reactions due to attack of
CH3NO2 by free radials (H, OH, and CH3) generated in the
subsequent reactions. The overall reaction is a chain process,
but the chain length is rather short. We then fitted the
experimental data with k2 as an adjustable parameter. These
values are represented by line 5 in Figure 2. The fact that lower
values for k2 need to be used to fit the experimental data suggest
that values of k1 and k2 reported by Gl a¨ nzer and Troe are too
large.
There are two channels for the reaction between CH3NO2
and H. One leads to CH2NO2 and H2 (reaction 76) and the
other to CH3 and HNO2 (reaction 67). The rate of the second
channel was studied by Thomsen et al.18 at 298 K; they found

Modeling the Decomposition of Nitromethane
J. Phys. Chem. B, Vol. 101, No. 43, 1997 8721
Figure 4. Computed kinetic behaviors of all chemical species appearing
in the mechanism of Table 1. T ) 1090 K. All other conditions are the
same as those in Figure 1. Numbers in the figure represent chemical
Figure 3. Experimental data (symbols) of Hsu and Lin10 and
simulations from the mechanism in Table 1 for CO and NO in the
1
6
CH
3
NO
2
decomposition reactions. k
2
) 4.2 × 10 exp{(-42 kcal/
species. They are as follows: 1, NO; 2, H
2
2
2
; 3, CO; 4, H
; 11, OH; 12, CH
CHO; 17, CH OH; 18, O
; 23, HNO ; 24, N
; 29, HNO; 30, H; 31, C
O; 35, CH ONO; 36. NO
2
O; 5, CH
4
; 6,
3
mol)/RT} (cm /(mol s)) for reaction 2 was used in the simulations.
C
2
H
6
; 7, C
; 14, CH
; 20, CH
NO ; 26, CH
2, HCO; 33, CH
2
H
4
; 8, CO
CHO; 15, CH
OH; 21, CH
2
; 9, HCN; 10, HNO
2
NO ; 13,
2
C
2
H
2
3
3
NO; 16, CH
3
2
;
;
1, 2, and 12 with the appropriate rate constants for (1) and (2)
1
2
3
9, C
5, CH
2
H
3
3
2
3
CO; 22, N
; 28, CH
; 34, CH
2
O
3
2
2
O
4
(
see Figure 5b), suggests that the assumption that NO2 reacts
2
2
O; 27, NO
2
3
2 5
H ;
7
mainly with CH3 made by Gl a¨ nzer and Troe might also be an
oversimplification. Therefore, it appears that a redetermination
of the rate constant of reaction 12 should be undertaken.
Sensitivity Analysis and Simplification of the Reaction
Mechanism. Over the past decades, sophisticated mathematical
methods have been developed to identify the important reactions
and to reveal their roles in complicated reaction networks.
We utilized the method of principal component analysis
developed by Turanyi et al. A brief outline of the method is
3
O NO
2
3
3
3
.
temperatures and initial CH3NO2 and Ar concentrations. In each
case, several points distributed throughout the duration of the
reaction were chosen for analysis. Table 2 shows the results
of such an analysis for a reaction at 1090 K, with [CH3NO2]0
1
9,20
-4
) 3.7 × 10 M and [Ar] ) 0.055 M, at four reaction times:
-
6
-5
-4
-3
5 × 10 , 2 × 10 , 3 × 10 , and 1.5 × 10 s. For each
reaction time, the KINAL principal component analysis leads
to a set of eigenvalues and associated eigenvectors. Each
eigenvector contains a group of elements of relatively large
21
2
2
presented in the Appendix. The program package KINAL
was used to analyze the mechanism in Table 1, at several

8722 J. Phys. Chem. B, Vol. 101, No. 43, 1997
Zhang and Bauer
elements in all eigenvectors, or to large elements in eigenvectors
but are associated with small eigenvalues, may be eliminated
from the mechanism. A reaction is considered essential if it
-
4
belongs to a reaction group with eigenvalues > 10 , and the
elements in the corresponding eigenvectors exceed 0.1.
The principal component analysis in Table 2 indicates that
there are 40 reactions that are not important, and these reactions
may be eliminated from the mechanism without affecting the
kinetic behaviors of any of the chemical species in the system.
Simulations carried out with the reduced mechanism showed
that this is indeed the case. Deviations in species concentrations
remain less than 5% for all species except for CH3CHO (∼14%)
and OH (∼10%). The mechanism can be further simplified by
noting that several species are in rapid equilibrium with other
species during the entire reaction. These are CH3ONO2, N2O3
and N2O4, CH3NO. Therefore, reaction pairs 26,27; 23, 96,
and 22, 80 are also redundant. Some reactions are important
only in parts of the reactions sequence. Their influence can be
tested by trial and error. It should be pointed out that the
analysis was carried out by assuming that all of the species are
major. The reduced mechanism is the minimum required to
reproduce the concentration profiles of all of the species.
However, in practice only a few of the total species in a complex
chemical system are measurable, so that the immediate goal is
to reproduce their behaviors. When this restriction is applied,
the mechanism may be further simplified. The simplified
mechanism can be compared with those of Hsu and Lin and of
Perche et al. All 37 reactions of the Hsu and Lin set were
included in Table 1. We found that 11 of them are not important
in any parts of the reaction and therefore can be deleted; 3 of
3 2 2
Figure 5. Kinetic behavior of CH NO and NO from simulations.
All conditions are the same as those in Figure 4. Solid lines in both a
and b are from simulations based on the mechanism in Table 1. The
dashed line in a is the least squares fit to the solid line. The dashed
line in b is from a simulation with a mechanism that consists only of
2
reactions 2 and 12, with the rate constant k that is calculated from a
1
0
-1 -1
and the rate constant for (12) of 1.3 × 10
M
s .
magnitude that identify the major reactions that correspond to
the associated eigenvalues. Reactions that lead to only small
TABLE 2: Principal Component Analysis at Four Points during the Reactiona
a
Temperatures and other conditions are as in Figure 4. Important reactions are shaded in the table.

Modeling the Decomposition of Nitromethane
J. Phys. Chem. B, Vol. 101, No. 43, 1997 8723
TABLE 3: Dominant Reactions of Different Species during the Reactiona
-
6
-5
-4
-3
species
t ) 5 × 10
2, 76
11, 68
13
61
99
s
t ) 2 × 10
s
t ) 3 × 10
2, 76, 67, 77
68, 94
13, 91
61, 93
99
s
t ) 1.5 × 10
2, 76, 67
68, 94, 15, 57
13, 69, 91
61, 93
s
CH
CH
3
NO
4
2
2, 76, 77, 67
68, 11
C
2
C
2
C
2
H
6
H
4
H
2
13
61
99
99
CO
NO
NO
95
95, 87
95, 87
12, 73, 78, 22, 70
2, 12, 73, 68
95, 89
22, 80, 73, 12, 78
2, 73, 12
22, 80, 2, 12, 13
73, 70, 84, 61, 76, 69, 67, 89, 58
73, 84, 91, 89
87, 81, 82
95, 70, 78
61, 69, 91
95, 84, 76, 69
89
12, 78, 73
2, 12
2, 12, 13
70, 76, 67, 73
73, 77
87, 82, 81, 34
70, 78
60, 61
76
12, 78, 73
2, 12, 73
2, 12, 13, 67
70, 76, 73, 67
73, 77, 82
87, 82, 81
70, 78, 95
61, 91, 60
76, 95
89
2
CH
H
3
2, 12, 13, 68, 67, 22, 80
70, 73, 76, 87, 67, 84
73, 82, 84, 77, 91
87, 82, 81
95, 70, 78, 82
61, 91
95, 76, 84
89
OH
HCO
CH
2
O
5
C
2
H
H
2
CO
2
89
C
H
2
H
3
97, 99
77
20
97, 99
77, 82
20, 21
67, 68
70, 12
78, 76, 77
55, 56, 54
47, 53
79
97, 99
82, 84, 77, 91
21, 20
68, 67, 86
12, 70
78, 76, 77
55
97, 99
84, 91, 79, 94
21, 20
67, 68, 86
12, 70
78, 76
55, 32
47
79
2
O
NO
HNO
CH
CH
CH
CH
3
2
67
3
2
3
3
O
12, 70
76, 78, 77
55, 56
47, 53
79
NO
OH
CO
2
47, 53
79
HCN
CH
CH
3
ONO
CHO
2
26, 27
42
39
26, 27
42
39
27, 26
42
39
27, 26
58, 42
39
3
O
2
CH
CH
CH
CH
2
2
3
3
OH
CHO
NO
32
58
22, 80
5, 10
10
23, 96
16, 18
32
58
22, 80
5, 10
10
23, 96
16, 18
32
58
22, 80
10, 5, 8, 6
50, 57, 10
23, 96
32
58
22, 80
10, 5, 8, 6
57, 50, 83, 10
23, 96
ONO
HNO
N
N
2
O
O
3
2
4
16, 18
16, 18
a
Temperature and other conditions are as in Figure 4.
them are only important in some parts of the reaction. The
most striking difference between the present and Hsu-Lin
mechanisms is that reaction 34 in Table 1 is crucial in their set,
but its rate constant has to be raised by 30-fold in order to
reproduce the experimental results on CO and NO. In the
present mechanism no. 34 is important only in part of the
reaction. The experimental data for CO and NO still can be
reproduced equally well. Unlike the present mechanism, the
Hsu and Lin mechanism performs poorly in reproducing the
experimental results on light hydrocarbons. Among the 26
reactions in the Perche et al. mechanism we found that 12 of
them are important in the present mechanism; the rate constants
of most of these reactions were updated.
The results in Table 3 show the dominant reactions associated
with each chemical species at several times during the reaction.
Species associated with only one chemical reactions are usually
inert products, while species associated with a pair of reaction
are usually in rapid equilibrium or in a quasi-stationary state.
The most reactive species are H and CH3; these lead to the chain.
for emission spectra. To date, only semiquantitative rate
constants were derived. We did demonstrate that under the
conditions used for nitromethane no detectable photolysis by
the incident radiation occurred during the overall exposure of
the driven sample to light emitted by the xenon arc lamp (Oriel
no. 6256).
5
5
The emitted light was focused through the quartz rear shock-
tube window to a 5 mm “disk” at the position of the diaphragm,
thus minimizing perturbation in the intensity that arises from
flapping edges of the broken diaphragm. Downstream, at the
end of the driven section, the emergent beam is focused onto
the entrance slit of a grating monochromator (with suitable filters
to eliminate stray light and overlapping orders). Signals from
an IP28 photomultiplier and from the piezoelectric gauges were
recorded simultaneously, digitized with Biomation 8100 and
Tracor Northern NS-575A digital signal analyzer, and stored
in an IBM AT computer. Typical records are shown in Figure
6 a (with only Ar in the test section) and Figure b (with 2%
CH NO -Ar mixture). Fluctuations in the transmitted light
3
2
intensity are probably due to the flapping of edges of the broken
diaphragm. This effect is relatively small and can be corrected.
IV. Spectrophotometric Measurements: Test of a
Technique
Modeling based on shock tube/GC data indicates that the
disappearance of CH3NO2 during pyrolysis, while not strictly
unimolecular, remains pseudo-first order. Therefore, in the
following analysis we assumed that an empirical first-order rate
constant would be obtained from the experimental data. The
voltage signal from the photomultiplier was converted to
absorbance with A(t) ) ln (I0/I), where I0 and I are {V(dark) -
The experiments described below were designed to record
time dependent absorption spectra of a pyrolyzing substance
using a small-diameter shock tube. A well-focused beam is
directed axially from the end of the driver section downstream
through the shock heated gas, with conditions adjusted so that
pyrolysis is limited to the reflected shock domain. This is an
5
4
V(Ar)} and {V(dark) - V(CH NO )}, respectively.
extension of the procedure described by Stephens and Bauer,
3
2
which was used to record IR and visible emissions from shock
heated hydrocarbons. However, the conversion of recorded
signals to rate constants is more involved for absorption than
At any time after the incident shock arrived at the end plate
(refer to Figure 7) the beam passes through a length x2 of sample
at T2 (not reacted) and a length x5 at T5 over which some reaction

8724 J. Phys. Chem. B, Vol. 101, No. 43, 1997
Zhang and Bauer
coefficients of CH3NO2 in the respective regions. Since the
extent of reaction in the reflected shock region depends on x,
[CH3NO2]5*(t) represents a distance-integrated magnitude.
For a unimolecular decay,
u5t
[
CH NO ] *(t) ) (1/u t)
∫
[CH NO ] (F /F )
3 2 1 5 1
3
2 5
5
0
exp[(-k (1 - x/u t)t] dx
u
5
)
(1/u t){[CH NO ] (u /k )(F /F )[1 -
5 3 2 1 5 u 5 1
exp(-k t)]} (II)
u
where x5 has been replaced by u5t, u5 is the reflected shock
speed, and F is the density. The term [CH3NO2]2x2 in (I) is
obtained from mass balance [l is the total length of the driven
section],
[
CH NO ] l )
[CH NO ] x
2 2 2
incident shock region
CH NO ] °x
5
+
3
2 1
3
total
[
(III)
3
2 5
reflected shock region
if no reaction occurs
[
CH NO ] x ) [CH NO ] l - [CH NO ] °u t
3 2 2 2 3 2 1 3 2 5 5
)
[CH NO ] (l - (F /F )u t)
3 2 1 5 1 5
(IV)
therefore
Figure 6. Recorded pressure and light intensity, typical scans: (a) Ar
only; (b) 2% CH NO in Ar.
3
2
A(t) ) ꢀ [CH NO ] [l - (F /F )u t] +
2
3
2 1
5
1
5
ꢀ5
[CH NO ] (u /k )(F /F )[1 - exp(-k t)] (V)
3 2 1 5 u 5 1 u
has occurred. Hence,
A(t) ) ꢀ [CH NO ] *(t) x (t) + ꢀ [CH NO ] x (t) (I)
For nitromethane the temperature dependence of ꢀ at 230 nm
has been experimentally determined by Gl a¨ nzer and Troe7
(Figure 8). We assume the same temperature dependence
applies to 300 nm. u5 can be determined from the pressure
5
3
2 5
5
2
3
2 2
2
where subscripts 1, 2, and 5 refer to preshock, incident shock,
and reflected shock regions and ꢀ2 and ꢀ5 are the extinction
Figure 7. Wave diagram that is the basis for converting light intensity signals to time dependent absorbance.

Modeling the Decomposition of Nitromethane
J. Phys. Chem. B, Vol. 101, No. 43, 1997 8725
problem, and the best way to determine the unimolecular decay
of CH3NO2 would be to add a large amount of radical
scavengers to the system. The kinetic curve for NO2 derived
from the extended mechanism is very different from the
previously proposed mechanism, which was used by Gl a¨ nzer
and Troe to derive the rate constant of the reaction between
CH3 and NO2. To fully unravel this pyrolysis, it appears
necessary to extend the temperature range over which the
reaction is investigated and to identify and monitor more reaction
intermediates and products.
The recorded time dependence of the absorption spectra in a
small-diameter shock tube, using the axial incidence of radiation,
did permit estimation of unimolecular rate constants within a
factor of 3. This technique merits further developments.
Acknowledgment. The authors gratefully acknowledge the
financial support from the Army Research Office under Grant
No. DAAH04-95-1-0130 for this investigation.
Figure 8. Temperature dependence of extinction coefficients.
Appendix
Principal Component Analysis of the Rate Sensitivity
Matrix. Mathematical tools and their applications for analyzing
complex kinetic systems have been thoroughly reviewed by
1
9
Turanyi.
We applied the so-called principal component
method to analyze the mechanism in Table 1. This procedure
1
9,21,23
was discussed in several previous publications;
present a brief outline.
here, we
In a homogenous isothermal chemical system, the reactions
involved can be described by a set of ordinary differential
equations.
dc/dt ) f(k,c)
(A1)
where c(t) is the n-vector of species concentration with c(t)0)
)
co and k is the p-vector of kinetic parameters. The basic
quantity that determines concentration sensitivity is
Figure 9. Comparison of k
u
values derived spectrophotometrically
(open circles) with the curve based on GC analyses (solid line).
S (k ,c ,t ,t ) ) ∂ c˘ (t )/∂k
j
(A2)
ij
0
0
1
2
i
2
trace in Figure 6, and F5/F1 can be computed from the measured
incident shock speed.
which reflects the effect of a change in the value of the jth
parameter in k0 at t1 on the values of ci at t2. For most chemical
systems, direct differentiation of the kinetic equations in (A1)
to obtain Sij is impractical; it can be more readily obtained
through numerical methods. The rate sensitivity matrix,
In the above equations t < tmax, where tmax is where the
reflected shock is intersected by the interface. However, our
experiments indicate that tmax is considerably shorter than the
heating time indicated by the pressure trace; tmax is approximated
by l/{(F5/F1)u5}.
Experimental A(t) Vs time curves were fitted to eq 7.
Although the predicted curves resemble the experimental ones,
quantitative agreement was not achieved. Per the fitted relation,
the calculated peak absorbance always appeared earlier than the
experimentally recorded times, indicating that the value of ku
used in fitting (7) was too large, whereas the predicted slope of
the latter part of the curve was always smaller.
In Figure 9 magnitudes of ku derived from the photometric
measurements were plotted for comparison with the Arrhenius
curve 3 (Figure 2). It is probable that the scatter is due in part
to inaccurate estimates of T5, which for these runs were
computed from recorded reflected shock speeds.
F (k ,c ,t) ) ∂ c˘ (t)/∂kj
(A2′)
ij
0
0
may be written in normalized form,
F (k ,c ,t) ) {∂ ln f /∂ ln k } ) {V R /f }
(A3)
ij
0
0
i
j
ij j j
The V’s in (A3) comprise the stiochiometric matrix, Rj the rate
of reaction j, and fi the production rate of species i. The rate
sensitivity has the advantage of not having two time depend-
encies as in the case of local concentration sensitivity where
both t1 and t2 need to be considered.
To evaluate the importance and the interdependence of the
kinetic parameters, one must study the effect of parameter
change on the concentrations of a group chemical species. This
can be treated mathematically with the following objective
function:
V. Conclusion
The reaction mechanism proposed in Table 1 reproduces our
experimental results on the production of hydrocarbons, and
those of Hsu and Lin on the kinetics of NO and CO. The net
rate constant for the decay of CH3NO2 is consistent with that
of Gl a¨ nzer and Troe. Overall, the pyrolysis of CH3NO2 is found
to be a chain process. About 40% of the nitromethane is lost
through secondary reactions. Simulations with the proposed
mechanism indicate that simple dilution cannot overcome this
n
f (R,c) - f (R ,c)
2
i
i
0
Q(R,c) )
(A4)
∑
[
]
i)1
f (R ,c)
i
0
Q(R,c) is a measure for the change in reaction rate when a
kinetic parameter is perturbed from R0j ) ln k0j to Rj ) ln kj.

8726 J. Phys. Chem. B, Vol. 101, No. 43, 1997
Zhang and Bauer
Q(R,c) can be approximated by the quadratic expression
(7) Gl a¨ nzer, K.; Troe, J. HelV. Chim. Acta 1972, 55, 2884.
8) Perche, A.; Tricot, J. C.; Lucquin, M. J. Chem. Res. Synop. 1979,
04; J. Chem. Res., Miniprint 1979, 3219.
(9) Perche, A.; Lucquin, M. J. Chem. Res., Miniprint 1979, 3257.
10) Hsu, D. S. Y.; Lin, M. C. J. Energ. Mater. 1985, 3, 95.
(
3
T
T
Q(R) ) (∆R) F F(∆R)
(A5)
(
(
11) (a) Toby, A.; Kutschke, K. O. Can. J. Chem. 1959, 37, 672. (b)
where Q(R) = Q(R,c) in the neighborhood of R0. The rank
order of the importance of the reactions and the interconnections
of the reactions are revealed by performing eigenvalue-
Balke, A. R.; Kutschke, K. O. Can. J. Chem. 1959, 37, 1462.
12) Choudhury, T. K.; Sanders, W. A.; Lin, M. C. J. Phys. Chem. 1989,
93, 5143.
(13) Bradley J. Trans. Faraday Soc. 1961, 57, 1750.
14) Mallard, G. W.; Westley, F.; Herron, J. T.; Hampson, R. F. NIST
(
T
eigenvector decomposition of the matrix F F.
(
Equation A4 can be rewritten in canonical form by introduc-
Chemical Kinetics Database, Version 6.0; NIST Standard Reference Data;
National Institute of Standards and Technology: Gaithersburg, MD, 1994.
(15) Miyauchi, T.; Mori, Y.; Imamura, A. Symp. (Int.) Combust., [Proc.]
T
T
ing a new set of parameters Ψ ) U R, where U is the matrix
T
T
of normalized eigenvector uj of F F such that uj uj ) 1 (j ) 1,
, ..., p).
1
977, 16, 1073.
16) Slagle, I. R.; Gutman, D.; Davies, J. W.; Pilling, M. J. J. Phys.
Chem. 1988, 92, 2455.
17) Davidson, D. F.; Di Rosa, M. D.; Chang, E. J.; Hanson, R. K.;
Bowman, C. T. Int. J. Chem. Kinet. 1995, 27, 1179.
18) Thomsen, E. L.; Nielsen, O. J.; Egsgard, H. Chem. Phys. Lett. 1993,
15, 257.
2
(
p
(
2
Q(Ψ) ) λ (∆Ψ )
(A6)
∑
j
j
(
j)1
2
(
19) Turanyi, T. J. Math. Chem. 1990, 5, 203.
The new set of parameters are called principal components. ∆Ψ
(20) Clarke, B. L. AdV. Chem. Phys. 1980, 43, 1.
(21) Turnyi, T.; Berces, T.; Vajda, J. Int. J. Chem. Kinet. 1989, 21, 83.
(
Hungarian Academy of Sciences, Budapest, Hungary. See also: Turanyi,
T. Comput. Chem. 1990, 14, 253.
(23) Vajda, S.; Valko, P.; Turanyi, T. Int. J. Chem. Kinet. 1985, 17, 55.
(
(
Phys. Chem. 1979, 83, 217.
(26) Batt, L.; McCulloch, R. D.; Milne, R. T. Int. J. Chem. Kinet. 1975,
, 441.
(
Technol. 1975, 10, 203.
(28) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F.; Jr.; Kerr,
J. A.; Troe, J. J. Phys. Chem. Ref. Data 1989, 18, 881.
T
T
)
U (∆R); λ1 > λ2 > ... > λp are the eigenvalues of F F.
22) Turanyi, T. Central Research Institute for Chemistray of the
When a parameter is perturbed along an eigenvector uj in the
space of the transformed coordinates Ψj, ∆Ψj ) 0 for i * j.
2
Q(Ψ) ) λj(∆Ψj) , and therefore λj measures the significance
24) Gl a¨ nzer, K.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1974, 78, 182.
25) Canosa, C.; Penzhorn, R.-D.; von Sonntag, C. Ber. Bunsen-Ges.
of reactions that occur in the principal component Ψj. Those
reactions that are characterized by large eigenvectors and at the
same time also belong to a reaction group characterized with a
large eigenvalue are identified as the most important reactions
in a mechanism. In practice, threshold values of eigenvalue
and eigenvector are chosen so that chemical reactions that belong
to a reaction group characterized with a small eigenvalue or
reactions that belong to a reaction group characterized by a large
eigenvalue but correspond to an eigenvector below the threshold
value are considered redundant.
Close examination of the elements of an eigenvector that
belongs to a specific eigenvalue may reveal connections among
the reactions. For example, fast equilibria can be readily
identified by two large eigenvector elements of equal value but
of opposite signs. This may also be applied to a situation where
species i is produced by one or more reactions and removed
quickly by another set of one or more reactions; i.e., species i
is then in a pseudo-steady state. These reactions and species
are usually redundant because they have no effect on the kinetic
behaviors of other species in the system.
In eq A5, all of the chemical species have been considered.
Therefore, the reduced reactions mechanism should reproduce
the kinetic behaviors of all species. In some cases, however,
one might be interested only in reproducing the kinetic behaviors
of all major chemical species or the “observed species”; then
the mechanism can be greatly simplified. This type of restricted
principal component analysis can also be used to identify
reactions critical to the formation of individual chemical species.
A FORTRAN program package called KINAL22 was devel-
oped by Turanyi to perform principal component analysis on
both concentration sensitivity and rate sensitivity matrices. This
package was used extensively in our analysis of the mechanism
in Table 1.
7
27) Maloney, K. L.; Gangloff, H. J.; Matula, R. A. Combust. Sci.
(
29) Batt, L.; Milne, R. T.; McCulloch, R. D. Int. J. Chem. Kinet. 1977,
, 567.
30) Ohmori, K.; Yamasaki, K.; Matsui, H. Bull. Chem. Soc. Jpn. 1993,
66, 51.
9
(
(
31) Tsang, W.; Hampson, R. F. J. Phys. Chem. Ref. Data 1986, 15,
1
087.
(32) Borrell, P.; Cobos, C. J.; Luther, K. J. Phys. Chem. 1988, 92, 4377.
(33) Tsang, W.; Herron, J. T. J. Phys. Chem. Ref. Data 1991, 20, 609.
(
(
34) Gl a¨ nzer, K.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1974, 78, 71.
35) Jodkowski, J. T.; Ratajczak, E.; Sillesen, A.; Pagsberg, P. Chem.
Phys. Lett. 1993, 203, 490.
36) Markwalder, B.; Gozel, P.; van den Bergh, H. J. Phys. Chem. 1993,
97, 5260.
(
(
37) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F., Jr.; Kerr,
J. A.; Troe, J. J. Phys. Chem. Ref. Data. 1992, 21, 1125.
(
38) Zaslonko, I. S.; Smirnov, V. N.; Tereza, A. M. Kinet. Catal. 1993,
34, 531; Kinet. Katal. 1993, 34, 599.
39) Batt, L.; Milne, R. T.; McCulloch, R. D. Int. J. Chem. Kinet. 1977,
, 567.
(
9
(
40) Koda, S.; Tanaka, M. Combust. Sci. Technol. 1986, 47, 165.
(41) Chan, W. H.; Nordstrom, R. J.; Calvert, J. G.; Shaw, J. H. Chem.
Phys. Lett. 1976, 37, 441.
42) Anastasi, C.; Hancock, D. U. J. Chem. Soc., Faraday Trans. 2 1988,
4, 1697.
(
8
(
43) Tsang, W. J. Phys. Chem. Ref. Data 1987, 16, 471.
(44) Slack, M. W.; Grillo, A. R. Combust. Flame 1989, 40, 155.
(
45) Streit, G. E.; Wells, J. S.; Fehsenfeld, F. C.; Howard, C. J. J. Chem.
Phys. 1979, 70, 3439.
46) Lin, C-Y.; Wang, H.-T.; Lin, M. C.; Melius, C. F. Int. J. Chem.
Kinet. 1990, 22, 455.
47) Warnatz, J. Rate coefficients in the C/H/O system. In Combustion
Chemistry; Gardiner, W. C., Jr., Ed.; Springer-Verlag, New York, 1984; p
97.
(
(
1
(
(
(
(
48) Fifer, R. A. Ber. Bunsen-Ges. Phys. Chem. 1975, 10, 613.
49) Kelly, N.; Heicken, J. J. Photochem. 1978, 8, 83.
50) He, Y.; Sanders, W. A.; Lin, M. C. J. Phys. Chem. 1988, 92, 5474.
51) Laidler, K. J.; Sagert, N. H.; Wojciechowski, B. W. Proc. R. Soc.
References and Notes
(
1) Tsang, W.; Robaugh, D.; Mallard, W. G. J. Phys. Chem. 1986, 90,
968.
2) Adams, G. F.; Shaw, R. W.; Jr. Annu. ReV. Phys. Chem. 1992, 43,
London 1962, 270, 254.
5
3
(52) Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Esser, C.; Frank, P.; Just,
Th.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker, R. W.; Warnatz, J. J.
Phys. Chem. Ref. Data 1992, 21, 411.
(
11.
(
3) Anex, D. S.; Allman, J. C.; Lee,Y. T. In Chemistry of Energetic
Materials; Bulusu, S. N. Ed.; Academic Press: New York, 1991; Chapter
(53) Kern, R. D.; Singh, H. J.; Wu, C. H. Int. J. Chem. Kinet. 1988, 20,
731.
(54) Stephens, K. M.; Bauer, S. H. Spectrochim. Acta 1994, 50A, 741.
(55) Kilie, H. S.; et al. J. Phys. Chem. 1997, 101A, 817.
(56) Frost, M. J.; Smith, I. W. M. J. Chem. Soc., Faraday Trans. 1990,
86, 1751.
2
.
(4) Shaw, R.; Walker, F. E. J. Phys. Chem. 1977, 81, 2572.
(5) Zhao, X.; Hintsa, E. J.; Lee, Y. T. J. Chem. Phys. 1988, 88, 801.
(6) Borman, S. Chem. Eng. News 1994, 72 (3), 18.