A shock tube study of benzylamine decomposition: Overall rate coefficient and heat of formation of the benzyl radical

Article abstract of DOI:10.1021/jp020085l

The decomposition rate of benzylamine (C₆H₅CH₂NH₂) and the heat of formation of the benzyl radical (C₆H₅-CH₂) were determined in shock tube experiments combined with RRKM calcula

Full text of DOI:10.1021/jp020085l

6094
J. Phys. Chem. A 2002, 106, 6094-6098
A Shock Tube Study of Benzylamine Decomposition: Overall Rate Coefficient and Heat of
Formation of the Benzyl Radical
Soonho Song, David M. Golden,* Ronald K. Hanson, and Craig T. Bowman
Department of Mechanical Engineering, Stanford UniVersity, Stanford, California 94305
ReceiVed: January 11, 2002; In Final Form: April 5, 2002
The decomposition rate of benzylamine (C
CH ) were determined in shock tube experiments combined with RRKM calculations. To obtain the
decomposition rate of benzylamine, the NH mole fraction was measured using frequency-modulation absorption
spectroscopy behind reflected shock waves. The initial slope of the NH concentration is directly proportional
to the decomposition rate and the initial concentration of benzylamine. The rate expression for the decomposition
reaction for the temperature range 1225-1599 K and the pressure range 1.19-1.47 bar is k
) (5.49 ×
6 5 2 2 6 5
H CH NH ) and the heat of formation of the benzyl radical (C H -
2
2
2
1
1
4
-33110/[T(K)] -1
1
0 )e
s
with an uncertainty of (15%. To obtain the high-pressure-limit rate expression for
benzylamine decomposition, we performed RRKM calculations using the parameters obtained from the
experimental data of this study and those of the VLPP study of Golden et al. The resulting high-pressure-
4
1
6.0 -36470/[T(K)] -1
limit rate for the temperature range 1000-1600 K is k
∞
) (1.07 × 10 )e
s . From the RRKM
calculations, we determined the C-N bond dissociation energy of benzylamine at 0 K to be 305 ( 4 kJ
-
1
mol , and with this value and the thermochemical properties of benzylamine and NH
2
, the heat of formation
-
1
of the benzyl radical was calculated. The heat of formation of benzyl radical at 298 K is 210 ( 5 kJ mol ,
5
6
which agrees with the result of Ellison et al. and the value recommended by Tsang.
Introduction
as a fitting parameter for the experimental data and obtained
the value of E0 compatible with the data.
Benzylamine (C6H5CH2NH2) is an attractive source of NH2
for shock tube kinetics experiments at temperatures as low as
Prior to this investigation, there have been several studies
2
measuring the decomposition rate of benzylamine. Szwarc used
1200 K, since benzylamine easily decomposes to produce NH2
the toluene-carrier technique and determined the first-order
reaction rate of benzylamine decomposition around 1000 K. Kerr
and the benzyl (C6H5CH2) radical via reaction R1. This
3
and co-workers also used the toluene-carrier flow technique
C H CH NH f NH + C H CH
2
(R1)
6
5
2
2
2
6
5
to study pyrolysis of benzylamine for the temperature range of
8
30-1060 K. The results of a VLPP (very low pressure
temperature corresponds approximately to the lower end of the
shock tube operating conditions and the high-temperature limit
of flow tube experiments. In addition, the benzyl radical is very
stable and unlikely to react at such low temperatures.
pyrolysis) study of benzylamine decomposition for the temper-
ature range 1040-1250 K have been reported by Golden et al.4
Since the unimolecular rate coefficient obtained from their VLPP
experiment was in the falloff regime, they combined experi-
mental data with the results of an RRKM calculation, using a
model transition state, to determine the high-pressure-limit rate
coefficient.
In our previous shock tube study of the NH2 + NO reaction,
we used benzylamine as a source of NH2 for the temperature
1
range 1262-1726 K and pressure range 1.14-1.44 bar. To
obtain the overall rate coefficient of this reaction, we needed
to properly model the production of NH2 from benzylamine
pyrolysis. However, the decomposition rates determined in
previous benzylamine pyrolysis studies2 were not directly
applicable for the temperatures and pressures of interest. For
this reason, we measured the rate coefficient for benzylamine
decomposition, k1, for temperatures and pressures required in
the NH2 + NO reaction study using the shock tube facility. To
obtain k1 values, we measured the concentration time history
of the NH2 radical produced from benzylamine pyrolysis using
frequency modulation (FM) absorption and determined the
decomposition rate of benzylamine by analyzing the initial rate
of NH2 production.
Recently, Ellison and co-workers reported the thermochemical
properties of benzyl and allyl radicals. In their experiments,
5
they used a flowing afterglow/selected ion flow tube. Tsang
has summarized the results of three different studies and/or
-4
6
reviews of the heat of formation of benzyl radical. This included
7
8
work by McMillen and Golden, Hippler and Troe, and Walker
and Tsang.
9
Experiments
The shock tube facility and diagnostics used in the present
study were the same as those used in our previous study of the
1
NH + NO reaction. The NH concentration was measured
2
2
Another objective of this study is to determine the heat of
formation of the benzyl radical. This value can be calculated
from the bond dissociation energy, E0, of the C-N bond of
benzylamine at 0 K. Since E0 is one of the input parameters for
the RRKM calculation needed to evaluate the data, we used E0
behind reflected shock waves using an FM absorption technique.
With FM absorption, at least a factor of 10 reduction in the
NH2 detection limit can be achieved in comparison with direct
laser absorption. The temperature and pressure behind the
reflected shock wave were calculated from the initial temper-
1
0.1021/jp020085l CCC: $22.00 © 2002 American Chemical Society
Published on Web 05/31/2002

A Shock Tube Study of Benylamine Decomposition
J. Phys. Chem. A, Vol. 106, No. 25, 2002 6095
TABLE 1: Summary of k with Experimental Conditions
1
-
3
-3
T
P
x
BA
k
1
× 10
T
P
x
BA
k
1
× 10
-
1
-1
(
K) (bar) (ppm)
(s
)
(K) (bar) (ppm)
(s )
1
225 1.24
227 1.19
241 1.19
261 1.24
266 1.27
274 1.26
294 1.28
309 1.33
313 1.34
320 1.35
329 1.35
336 1.34
338 1.32
356 1.33
363 1.34
369 1.35
374 1.33
390 1.30
399 1.33
402 1.34
50
36
36
40
36
36
39
20
24
21
25
38
20
28
20
24
23
27
26
26
1.00
1.34
1.58
2.70
2.90
3.50
5.40
7.40
7.50
8.30
9.30
11.4
9.00
18.4
14.3
22.0
21.0
27.0
28.0
26.5
1405 1.41
1405 1.41
1410 1.39
1431 1.42
1432 1.35
1434 1.40
1453 1.47
1468 1.39
1475 1.39
1486 1.22
1488 1.37
1489 1.40
1496 1.37
1498 1.43
1499 1.33
1541 1.26
1544 1.32
1573 1.39
1598 1.30
1599 1.36
25
25
25
25
25
25
26
29
28
23
30
25
28
28
27
20
29
26
31
23
28.0
36.7
44.0
67.0
50.0
62.0
73.0
97.0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
103
141
125
130
150
137
160
270
280
420
647
610
Figure 1. Example NH
2
mole fraction profiles: (a) 20 ppm C
6
H
H
5
-
-
CH
CH
2
NH
NH
CH
2
/Ar balance, T ) 1309 K, P ) 1.33 bar; (b) 25 ppm C
6
5
2
2
/Ar balance, T ) 1410 K, P ) 1.39 bar; (c) 24 ppm
C
6
H
5
2
NH /Ar balance, T ) 1489 K, P ) 1.40 bar. Solid lines are
2
21
experimental data. Dashed lines are results of the CHEMKIN
calculations using the reaction mechanism reported in ref 1.
expression for the pressure- and temperature-dependent value
of k1 for the experimental conditions of this study is
k1/s- ) 5.49 × 10 exp[-33110/[T (K)]](1225 < T (K) <
1
14
1
599 and 1.19 < P (bar) < 1.47) (1)
The major sources of uncertainty are the uncertainty in the initial
benzylamine concentration and the NH2 absorption coefficient
for the probe beam. The combined uncertainty is less than
(
15%. Due to the direct measurement of the decomposition
rate, the influence of secondary reactions is negligible. The
measured rate coefficients and experimental conditions are
tabulated in Table 1.
RRKM Calculation
RRKM calculations were performed to obtain the rate
coefficient for benzylamine decomposition in the high-pressure
limit and the bond dissociation energy of the C-N bond in
benzylamine. To perform RRKM calculations. the structure and
frequencies of the transition state are needed along with the
critical energy and some knowledge of energy transfer. The
structure and frequencies of the transition state yield the high-
pressure A factor. If this is known, the critical energy can be
used as a fitting parameter. In the earlier VLPP study of
Figure 2. Result of SENKIN22 calculation for NH
the reaction mechanism reported in ref 1: 25 ppm C
balance, T ) 1410 K, P ) 1.39 bar (conditions of Figure 1b).
2
sensitivity using
CH NH /Ar
6
H
5
2
2
ature and pressure and the shock speed measured over four
intervals using five piezoelectric pressure gauges. The estimated
uncertainty in the reflected shock temperature was less than (20
K at 1400 K over the time intervals of interest.
4
benzylamine, Golden et al. used a simple fixed transition state.
Liquid benzylamine (>99.5%, Aldrich) was evaporated in a
temperature-controlled bubble saturator, from which a mixture
of Ar (>99.9999%, Praxair) and benzylamine vapor was
continuously supplied to the shock tube. The flow scheme
reduces the uncertainty in the initial concentration of benzyl-
amine caused by wall adsorption. To measure the actual
concentration of the benzylamine entering the shock tube, the
absorption of benzylamine was measured between the bubble
saturator and the shock tube using a 3.39 µm HeNe laser.
Experiments were performed in the temperature range 1225-
In this work, we treated the transition states using the “hindered-
Gorin” model since a fixed transition state is an inadequate
10
model for simple bond fission reactions. With a fixed transition
state, the heat capacity of the transition state is too high and
the A factor for the dissociation reaction cannot be made
compatible with the reverse recombination reaction when fixed
vibrational frequencies are used for the low-frequency modes
of the transition state. In the Gorin model, the internal modes
of the transition state are the vibrations and rotations of the
independent NH2 and benzyl fragments. In other words, the
transition state is treated as if NH2 and benzyl radical were not
covalently bonded but completely free to rotate. However, it
has been noted that if the NH2 and benzyl fragments were placed
at a distance apart corresponding to the centrifugal maximum
in a Lennard-Jones attractive potential, they would interact as
they rotated, considering their van der Waals radii. Thus, the
tightness of the transition state is characterized using the
hindrance parameter, η, described by Smith and Golden,10 as
1
599 K, and the pressure range 1.19-1.47 bar. In total, 40 NH2
traces were analyzed. The initial benzylamine concentration was
varied from 20 to 50 ppm. Typical NH2 traces are shown in
Figure 1. When we analyzed the NH2 traces, the initial slope
of the NH2 concentration was measured, and as can be seen
from the sensitivity analysis in Figure 2, the initial slope is
directly proportional to the decomposition rate of benzylamine
and the initial concentration of benzylamine. The best fit rate

6096 J. Phys. Chem. A, Vol. 106, No. 25, 2002
Song et al.
TABLE 2: Inputs for the RRKM Calculations
average energy transferred in a single collision, 〈∆E〉all. Since
the 〈∆E〉all value depends mostly on the bath gas (argon) rather
than the reactant (benzylamine) and is a very weak function of
T, we can estimate the range of 〈∆E〉all values of benzylamine-
argon collisions even though experimental data are not available.
C6H5CH2NH2 (Molecule)
frequencies (cm-1)
3405, 3335, 3060, 3050, 3040, 3025,
3
1
1
1
8
3
025, 2945, 2910, 1600, 1580, 1560,
465, 1430, 1425, 1335, 1315, 1300,
280, 1170, 1155, 1135, 1110, 1050,
035, 1010, 975, 960, 935, 890, 875, 850,
20, 770, 735, 685, 610, 565, 475, 395,
-
1
The estimated 〈∆E〉all was -150 ( 50 cm , which is similar
1
5
to that in toluene-argon collisions. After determining the
〈∆E〉all value and calculating âc from a given 〈∆E〉all, we obtained
E0 within uncertainty limits corresponding to the range of A∞
values.
50, 310, 245, 130, 45
5
product of adiabatic moments 4.022 × 10
-
80
2
4
of inertia (10 g cm )
Moment of inertia for active
182.2
-
40
2
external rotor (10 g cm )
To reduce the uncertainty of the E0 values, we needed to use
(1) more accurate values of A∞ or (2) other independent
experimental data. To obtain the true value of A∞, experiments
should be performed at sufficiently high pressure. However,
Brouwer and co-workers have reported that the ethylbenzene
decomposition reaction (R2) was still in the falloff regime even
C6H5CH2‚‚‚NH2 (Transition State)
3305, 3230, 3115, 3065, 3055, 3050,
frequencies (cm-1)
3
1
1
9
4
040, 3035, 3025, 1530, 1515, 1495,
445, 1440, 1420, 1305, 1270, 1235,
140, 1130, 1075, 995, 960, 955, 940,
35, 865, 800, 745, 680, 660, 605, 515,
85, 460, 375, 345,190
13
at the highest experimental pressure, which was 20 times
5
product of adiabatic moments 9.097 × 10 at 1150 K
-
80
2
4
5
higher than our experimental pressure. So instead, we reanalyzed
the VLPP experimental data to obtain values of E0 and A∞ more
accurately.
of inertia (10 g cm )
8.696 × 10 at 1400 K
moment of inertia for active
253.5
-
40
2
external rotor (10 g cm )
moment of inertia for active
2.012 (σ ) 2), 376.8 (σ ) 1)
2.145 (σ ) 3)
-
40
2
In contrast to the shock tube data analysis, where energy
transfer is with gas-gas collisions, the efficiency of a gas-
wall collision used in the VLPP, âw, was required for the RRKM
calculations. For some molecules, the âw values were obtained
experimentally, but data for benzylamine were not available,
so we estimated the range of âw values on the basis of a study
2
-D rotor (10 g cm )
moment of inertia for active
-
40
2
1
-D rotor (10 g cm )
TABLE 3: Data Used in Eq 4
species
T (K)
∆
f
H° (kJ mol-1)
uncertainty
ref
benzylamine
0
0
115.5
192
(2.7
(1
23
24
16
by Dick et al., who pointed out that gas-wall collision under
NH
2
VLPP conditions had collision efficiencies of âw ) 0.5 ( 0.1.
4
16
In the VLPP study performed prior to the work of Dick et al.,
the percentage of the 4π steradians unavailable to the rotating
species. In effect, we are treating the rotations by varying the
rotational level spacing through use of η, thereby controlling
the entropy and heat capacity of the transition state. The
hindrance is introduced into the RRKM code by multiplying
the adiabatic two-dimensional rotor moments of inertia of the
NH2 and benzyl fragments in the transition state each by (1 -
a unit gas-wall collision efficiency (âw ) 1) was used. From
the RRKM calculations with the given input parameters, we
obtained combinations of A∞ and E0 fitting the VLPP as well
as the shock tube data. The ranges of the 〈∆E〉all and âw values
automatically determine the uncertainty of the A∞ and E0 values.
In addition to the RRKM calculations, we used the Multiwell
1
7,18
code,
which solves the master equation using a stochastic
1
/2
η) .
To analyze the shock tube data alone, employing the RRKM
method. The average energy transfer used for deactivating
-
1
collisions with argon, 〈∆E〉down, was 550 cm corresponding
calculations, we had to estimate the high-pressure A factor, A∞.
The input parameters for the RRKM calculations cannot be
determined by a single set of experimental data; therefore, either
E0 or A∞ has to be estimated reasonably. We assumed that
ethylbenzene (C6H5CH2CH3) decomposition chemistry was
similar to that of benzylamine decomposition and used the A∞
values of ethylbenzene for the RRKM calculations of benzyl-
amine decomposition.
-
1
to 〈∆E〉all ) -150 cm , and the results of the Multiwell
calculation were consistent with those of the RRKM calcula-
1
9
tions.
The frequencies and moments of inertia of the molecule and
transition state were calculated using Gaussian 98, revision 7,20
at the B3LYP/6-311G(d,p) level, and are tabulated in Table 3
with other input parameters for the RRKM calculation.
C H CH CH f CH + C H CH
(R2)
Results and Discussion
6
5
2
3
3
6
5
2
From the RRKM calculations, we determined the high-
pressure-limit rate, k∞, and the bond dissociation energy of
the C-N bond of benzylamine at 0 K. Using the input
parameters given in Table 3, the high-pressure rates were
calculated every 100 K from 1000 to 1600 K. Fitting these rate
coefficients linearly on an Arrhenius plot, we derived the rate
expression
1
1
According to Baulch et al.’s review, the recommended A∞
15 -1
value for reaction R2 is 7.1 × 10
s
for the temperature range
70-1800 K. Considering only papers published since 1980,
7
1
2
13
15
the minimum and maximum values were 2.0 × 10 and
1
7 -1
1
.3 × 10 s , respectively. We set the uncertainty of A∞ as a
factor of 4, and the corresponding range of A∞ used for the
15
16 -1
RRKM calculations was from 1.6 × 10 to 2.5 × 10 s .
Within this range of A∞, we calculated η and found the
relationship between A∞ and η at the mean temperature of the
experimental conditions.
-
1
16
k /s ) 1.07 × 10 exp[-36470/[T (K)]] (1000 K < T <
∞
1600 K) (2)
As stated earlier, RRKM calculations also require some
knowledge of energy transfer. The simple pseudo-strong-
collision version seems adequate for this study, which means
knowing the value of the collision efficiency, âc. Troe has
suggested that the collision efficiency, âc, is related to the
The A∞ value given in eq 2 is 7 times the A∞ value reported by
Golden et al. and 50% higher than the A factor for the
4
1
4
ethylbenzene decomposition reaction recommended by Baulch
1
1
et al. The lower temperature limit of our experiments corre-

A Shock Tube Study of Benylamine Decomposition
J. Phys. Chem. A, Vol. 106, No. 25, 2002 6097
TABLE 4: Summary of Data on the High-Pressure-Limit Rate of Benzylamine Decomposition
A
∞
E
authors (year)
methods (temperatures)
(s-1)
(kJ mol-1)
ref
1
1
2
3
Szwarc (1949)
toluene-carrier technique (920-1070 K)
toluene-carrier technique (830-1060 K)
VLPP, RRKM (1040-1250 K)
6.0 × 10
1.0 × 10
247
250
301
303
2
3
4
Kerr et al. (1963)
Golden et al. (1972)
Song et al. (2002)
1
5
1.58 × 10
1.07 × 10
4
16
shock tube, VLPP, RRKM (1050-1600 K)
this study
TABLE 5: Summary of Data on the Benzyl Radical Heat of Formation
authors (year)
methods
∆
f
H°benzyl(300 K)
ref
McMillen and Golden (1982)
Hippler and Troe (1990)
Walker and Tsang (1990)
Tsang (1996)
Ellison et al. (1996)
Song et al. (2002)
review
200 ( 6
210.5 ( 4
203 ( 6
207 ( 4
208 ( 3
210 ( 5
7
8
9
6
shock tube (pyrolysis of toluene, benzyl iodide, and dibenzyl)
shock tube (pyrolysis of n-pentylbenzene)
recommended value based on refs 7-9
flowing afterglow/selected ion flow tube
shock tube, VLPP
5
4
this study
1
Figure 3. Shock tube experimental data for k : 0, experimental data
from this study (P ≈ 1.3 bar); -‚-, best fit to the experimental data
Figure 4. VLPP experimental data for k
1
taken from Table 3 and Figure
near 1.3 bar, eq 1; solid line, results of the RRKM calculations at 1.3
4
1
in ref 4: O, VLPP experimental data (new reactor); 0, VLPP
bar; dashed line, results of the RRKM calculations for k
∞
, eq 2.
4
experimental data (old reactor); dashed line, results of the RRKM
4
calculations; solid line, results of the RRKM calculations in this study.
2
sponds to the high-temperature limit of Szwarc’s and Kerr
etal.’s studies. At 1050 K, our k∞ value is 2 times higher than
3
K, an appropriate heat capacity correction is required as shown
in eq 4.
that reported by Szwarc and 1.5 times higher than the value of
Kerr et al. The extrapolated k∞ values of eq 2 near 900 K agree
with data from Szwarc and Kerr et al. within 20%. However, it
∆fH°benzyl(298 K) ) ∆ H°benzyl(0 K) - [H°(0 K) -
f
13
-1
H°(298 K)]benzyl + 7[H°(0 K) - H°(298 K)] +
is obvious that their A∞ values (∼10 s ) are too low for the
high-pressure-limit rate of the unimolecular decomposition
reaction. The data from the shock tube experiments and the
results of the RRKM calculation for k1 (1.3 atm) and k∞ are
shown in Figure 3. The shock tube experimental conditions were
in the falloff regime with k1/k∞ varying from 0.90 at 1200 K to
C
7/2[H°(0 K) - H°(298 K)]H2 (4)
-
1
The sum of all correction terms is -18 kJ mol , and the
-
1
resulting value of ∆fH°benzyl(298 K) was 210 ( 5 kJ mol .
This value is in good agreement with the result of Ellison et
5
-1
al.’s study, 208 ( 3 kJ mol , and Tsang’s recommended
0
.39 at 1600 K. The range of k1/k∞ was from 0.146 at 1050 K
6
-1
value, 207 ( 4 kJ mol .
to 0.0292 at 1250 K for the VLPP experiments. The RRKM
calculation for the VLPP data is shown in Figure 4.
Table 4 summarizes values for the high-pressure-limit rate
coefficient from past studies and the present study. Table 5
summarizes values for the heat of formation of benzyl radical.
Using only the shock tube data, we calculated the E0 value
-
1
as 297 ( 12 kJ mol , but we were able to obtain a more
accurate value by combining the shock tube and VLPP data.
The resulting E0 value was 305 ( 4 kJ mol- . The heat of
formation of benzyl radical at 0 K, ∆fH°benzyl(0 K), was
calculated by eq 3, and the data are given in Table 5.
Conclusions
1
We measured the benzylamine decomposition rate using
frequency modulation absorption for NH2 detection behind
reflected shock waves in the temperature range 1225-1599 K
around 1.3 bar. Combining the shock tube experimental data
with earlier VLPP data, the high-pressure rate expression for
benzylamine decomposition and the bond dissociation energy
of the C-N bond of benzylamine were determined by applying
RRKM calculations. The corresponding heat of formation of
the benzyl radical was obtained from the bond dissociation
∆fH°benzyl(0 K) ) E + ∆ H°benzylamine(0 K) -
0
f
-
1
∆fH°NH2(0 K) ) 228 ( 5 kJ mol (3)
To calculate the heat of formation of benzyl radical at 298

6098 J. Phys. Chem. A, Vol. 106, No. 25, 2002
Song et al.
energy of the C-N bond of benzylamine and the thermochemi-
cal properties of benzylamine and NH2.
(13) Brouwer, L.; M u¨ ller-Markgraf, W.; Troe, J. Ber. Bunsen-Ges. Phys.
Chem. 1983, 87, 1031.
(14) (a) Troe, J. J. Chem. Phys. 1977, 66, 4745. (b) Troe, J. J. Chem.
Phys. 1977, 66, 4758.
Acknowledgment. This work was supported by the U.S.
Department of Energy, Office of Basic Energy Sciences,
Division of Chemical Sciences. We thank Juan Senosiain for
performing the DFT calculations and John Barker for helpful
discussions concerning use of the Multiwell code.
(15) Heymann, M.; Hippler, H.; Troe, J. J. Chem. Phys. 1984, 80, 1853.
(16) Dick, P. G.; Gilbert, R. G.; King, K. D. Int. J. Chem. Kinet. 1984,
6, 1129.
1
(17) Barker, J. R. Multiwell, 1.1.3 ed.; http://aoss.engin.umich.edu/
multiwell/; Ann Arbor, MI, 2001.
(18) Barker, J. R. Int. J. Chem. Kinet. 2001, 33, 232.
(19) Barker, J. R.; Golden, R. E. J. Chem. Phys. 1984, 88, 1012.
(20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
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