Rate constants for the decomposition of 2-butoxy radicals and their reaction with NO and O2

Article abstract of DOI:10.1039/b405134c

The reactivity of 2-butoxy radicals has been investigated using the laser photolysis/laser induced fluorescence technique. Three reactions have been studied: (i) The rate constants for the reaction with NO have been measured by the same technique at total pressures between 0.03 < p < 0.4 bar of helium and at five temperatures between 295-348 K. No pressure dependence has been found within the experimental error, and a small negative temperature dependence has been found, in agreement with earlier studies: k₁ = (4.4 ± 0.6) × 10^-12 exp((4.9 ± 0.3) kJ mol ^-1/RT) cm³ s^-1. (ii) The rate constant with O₂ has been measured at room temperature and 0.131 bar of helium: k₂ = (9 ± 2) × 10^-15 cm³ s ^-1. Significant quenching of 2-butoxy fluorescence by O₂ prevented experiments in a larger temperature range: k_q,O2 = (4 ± 1) × 10^-11 cm³ s^-1. (iii) The temperature and pressure dependence of the unimolecular decomposition at total pressures between 0.01 < p < 0.8 bar of helium and at four temperatures between 291-348 K. The low and the high pressure limiting rate constants as well as the broadening factor F_cent have been extracted from a falloff analysis of the experimental results: k_3,0,He = 3.2 × 10 ^-8 exp(-35.9 kJ mol^-1/RT) cm³ s^-1, k_3,∞ = 1.1 × 10¹⁴ exp(-53.6 kJ mol ^-1/RT) s^-1, and F_3.c = 0.87 - T/870 K. We anticipate an uncertainty of ±30% for these rate constants. These results are in excellent agreement with earlier predictions (C. Fittschen, H. Hippler and B. Viskolcz, Phys. Chem. Chem. Phys., 2000, 2, 1677-1683 (ref. 1); R. Mereau, M.-T. Rayez, F. Caralp and J.-C. Rayez, Phys. Chem. Chem. Phys., 2000, 2, 3765 (ref. 2)).

Full text of DOI:10.1039/b405134c

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R E S E A R C H P A P E R
Rate constants for the decomposition of 2-butoxy radicals and
their reaction with NO and O2
a
b
c
a
a
G. Falgayrac, F. Caralp, N. Sokolowski-Gomez, P. Devolder and C. Fittschen*
a
Physicochimie des Processus de Combustion et de l’Atmosphe`re, UMR 8522 CNRS/Universite´
de Lille 1, Centre d’Etudes et de Recherches Lasers et Applications, 59655 Villeneuve d’Ascq,
France
b
c
Laboratoire de Physicochimie Mole´culaire, UMR 5803 CNRS/Universite´ de Bordeaux 1,
3
3405 Talence Cedex, France
Groupe de Spectroscopie Mole´culaire et Atmosphe´rique, UMR 6089 CNRS/Universite´ Reims
Champagne-Ardenne, 51687 Reims Cedex, France
Received 6th April 2004, Accepted 3rd June 2004
First published as an Advance Article on the web 22nd June 2004
The reactivity of 2-butoxy radicals has been investigated using the laser photolysis/laser induced fluorescence
technique. Three reactions have been studied: (i) The rate constants for the reaction with NO have been
measured by the same technique at total pressures between 0.03 o p o 0.4 bar of helium and at five
temperatures between 295–348 K. No pressure dependence has been found within the experimental error, and a
small negative temperature dependence has been found, in agreement with earlier studies: k
ꢂ12
1
¼ (4.4 ꢀ 0.6) ꢁ
ꢂ1
3
ꢂ1
1
temperature and 0.131 bar of helium: k
0
exp((4.9 ꢀ 0.3) kJ mol /RT) cm s . (ii) The rate constant with O has been measured at room
2
ꢂ15 ꢂ1
3
2
¼ (9 ꢀ 2) ꢁ 10
cm s . Significant quenching of 2-butoxy
¼ (4 ꢀ 1) ꢁ 10
ꢂ11
3 ꢂ1
cm s .
fluorescence by O prevented experiments in a larger temperature range: k
2
q,O
2
(
iii) The temperature and pressure dependence of the unimolecular decomposition at total pressures between
0.01 o p o 0.8 bar of helium and at four temperatures between 291–348 K. The low and the high pressure
limiting rate constants as well as the broadening factor Fcent have been extracted from a falloff analysis of the
ꢂ8
ꢂ1
3
ꢂ1
14
experimental results: k
ꢂ1
¼ 3.2 ꢁ 10 exp(ꢂ35.9 kJ mol /RT) cm s , k3,N ¼ 1.1 ꢁ 10
3
,0,He
ꢂ1
exp(ꢂ53.6 kJ mol /RT) s , and F3,c ¼ 0.87 ꢂ T/870 K. We anticipate an uncertainty of ꢀ30% for these rate
constants. These results are in excellent agreement with earlier predictions (C. Fittschen, H. Hippler and
reau, M.-T. Rayez, F. Caralp and
J.-C. Rayez, Phys. Chem. Chem. Phys., 2000, 2, 3765 (ref. 2)) .
B. Viskolcz, Phys. Chem. Chem. Phys., 2000, 2, 1677–1683 (ref. 1); R. Me
´
The obtained rate constants from both studies at 293 K differ
by nearly a factor of 2.
The decomposition reaction has been studied twice in a smog
Introduction
Alkoxy radicals are important intermediates in the photo-
oxidation of saturated hydrocarbons. Low temperature com-
bustion as well as pyrolysis of oxygen containing compounds
proceed via alkoxy radicals. Therefore, many experimental
studies have been devoted to alkoxy radical reactions and
several review articles have appeared.
studies of the reactivity of 2-butoxy radicals are rare, the laser
induced fluorescence excitation spectrum of this radical has
12
13
chamber by Meunier et al. and by Libuda et al. , leading to
the ratio of k /k . The only absolute determination is the
2
3
11
above-mentioned work by Hein et al. at 293 K and 50 mbar.
No systematic determination of the temperature and pressure
dependence of this rate constant has been published.
In the present work we have studied reactions (R1) and (R3)
as a function of temperature and pressure, while (R2) could be
studied only at ambient temperature, due to significant fluor-
escence quenching.
3
–8
Nevertheless, direct
1
7
first been published only in 1999 by Wang et al.
The reactions studied in this work
d
2
-C H O þ NO - product 1
(R1)
(R2)
(R3)
4
9
d
Experimental
2
-C H O þ O - product 2
4
9
2
d
Experiments have been performed by laser flash photolysis
(LFP) of 2-butylnitrite (2-C H ONO) using helium as bath gas
4 9
and 2-butoxy radicals were detected by laser induced fluores-
2
-C H O þ M - C H þ C H O þ M
4
9
2
5
2
4
have been the subject of some earlier papers:
The reaction with NO has been studied twice using the same
technique of LP/LIF by Deng et al. and Lotz et al. Both
found in the temperature range 223 K o T o 311/305 K a
negative activation energy and no pressure dependence.
cence. Details of the experimental set-up have been described
14,15
9
10
earlier
follows.
so only some principal features are given here, as
Like all alkyl nitrites, 2-butylnitrite has two absorption
bands in the UV region, particularly suitable for excimer laser
photolysis: one broad band with a maximum at 223 nm and a
2 2
The rate constant k for the reaction with O has been the
9
subject of two papers: Deng et al. studied this reaction
between 223 and 311 K, using the direct LIF technique, while
ꢂ1
decadic absorption coefficient of e(223.5 nm) ¼ 1650 L mol
1
1
ꢂ1
Hein et al. measured at 293 K and 50 mbar in a somewhat
indirect experiment. They fit NO and OH concentration-time
profiles, obtained during pulse initiated oxidation of 2-bromo-
butane in the presence of O and NO, to a complex mechanism.
cm and a second weaker and more structured transition
ꢂ1
ꢂ1 16
2
around 350 nm (emax(358/346.2 nm) ¼ 67/51 L mol cm
)
The 2-butylnitrite has been photolysed at 351 nm. Earlier
1
experiments on the decomposition of t-butoxy radicals have
2
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 1 2 7 – 4 1 3 2
4127

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1
observed up to 50 bar He. The same, very different quenching
behaviors have already been observed for propoxy radicals :
i-propoxy does not show any observable quenching with He,
while n-propoxy has nearly the same quenching rate with He
shown an increased decomposition rate of t-butoxy radicals at
pressures below 0.15 bar after 248 nm photolysis compared to
1
9
3
51 nm: at low pressures thermalization of the 2-butoxy
radicals from 248 nm photolysis can probably not be achieved
fast enough.
The photolysis laser beam (Lambda Physik LPX 202i) was
focused with two cylindrical lenses, leading to average pulse
ꢂ12
3
ꢂ1
(kq,He ¼ 3.6 ꢁ 10
cm s ) as 2-butoxy. Quenching with O
ꢂ11
2
3
cm s ), thus
ꢂ1
was also significant, (k
¼ (4 ꢀ 1) ꢁ 10
q,O
2
limiting the [O
ments to [O ] r 10 cm
2
] concentration usable in the kinetic experi-
ꢂ3
ꢂ2
18
energies of 50 mJ cm at 351 nm. The 2-C H ONO concen-
4
.
9
2
1
5
ꢂ3
trations were varied between 0.5–3 ꢁ 10 cm . With a
From an extrapolation of different Stern–Volmer plots to
zero concentration a radiative lifetime of trad ¼ (340 ꢀ 50) ns
has been obtained, in good agreement with ref. 10 (440 ns).
ꢂ1
decadic absorption coefficient of e(351 nm) ¼ 45 L mol
ꢂ1 16
cm and an assumed photodissociation quantum yield of
unity the 2-C H O radical concentration was always below
d
4
9
1
3
ꢂ3
2
ꢁ 10 cm
.
We followed the temporal evolution of the 2-C H O radical
concentration by laser induced fluorescence (LIF), excited
near 369 nm. Excitation beam was from a YAG pumped dye
laser (Quantel TDL50) using frequency mixing with Rhodamin
Reaction of 2-butoxy with NO
d
4
9
1
7
The rate constant for the reaction of 2-butoxy radicals with
NO has been obtained under pseudo-first order condi-
tions: 2-butoxy radical decays have been observed with a large
excess of NO. Under these conditions 2-butoxy radicals decay
mono-exponentially through two reaction pathways: reaction
with NO
5
90. The fluorescence was collected perpendicular to the
fluorescence excitation laser beam through a cut-off filter at
l 4 380 nm.
The 2-butylnitrite was prepared according to a well-known
d
2
-C H O þ NO - product 1
(R1)
4
9
1
8
procedure through drop by drop addition of concentrated
sulfuric acid to a saturated solution of NaNO and 2-butanol.
-butylnitrite appears as a pale yellow liquid and can be stored
and decomposition:
2
2
d
2
-C
4
H
9
O þ M - C
2
H
5
þ C
2
H
4
O þ M
(R3)
for weeks at ꢂ20 1C. Gaseous mixtures, highly diluted in He,
did not markedly decompose at room temperature in a
darkened glass bulb. The carrier gas He (99.995%, Air
Liquide) was used without further purification.
The helium pressure in the experiments extended from 0.01
to 0.8 bar, the temperature range was restrained between 291
and 348 K. At the high temperature limit, 2-butoxy radical
decomposition approached the time resolution of the experi-
ment while at the lower temperature limit unimolecular decom-
position could no longer be separated from 2-butoxy loss in
bimolecular reactions. All given errors are statistical only.
Accordingly, the 2-butoxy radical decay follows a pseudo-first-
order rate law
ꢃ
d½2 ꢂ C4H9O ꢄ
ꢂk 11 st½2 ꢂ C4H9Oꢃꢄ
¼
dt
where the total pseudo-first order rate constant kobs is given by
1st
k
1
¼ k
1
[NO] þ k
3
Fig. 2 shows typical decays at fixed pressure and temperature
using different NO concentrations. A plot of the obtained
pseudo-first-order rates versus [NO] is shown Fig. 3 for one
temperature and three different pressures: the slope of this plot
Fluorescence lifetime and quenching
The fluorescence lifetime t
expression:
fl
is given by the following
1
gives the rate constant k , while the intercept leads to the rate
constants for the decomposition k . Other processes like diffu-
3
flꢂ1
¼ tradꢂ1 þ k
sion out of the observation volume and reaction with the
precursor appear also in the intercept, but are minor compared
to k and have been neglected (see section Thermal de-
3
composition). The NO concentration has generally been varied
in a range to double at least the pseudo-first order rate
t
q
[t ꢂ C
4
H
9
ONO] þ kq,He [He] þ kq,R [R]
, kq,He and kq,R are
in which trad is the radiative lifetime and k
the fluorescence quenching rate constant with the precursor
2
t-butylnitrite, with He and with the reactant (O or NO),
q
respectively. Quenching with the precursor 2-butylnitrite was
very efficient and from the shortening of the fluorescence
1
constant, i.e. at the highest [NO] concentration k [NO] Z
k
3
: the explored temperature range is thus limited (295 K o
lifetime we found a rate constant of k
ꢂ10
q
¼ (4 ꢀ 1) ꢁ
T o 348 K) by the increasing importance of the decomposition
3
cm s . This result is in accordance with Lotz et al.
ꢂ1
10
1
0
reaction at higher temperatures.
1
and also with our results on other alkoxy radicals. The
quenching efficiency with He (Fig. 1) has also been found to
All results (k
experimental conditions (results for k
1
and k
3
) are shown in Table 1 together with the
are discussed below).
3
ꢂ12
3
cm s . This is in contrast
ꢂ1
be significant: kq,He ¼ 3.2 ꢁ 10
No marked pressure dependence has been observed for this
reaction within the experimental error, in accordance with
to t-butoxy radicals, where no measurable quenching has been
Fig. 2 Typical mono-exponential decays for the reaction of 2-butoxy
1st
/
1
5
ꢂ3
Fig. 1 Fluorescence lifetime of 2-butoxy radicals excited at 369 nm at
radicals with NO: p ¼ 0.065 bar, T ¼ 314 K: [NO]/10 cm (k
1
3
ꢂ1
295 K as a function of [He]-concentration, 20 ms after photolysis. Error
10 s ): &: 3.41 (111 ꢀ 1); m: 2.05 (88 ꢀ 1); n: 1.17 (55 ꢀ 2);E: 0 (25.7 ꢀ
bars represent an estimated error of ꢀ10%.
0.9), given errors are statistical only.
4
128
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 1 2 7 – 4 1 3 2
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

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1
st
Fig. 3 Plot of k
three different pressures (error bars represent an estimated experimen-
1
as a function of NO-concentration at 314 K for
Fig. 4 Arrhenius plot for the rate constant of 2-butoxy radicals with
NO (R1), & Lotz et al. n Deng et al. K this work (error bars
represent 15% estimated experimental error).
10
9
ꢂ11
3
ꢂ1
3
ꢂ1
tal error of 15%) k
¼ 2.95 ꢀ 0.13, k
; .197 mbar: k
¼ 3.06 ꢀ 0.10, k
only).
1
(in 10
¼ 25 ꢀ 3, n: 131 mbar: k
¼ 42 ꢀ 3 (given errors are statistical
cm s ) and k
3
(in 10 s ): ’: 65 mbar:
k
4
1
3
1
¼ 2.94 ꢀ 0.16, k ¼ 31 ꢀ
3
1
3
Reaction of 2-butoxy with O2
Table 1 Results and experimental conditions for the reaction of
-butoxy radicals with NO (R1). No. of exp: number of decays
measured at different [NO], k average: average over all pressures at
one temperature; k has been corrected for contribution of (R4).
Experimental error, including systematic errors, is estimated to ꢀ15%
The rate constant for the reaction of 2-butoxy radicals with O
2
(R2) has been obtained in the same way as (R1): mono-
exponential decays of 2-butoxy fluorescence have been
measured under excess [O ]. Under these conditions 2-butoxy
2
radicals decay mono-exponentially through two reaction
2
1
3
pathways: reaction with O
2
15
ꢂ11
T
p
bar
[NO]/10
ꢂ3
No. of
exp.
k
3
ꢂ1
k
1
/10
k
1
3 ꢂ1
cm s
d
K
cm
s
average
2-C
H
O þ O
- 2-C
4
H
O þ HO
(R2)
(R3)
4
9
2
8
2
2
95
0.026
0.0–3.5
0.0–4.5
1.0–3.7
1.0–5.0
1.0–5.0
0–3.0
0–3.5
0–3.5
0–3.5
0–5.0
0–3.7
0–3.0
0–4.0
0–4.0
0–3.0
0–5.0
0–5.0
0–3.0
0–3.0
0–3.0
0–3.0
0–3.0
5
5
3
5
5
4
5
5
4
5
5
4
5
5
4
5
5
4
5
4
5
5
8000
2.98
3.12
3.39
3.05
3.39
2.78
2.95
3.04
2.94
3.06
2.72
2.86
2.97
2.43
2.85
2.55
2.35
2.46
2.10
2.16
2.95
2.16
3.19
and decomposition:
0
0
0
0
.065
.131
.197
.394
11700
14400
19800
21500
11100
25100
22600
30800
42200
49000
18350
28070
38200
33400
63000
57800
28600
42600
80000
68100
80400
d
2
-C H O þ M - C H þ C H O þ M
4
9
2
5
2
4
Accordingly, the 2-butoxy radical decay follows a pseudo-first-
order rate law
314
0.026
2.92
2.66
0
0
0
0
0
.065
.065
.131
.197
.197
ꢃ
d½2 ꢂ C4H9O ꢄ
¼ ꢂk 12 st½2 ꢂ C4H9Oꢃꢄ
dt
1st
2
where the total pseudo-first order rate constant k
is given by
323
0.026
1st
2
k
¼ k
2
[O
2
] þ k
3
0
0
0
0
0
.065
.065
.065
.197
.197
9
Deng et al. observed a negative temperature dependence of
this reaction, in consistence with a proposed mechanism for
this reaction involving a pre-equilibrium
d
3
3
34
48
0.026
0.026
2.46
2.34
2-C
4
H
9
O þ O
followed by subsequent decomposition of the transient trioxy
2
2 2-C
4
H
9
O
3
(R2)
0
0
0
.065
.065
.197
radical by HO -elimination. Unfortunately, we have not been
2
able to confirm the temperature dependence by enlarging the
temperature range to higher temperatures: due to significant
fluorescence quenching by O
1
2
the usable O
2
concentration
range was limited to ca. 10 cm ; giving the low rate constant
8
ꢂ3
9
,10
for k
maximal ca. 10000 s . This is not enough to keep reaction
2
one can obtain pseudo-first order rate constants of
ꢂ1
earlier studies for (R1),
but also with studies on the
1
9
reactivity of smaller alkoxy radicals in our laboratory. (R1)
can proceed through two reaction channels:
(
R2) equivalent compared to (R3) at temperatures above
ambient temperature. We thus have measured (R2) only at
room temperature: all results together with the experimental
d
2
-C H O þ NO (þM) - 2-C H ONO (þM) (R1a)
4
9
4
9
1
st
d
conditions are resumed in Table 2, Fig. 5 shows k2 as a
function of [O ] for two temperatures: 291 and 295 K at
131 mbar. The obtained rate constant k
¼ (0.9 ꢀ
2-C
4
H
9
O þ NO - 2-C
4
8
H O þ HNO
(R1b)
2
Despite the lack of pressure dependence it is supposed in
analogy to smaller alkoxy radicals that the addition channel
is the major reaction path and that the high pressure limit has
been reached at our lowest pressure (26 mbar).
2, 295 K
ꢂ14
3
ꢂ1
9
0.3) ꢁ 10
((1.2 ꢀ 0.4) ꢁ 10
cm s is in good agreement with Deng et al.
ꢂ14
3
ꢂ1
11
cm s ), but also with Hein et al. (0.65 ꢁ
ꢂ14
3
cm s ). Nevertheless, with regard to the very indirect
ꢂ1
10
The temperature dependence of the rate constant k is shown
1
approach of Hein et al. we give more credit to the value of
Deng et al.
in Fig. 4, together with the results from the two former studies
9
,10
of this reaction:
the agreement between the absolute values
of the three different studies are very good, it seems that the
temperature dependence of our values fits better with the
results of ref. 10. We thus propose an Arrhenius expression
including the results of both studies:
Thermal decomposition of 2-butoxy
Experimental results
Under our experimental conditions 2-butoxy radicals decay
predominantly by unimolecular decomposition in reaction
k1 ¼ (4.4 ꢀ 0.6) ꢁ 10ꢂ12 exp[(4.9 ꢀ 0.3) kJ molꢂ1/RT] cm s
3
ꢂ1
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 1 2 7 – 4 1 3 2
4129

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Table 2 Results and experimental conditions for the reaction of
-butoxy radicals with O (R2). Given errors are statistical, overall
experimental error, including systematic errors, is estimated to ꢀ15%
2
2
1
8
ꢂ3
1st ꢂ1
ꢂ1
ꢂ3 ꢂ1
T/K [O
2
]/10 cm
k
2
/s
k
3
/s
k
2
/cm
s
291 1.2
19400
20500
14500
16000
16500
13600
14500
14400
19700
17000
19400
23000
16000
7000 ꢀ 3000 (0.9 ꢀ 0.3) ꢁ 10ꢂ14
1
1
1
0
0
0
.2
.0
.0
.7
.7
.7
295 0.0
15200 ꢀ 700 (0.9 ꢀ 0.2) ꢁ 10ꢂ14
0
0
0
0
0
.6
.3
.3
.8
.0
Fig. 6 Falloff curves of the first order rate constants k
3
at different
temperatures:E: 348 K, .: 331 K, ’: 315 K, m: 291 K (open symbols
1st
represent values obtained from the intercept in the plots of k
1
and
), for details on error bars see text;
lines: best fit using the falloff parameters mentioned in the text.
1st
k
2
as a function of NO and O
2
account. The error bars in Fig. 6 illustrate an estimated
ꢂ1
experimental error of ꢀ15% plus an error of ꢀ1000 s for
the correction due to (R4).
Rate constants obtained for (R3) are shown in Table 3; the
individual falloff curves for the first order decomposition rate
constant k
are the decomposition rates obtained from the intercepts in the
3
are illustrated in Fig. 6. Also shown in this figure
1
st
plots k ¼ f([NO] or [O
2
]) for the reaction (R1) and (R2): the
agreement is very good.
Theoretical methods and results
Experimental falloff curves are analysed using a conventional
RRKM calculation in the strong collision approximation.
20
Calculations were performed using the FALLOFF program
st
Fig. 5 Plot of k
(error bars represent an estimated error of 15%): k
1
2
as a function of O
2
-concentration at 131 mbar
3
ꢂ14
ꢂ1
2
/10
cm s (k
3
/
3
ꢂ1
0 s ) m 295 K: 0.9 ꢀ 0.3 (15.2 ꢀ 0.7) ’ 291 K: 0.9 ꢀ 0.3 (8 ꢀ 3)
0
with the aim of extracting the threshold energy E . The
(
given errors are statistical).
pressure dependence of the thermal dissociation rate constant
is then given by:
(R3) and to a lesser extent by a bimolecular reaction with the
precursor
Z
1
1
oꢁkðEÞ
oþkðEÞ
ꢁ NðEÞeꢂðE=RTÞ dE
kðTÞ ¼
d
Q
E0
2-C
H
4 9
O þ C
4 9
H ONO - other products
(R4)
Accordingly, the 2-butoxy radical decay follows a pseudo-first-
order rate law
Table 3 Results and experimental conditions for the decomposition
reaction of 2-butoxy radicals (R3). k has been corrected for contribu-
tion of (R4). Experimental error, including systematic errors, is
3
ꢃ
d½2 ꢂ C4H9O ꢄ
1
3
¼
ꢂk st½2 ꢂ C4H9Oꢃꢄ
estimated to ꢀ15%
dt
12
ꢂ3
ꢂ1
3
/s
T/K
p/bar
[2-C
4
H
9
ONO]/10 cm
No. of exp.
k
1
where the total pseudo-first order rate constant k is given by
st
2
3
91
15
0.029
0.064
0.8–2.4
1.0
1.2
6
3
4
12
3
3
1
3
3
3
2
3
3
3
2
2
4
2
4
4
2
2
2
4000
7100
1
st
k3 ¼ k þ k [2 ꢂ C H ONO]
3
4
4
9
0
0
0
0
.088
.153
.351
.661
7350
9200
Total pseudo-first order rate constant for the 2-butoxy radical
decay were obtained from plots of the fluorescence yields versus
the delay time between the two laser pulses. Radical decay have
always been exponential.
The influence of reaction (R4) on the total pseudo-first-order
rate constant has been investigated by running experiments
1.4–2.4
3.7
2.5
10400
12800
6600
0.013
0.4
0.7
0
0
.029
.041
13300
17100
25600
29400
41500
57500
29000
46000
56000
59000
99000
139000
53000
85000
120000
197000
0.7
1.5
with different precursor concentrations: a rate constant of k
ꢂ12
4
¼
0.090
0.145
0.326
0.619
0.038
0.061
3
cm s has been found, in agreement with
ꢂ1
(
earlier experiments in our laboratory on other alkoxy radi-
2 ꢀ 1) ꢁ 10
1.6
1.6
1
,14,15
cals.
The pseudo-first order unimolecular decomposition
has either been obtained by an extrapolation
to zero precursor concentration or, knowing the
absolute precursor concentration, by subtracting the corres-
1.5
1.0
rate constant k
3
331
1
3
st
of k
1.0
1.2
0
0
0
0
.092
.132
.333
.618
1
st
0.8
1.3
ponding fraction k
4
[2-C
4
9
H ONO] from k
3
. While the rela-
tive contribution of this bimolecular reaction to the total
pseudo-first order rate can approach 50% or more at the
lowest temperature and pressures, it can be neglected at the
three highest temperatures. Diffusion is, compared to the other
1.3
0.9
3
48
0.038
0
0
.086
.132
1.1
1.2
processes, slow under our experimental conditions (a few
ꢂ1
0.326
1.3
1
00 s at the lowest pressures) and has not been taken into
4
130
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 1 2 7 – 4 1 3 2
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4

View Article Online
where Q is the partition function of the active degrees of
freedom of the radical; o ¼ b LJ[M] is the effective collision
frequency where b is the collision efficiency, ZLJ is the
Our RRKM analysis allows us to predict an Arrhenius
expression for the decomposition rate constant at 1 bar nitro-
c
Z
c
gen total pressure. For this purpose, it is assumed that b
2b (He) and we obtained:
c
(N
2
) ¼
Lennard-Jones collision frequency and [M] is the total gas
c
concentration. k(E) is the microcanonical rate constant
1
2
ꢂ1
k3,1 bar N2 ¼ 6.7 ꢁ 10 exp (ꢂ47.7 kJ mol /RT)
at 290 K o T o 350 K
#
rot
Q
GðE ꢂ E0Þ
kðEÞ ¼
4
ꢂ1
.
leading to k3, 298 K, 1 bar N2 ¼ 2.9 ꢁ 10 s
Qrot hNðEÞ
It is of interest to compare these results, yielded by RRKM
analysis of our direct measurements of the dissociation rate
#
In this expression, Qrot and Qrot are the partition functions of
the adiabatic rotations of the transition state and of the
13
constant, with those obtained by Libuda et al. and those from
1
Meunier et al. from relative rate measurements based on the
2
2
-butoxy radical, respectively, h is the Planck constant,
competition of thermal decomposition and reaction with O . In
2
G(E ꢂ E ) is the number of energetically accessible states at
0
3 2
these studies, experimental values of the ratio k /k were
the transition state and N(E) is density of the states corres-
ponding to active degrees of freedom of the radical. The
radical is treated as a symmetric top and the external K-rotor,
associated with the smallest moment of inertia, is treated as an
active degree of freedom completely coupled to the vibrations.
The density of states of the radical and the sum of states of the
transition state are derived by taking the inverse Laplace
transform of the corresponding partition function using the
structural parameters (vibrational frequencies and moments of
inertia) obtained from DFT calculations. The quantum chem-
istry calculations were carried out using the GAUSSIAN98
1
obtained at 298 K or as a function of temperature. From
2
13
4
ꢂ1 13
these ratios one obtains for k3, 298 K, 1 bar N2 ¼ 2.8 ꢁ 10 s
4
ꢂ1 12
ꢂ14 ꢂ1 9
3
or 3.5 ꢁ 10 s
with k ¼ 1.2 ꢁ 10
cm s . The value of
Libuda et al. is thus in perfect agreement with our results
2
1
3
1
2
while the result of Meunier et al. is only slightly higher. Using
ꢂ14 ꢂ1
3
our value of k
in perfect agreement and Libuda et al. slightly slower. Then a
2
¼ 0.9 ꢁ 10
cm s one finds Meunier et al.
very good coherence is observed between all experimental
results (direct and relative measurement of k , direct measure-
ment of k ) and results of quantum calculations. Therefore we
2
3
2
1
recommend for dissociation of 2-butoxy radical under atmo-
4
program package. The density functional theory with the
Becke’s three-parameter hybrid functional of Lee, Yang and
ꢂ1
spheric conditions k3, 298 K, 1 bar N2 ¼ (2.9 ꢀ 0.8) ꢁ 10 s
.
1
3
2
2
Libuda et al. found some evidence in their experimental
results that a portion of the 2-butoxy radicals will sponta-
neously decompose after formation before being thermalized.
Parr, B3LYP, and the double-zeta basis set 6-31G(d,p) have
been used throughout (DFT-B3LYP/6-31G(d,p)).
All parameters used in RRKM calculations are listed in
Table 4. No data being available for the Lennard-Jones para-
meters of the 2-butoxy radical, those of the near species
2
5
Caralp and Forst have confirmed this possibility by statistical
RRKM master equation calculations. Our results do not
permit any conclusion on this point because (i) the radical
generation is different (photolysis versus chemical reaction) and
thus the exothermicity and energy distribution and (ii) we
follow the decrease of the radical while Libuda et al. measure
the final product distribution: a spontaneous decomposition on
the nanosecond time-scale would thus not be detected in our
experiment, but would influence very well the final product
distribution.
2
-butanol was evaluated from the critical constant of this
1
/3
species, using the Stiel and Thodos expression: s ¼ 0.785V
c
2
3
and e/k ¼ 0.897T
c
. These values are reported in Table 4 along
with the Lennard-Jones parameters of the buffer gas He and N
2
2
4
available in the literature.
Calculations of the falloff curves were first performed at the
four experimental temperatures using the DFT calculated
ꢂ1
value of the threshold energy (E0,DFT ¼ 48.9 kJ mol ). Then
Pressure and temperature dependencies of the 2-butoxy
dissociation rate constant can be presented using the conven-
E
at best all experimental results. The resulting parameters are
0
c
and the collisional efficiency b , were adjusted in order to fit
2
6
ꢂ1
tional Troe’s expression:
E
0
¼ 49.3 kJ mol , very close to the DFT value, and b
c
¼ 0.12
ꢂ2.5
(
T/291)
He as buffer gas, but its temperature dependency (T
. The value of b ¼ 0.11 at 298 K is reasonable for
2
ꢂ1
c
k ðTÞ½Mꢄ
0
Fcð1þ½log10
ðk ðTÞ½Mꢄ=k1ðTÞꢄ Þ
ꢂ2.5
0
kðTÞ ¼ 1
) is
þ k0ðTÞ½Mꢄ=k1ðTÞ
in order to provide a quick and convenient way of calculating
rate constant values as a function of pressure and temperature
in the range 0.03–1 bar and 290–350 K. In analogy to our study
on the t-butoxy radical the broadening factor F has been
c
fixed (Fc,3, He ¼ 0.87 ꢂ T/870 K) and the two parameters k
ꢂ1
slightly too high, a T dependency being currently observed.
This may be due to the intervention of a non-thermalised
fraction of the alkoxy radical in the low part of the pressure
range. This would result in enhanced measured rate constants
that slightly modified the shape of the falloff curves in this
pressure range.
1
0
(T)
Table 4 Structural parameters for the 2-butoxy radical calculated by DFT-B3LYP/6-31G(d,p) method
ꢂ1
Vibrationals wavenumbers/cm
d
2-C
4
H
9
O
101 211 221 247 366 436 470 774 798 935 943 998 1040 1063 1076 1168
1
3
195 1242 1308 1350 1408 1423 1495 1502 1509 1511 1524 2842 3034
045 3050 3074 3111 3123 3136 3140
#
2-C
4
H
9
O
74 158 166 189 257 343 491 626 837 849 865 895 1073 1097 1124 1006
1
3
228 1377 1404 1408 1481 1485 1489 1492 1505 1601 2880 3010 3039
089 3108 3128 3137 3146 3227
ꢂ1
Rotational constants/cm
d
2-C
-C
4
H
H
9
O
O
0.088
0.080
0.114
0.101
0.287
0.269
#
2
4
9
Lennard-Jones parameters
d
N
2
He
2.551
10.22
2-C
5.1
4 9
H O
˚
s/A
3.798
71.4
(
e/k)/K
481
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 1 2 7 – 4 1 3 2
4131

View Article Online
and k
equation on the experimental results at various temperature:
N
(T) have then been derived from the fitting of the above
References
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2
3
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´
3
ꢂ1
k
3,0,He ¼ 3.2 ꢁ 10ꢂ8 exp(ꢂ35.9 kJ molꢂ1/RT) cm s
k3,N ¼ 1.1 ꢁ 10 exp(ꢂ53.6 kJ molꢂ1/RT) s
1
4
ꢂ1
Chem. Phys., 2000, 2, 3765.
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Fig. 6 together with the experimental values.
For convenient use in tropospheric conditions, the results
4
5
6
7
8
2
from the RRKM calculation in N bath gas have been adjusted
to yield the three Troe parameters as a function of temperature:
keeping the temperature dependence for k3,N and for Fc,3 from
the experiment, the best fit leads to
2
003, 103, 4657.
9
0
W. Deng, C. Wang, D. Katz, G. Gawinski, A. Davis and
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3
1
2
607–2613.
This allows an extrapolation to the experimental conditions of
the only other direct determination of k : at 293 K and 50 mbar
3
11 H. Hein, A. Hoffmann and R. Zellner, Ber. Bunsen-Ges. Phys.
Chem., 1998, 102, 1840–1849.
12 N. Meunier, J. F. Doussin, E. Chevallier, R. Duran-Jolibois, B.
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1
1
3
ꢂ1
N2 Hein et al. found k3 ¼ (3.5 ꢀ 2) ꢁ 10
s
application of the above Troe parameters leads to k
while an
¼ 7.5 ꢁ
3
5, 4834–4839.
3
0 s under the same conditions. The agreement is not very
ꢂ1
1
good, probably due to difficulties in the indirect approach of
Hein et al. The attempt to explain the discrepancy with a lower
1
3
H. G. Libuda, O. Shestakov, J. Theloke and F. Zabel, Phys.
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Chem. Phys., 1999, 1, 2935.
´
collision efficiency of N
.24 to bring together the two values, which is far too low.
With a low, but still reasonable b (N
) ¼ 0.15, the calculation
¼ 5.8 ꢁ 10 s : giving an uncertainty of
2
requires a b
c
(N
2
) ¼ 0.07 instead of
0
1
5
P. Devolder, Ch. Fittschen, A. Frenzel, H. Hippler, G.
Poskrebyshev, F. Striebel and B. Viskolcz, Phys. Chem. Chem.
Phys., 1999, 1, 675.
c
ꢂ1
2
3
returns k3
,293 K,N
2
3
0% on this value, the lower limit of our value is in agreement
16 J.-M. Avez, PhD Thesis, University of Lille, France, 1978.
17 C. Wang, L. G. Shemesh, W. Deng, M. D. Lilien and T. S. Dibble,
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1
1
8
9
P. Tarte, J. Chem. Phys., 1952, 20, 1570.
Conclusion
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Kinet., 1999, 31(12), 860.
Program FALLOFF (1993) QCMP 119:W. Forst, QCPE Bull.,
In the present work the reactivity of 2-butoxy radicals has been
studied. Absolute rate constants for their reactions with NO,
O and their thermal decomposition have been measured as a
2
2
0
1
1
993, 13, 21.
2
M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A.
Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery Jr,
R. E. Stratman, J. C. Burant, S. Dapprich, J. M. Millam, A. D.
Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V.
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Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith,
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Pople, Gaussian98, Revision A.9, Gaussian, Inc., Pittsburgh PA,
function of temperature and He-pressure by the experimental
technique of laser photolysis/laser induced fluorescence. The
rate constants for the two bimolecular reactions have been
found in good agreement with earlier data. Our absolute
determination of the decomposition rate constant confirms
predictions based on theoretical methods. The falloff
behaviour has been interpreted by RRKM calculations. The
reaction has been found in the falloff region under atmospheric
conditions and Troe parameters with N
extracted for convenience using b (N ) ¼ 2b (He).
2
as bath gas are
c
2
c
1
998.
Acknowledgements
2
2
(a) A. D. J. Becke, J. Chem. Phys., 1993, 98, 5648; (b) C. Lee,
W. Yang and R. G. Parr, Phys. Rev. B, 1988, 37, 785.
23 F. M. Mourtis and F. H. A. Rummens, and references herein,
The Laboratoire de Physicochimie des Processus de Combus-
tion is ‘‘Unite Mixte de Recherche de l’Universite de Lille 1
et du CNRS’’. The Centre d’Etudes et de Recherches Lasers
et Applications (CERLA) is supported by the Ministere charge
de la Recherche, the Region Nord-Pas de Calais and the Fonds
Europeen de Developpement Economique des Regions.
Fincancial support was provided by the ‘‘Region Nord-Pas-
´
´
Can. J. Chem., 1977, 55, 3007.
R. C. Reid and T. K. Sherwood, The properties of gases and
liquids, McGraw-Hill, New York, 2nd edn., 1987.
2
4
`
´
´
2
2
5
6
F. Caralp and W. Forst, Phys. Chem. Chem. Phys., 2003, 5, 4653.
(a) T. Troe, Phys. Chem., 1979, 83, 114; (b) W. C. Gardiner and
J. Troe, in Combustion Chemistry, ed. W. C. Gardiner, Springer
Verlag, Berlin, 1984.
´
´
´
´
de-Calais’’.
4
132
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 4 1 2 7 – 4 1 3 2
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 4