A combined experimental and theoretical investigation of the reactions of 3-pentoxy radicals : Reaction with O2 and unimolecular decomposition

Article abstract of DOI:10.1524/zpch.2000.214.4.449

The reactions of 3-pentoxy radicals with O₂ and their unimolecular decomposition were investigated using time-resolved and simultaneous detection of NO₂ and OH in the laser flash initiated oxidation of bromopentane combined with numerical simulation of the experimentally obtained concentration-time profiles. NO₂ was monitored by cw-LIF, whereas OH was detected by laser long-path absorption at 308 nm. 3-pentoxy radicals were produced selectively by the excimer-laser photolysis of 3-bromopentane at 248 nm and subsequent reaction of the 3-pentyl radicals with O₂ in the presence of NO. All experiments were performed at a temperature of 293 ± 3 K and 50 mbar total pressure. The following rate coefficients for reaction with oxygen (k_o2) and for thermal decomposition (k_decomp) of 3-pentoxy radicals were obtained: k_o2 = (7.2±3.5)X 10^-15 cm³ molecule^-1 s^-1 and k_decomp = (5.0×2.5) × 10³ s^-1. In addition to the experimental investigation, the unimolecular reaction channels of 3-pentoxy radicals were also analyzed by a combined ab initio/RRKM treatment. From the ab initio calculations structures of the 3-pentoxy radical and its decomposition transition states as well as energy barriers were determined. This information was used to solve the J-independent Master Equation which allowed thermal decomposition rate coefficients to be determined. The calculated rate constants are in good agreement with those determined experimentally. by Oldenbourg Wissenschaftsverlag, Muenchen.

Full text of DOI:10.1524/zpch.2000.214.4.449

Zeitschrift für Physikalische Chemie, 214, 4, 449Ϫ471 (2000)
by Oldenbourg Wissenschaftsverlag, München

A Combined Experimental
and Theoretical Investigation of the Reactions
of 3-Pentoxy Radicals: Reaction with O2
and Unimolecular Decomposition
By H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
Institut für Physikalische Chemie, Universität GH Essen, D-45117 Essen, Germany
Dedicated to Prof. Dr. Dr. h. c. mult. H. Gg. Wagner
on the occasion of his 70th birthday
(Received December 13, 1999; accepted January 17, 2000)
Alkoxy Radicals / Unimolecular Reactions /
RRKM-Theory Tropospheric Chemistry
The reactions of 3-pentoxy radicals with O
investigated using time-resolved and simultaneous detection of NO
flash initiated oxidation of bromopentane combined with numerical simulation of the
experimentally obtained concentration-time profiles. NO was monitored by cw-LIF,
2
and their unimolecular decomposition were
2
and OH in the laser
2
whereas OH was detected by laser long-path absorption at 308 nm. 3-pentoxy radicals
were produced selectively by the excimer-laser photolysis of 3-bromopentane at 248 nm
and subsequent reaction of the 3-pentyl radicals with O
experiments were performed at a temperature of 293 Ϯ 3 K and 50 mbar total pressure.
The following rate coefficients for reaction with oxygen (k 2) and for thermal decom-
position (kdecomp) of 3-pentoxy radicals were obtained: k ϭ (7.2Ϯ3.5)ϫ10 cm mole-
2
in the presence of NO. All
O
Ϫ15
3
O
2
Ϫ1 Ϫ1
3
Ϫ1
cule
s
and kdecomp ϭ (5.0Ϯ2.5)ϫ10 s .
In addition to the experimental investigation, the unimolecular reaction channels of
-pentoxy radicals were also analyzed by a combined ab initio/RRKM treatment. From
3
the ab initio calculations structures of the 3-pentoxy radical and its decomposition tran-
sition states as well as energy barriers were determined. This information was used to
solve the J-independent Master Equation which allowed thermal decomposition rate coef-
ficients to be determined. The calculated rate constants are in good agreement with those
determined experimentally.
1. Introduction
VOCs (Volatile Organic Compounds) constitute a class of gaseous com-
pounds which are important to tropospheric chemistry. The degradation of
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H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
Fig. 1. Possible reactions of 3-pentoxy radicals under atmospheric conditions. The 1,4-
H-shift isomerisation is only shown to illustrate an isomerisation pathway. Under atmos-
pheric conditions it will not occur for 3-pentoxy.
VOCs not only affects the oxidation capacity of the troposphere but also
leads to the formation of ozone. The resulting photochemical smog episodes
are of great concern because ozone is toxic to both humans and animals as
well as to plants [1, 2]. Thus in the last decades oxidation reactions of
VOCs have been the subject of intensive research. This research activity
led to a fairly comprehensive understanding of several processes involved
in the oxidation mechanisms [3, 4]. However, there are still some reactions
that remained largely unstudied. The most important class of these are the
reactions of alkoxy radicals. Depending on their structure and environmen-
tal as well as experimental conditions, alkoxy radicals are known to have
four distinct competitive reaction pathways [5]: (i) reaction with O , yield-
2
ing an aldehyde or a ketone and HO , (ii) unimolecular decomposition,
2
forming an aldehyde and an alkyl radical, (iii) isomerisation via a n-mem-
bered transition state (1,(nϪ1)ϪHϪshift; n ϭ 5, 6), and (iv) recombination
reaction with NO . These reactions are shown schematically in Fig. 1 using
X
3
-pentoxy radicals as an example. Note, however, that 3-pentoxy radicals
can only isomerize via a 5-membered transition state which is kinetically
unfavourable. Hence isomerisation in Fig. 1 is only shown for the sake of
completeness. From Fig. 1 can be seen that while reactions with O and
2
NO are chain terminating (with respect to the 3-pentoxy radical), de-
X
composition (and isomerisation) lead to the formation of carbon centered
radicals. These radicals are further oxidized, i.e. they rapidly add O and
2
react with NO to form another alkoxy radical. In summary, the reactions of
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A Combined Experimental and Theoretical Investigation of the Reactions .. .
451
alkoxy radicals strongly influence the distribution and the yield of oxidation
products.
Although alkoxy radicals represent a major branching point in VOC
oxidation schemes, only few kinetic data are available from the literature.
Alkoxy radicals investigated so far comprise mostly methoxy, ethoxy, and
propoxy [3, 4]. The number of studies related to alkoxy radicals with more
than three C-atoms is extremely limited.
In the present study absolute rate coefficients for reaction of 3-pentoxy
radicals with O
6)), viz.
CH CH CH(O)CH CH ϩ O → 3-pentanone ϩ HO
2
(reaction (5)) and for unimolecular decomposition (reaction
(
3
2
2
3
2
2
(5)
(6)
CH CH CH(O)CH CH ϩ M → propanal ϩ C H ϩ M
3
2
2
3
2
5
were determined. (The numbering of reactions is according to that in Ta-
ble 1.)
The method applied is the time-resolved detection of NO and OH in
2
the pulse initiated oxidation of 3-pentyl radicals followed by numerical
simulations of the profiles measured. One major advantage of this technique
is that the radicals under investigation are produced selectively. This simpli-
fies the mechanism used for the simulations, enabling us to derive absolute
rate coefficients.
In addition to the experiments ab initio/RRKM calculations on the de-
composition reaction (6) were performed. These calculations represent yet
one more application of quantum mechanical theory based calculations on
the unimolecular reactivity of alkoxy radicals [8, 9].
2. Experimental
The experimental technique applied in this study is a combination of photo-
lytic generation of alkyl radicals in the presence of O /NO and simultaneous
2
detection of NO and OH concentration-time profiles. From these profiles
2
rate constants are derived by numerical simulations using a complete chemi-
cal mechanism.
In order to produce 3-pentoxy radicals selectively, 3-bromopentane,
CH CH CHBrCH CH , was photolyzed at 248 nm by an excimer-laser. This
3
2
2
3
process produces 3-pentyl radicals which subsequently add oxygen and re-
act with NO to form 3-pentoxy radicals, viz.
CH CH CHBrCH CH ϩ hν → CH CH CHCH CH ϩ Br
(1)
3
2
2
3
3
2
2
3
CH CH CHCH CH ϩ O → CH CH CH(O )CH CH
(2)
3
2
2
3
2
3
2
2
2
3
CH CH CH(O )CH CH ϩ NO → CH CH CH(O)CH CH ϩ NO (3)
3
2
2
2
3
3
2
2
3
2
1
4
With a typical 3-bromopentane concentration of 1.0ϫ10 molecules
Ϫ3
Ϫ2
cm and a typical laser fluence of approx. 30Ϫ40 mJ cm , the initial
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H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
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A Combined Experimental and Theoretical Investigation of the Reactions .. .
453
concentration of 3-pentyl radicals and of Br atoms was estimated to be of
1
1
Ϫ3
the order of 10 molecules cm . Whilst the 3-pentyl radicals react to form
-pentoxy radicals in a few milliseconds, the concentration of Br atoms was
too small to perturb the oxidation mechanism.
NO was monitored by cw-laser induced fluorescence (LIF) after exci-
3
2
ϩ
tation at 488 nm using the direct output of a 10 W Ar -laser. The excitation
beam was coupled into a White cell to maximize the excitation volume and
hence to decrease the detection limit which in this set-up was approx.
1
0
Ϫ3
1
ϫ10 molecules cm . After detection of the fluorescence light by a PMT,
the LIF signal was further processed by a lock-in amplifier and a digital
storage oscilloscope before being stored in a computer.
OH radicals were detected by laser long-path absorption in the centre
2
ϩ
2
of the Q (4) line of the A Σ ϪX Π(0,0) transition at 308.417 nm. The de-
1
ϩ
tection wavelength has been supplied by an Ar -laser pumped ring-dye las-
er. The dye laser was equipped with an SHG unit converting the funda-
mental wavelength of 616 nm into the UV wavelength required for OH
detection. Again mirrors in White configuration were used to maximize the
detection efficiency. The typical absorption path length of 40 m yielded a
9
Ϫ3
detection limit of approx. 1ϫ10 molecules cm . Details of this exper-
imental arrangement have been described elsewhere [8Ϫ10].
The reaction mixture consisted of O , NO and 3-bromopentane. The
2
flows and hence the concentrations of all reactants were controlled by mass
flow controllers. Oxygen and NO were directly taken as delivered by the
manufacturer (Messer-Griesheim). A 3-bromopentane gas mixture was pre-
pared by expanding 10Ϫ20 mbar of 3-bromopentane vapour into a 20 l-
storage bulb and filling the bulb to a total pressure of 1000 mbar with
N . 3-Bromopentane was used without further purification (Fluka, ϳ97%).
2
18 Ϫ3
Typical concentrations were: [O ] ϭ 1.2ϫ10 molecules cm , [NO] ϭ
2
1
4
Ϫ3
14
(
1.0Ϫ5.0)ϫ10 molecules cm , [3-bromopentane] ϭ 1.0ϫ10 molecules
Ϫ3
cm . All experiments have been carried out at 293Ϯ3 K and a total pres-
sure of 50 mbar.
3. Theoretical methods
Theoretical calculations have been performed on the unimolecular de-
composition reaction of the 3-pentoxy radical. In order to calculate the com-
plete temperature and pressure dependence of reaction (6) large scale ab
initio calculations in combination with a RRKM/Master-Equation (ME)
treatment to determine fall-off curves at arbitrary temperatures were per-
formed.
These calculations have been performed independently of the current
experimental study and are part of a comprehensive investigation of the
unimolecular reactions of various linear alkoxy radicals. In the course of
this study a theory based microscopic SAR was developed which clarifies
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54
H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
Fig. 2. Ab initio derived structures of the 3-pentoxy radical and the transition state of the
decomposition channel.
in a general manner the most important aspects of the unimolecular reaction
behaviour of alkoxy radicals [6, 7, 11].
3
.1 Ab initio calculations
In our calculations we have used MP2(Full)/6-31G(d) optimized geometries
to perform single point calculations. As demonstrated previously [6, 7] this
approach yields very satisfactory results when applied to various alkoxy
radicals. The calculated structures of 3-pentoxy at equilibrium and for the
transition state for decomposition by CϪC split are shown in Fig. 2. These
structures were verified by a subsequent vibrational analysis and the occur-
rence of the correct number of negative eigenvalues of the Hesse-matrix as
well as the number of imaginary vibrational frequencies. Apart from a mod-
est lengthening of the CϪC bond in combination with a shortening of the
CϪO bond which turns into a double bond of one of the products the
equilibrium and transition state geometries are rather similar. There exists a
second transition state for decomposition which is simply an optical isomer
to the one shown. This results from the fact, that the 3-pentoxy radical has
an additional plane of symmetry made up by the reactive CHO-group. With
regard to subsequent RRKM-calculations both decomposition transition
states must be considered as being equivalent.
In addition to the structures their energy difference has to be determined
with sufficient accuracy. In a previous study [6] we found that in case of
the unimolecular alkoxy radical reactions a slightly improved G2(MP2,
SVP) model chemistry is favorable over a couple of similar or more costly
methods and is suitable to deliver critical energy barriers (E ) of chemical
0
accuracy. The modifications applied to the G2(MP2,SVP) standard method
comprise the inclusion of a zero point energy correction at the MP2(Full)/
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A Combined Experimental and Theoretical Investigation of the Reactions .. .
455
Table 2. Molecular data of the 3-pentoxy radical and its decomposition transition state
as used for the RRKM/ME calculations. Structural parameters and frequencies (scaled by
1
.0214) were calculated at the MP2(Full)/6-31G(d) level of theory. The critical energy
barrier has been determined by a modified G2(PMP2,SVP) approach.
˚
CH
3
CH
2
CH(O)CH
2
CH
3
Equilibrium structure (req ϭ 1.529 A)
Ϫ1
Ϫ1
External rotational constants: adiabatic: B
2
ϭ 0.0637 cm , B ϭ 0.0559 cm
3
Ϫ1
active: B ϭ 0.2623 cm
1
Vibrational frequencies:
3289, 3288, 3261, 3261, 3224, 3217, 3177, 3176, 3171,
3
1
1
4
164, 3043, 1608, 1606, 1597, 1596, 1587, 1578, 1505,
499, 1442, 1417, 1415, 1355, 1331, 1300, 1249, 1169,
148, 1121, 1099, 1056, 1028, 998, 895, 828, 803, 501,
Ϫ1
72, 411, 321, 256, 225, 200, 107, 98 cm
˚
CH
3
CH
2
··· CH(O)CH
2
CH
3
Transition state structure (r† ϭ 2.029 A)
Ϫ1
Ϫ1
External rotational constants: adiabatic: B
2
ϭ 0.0588 cm , B ϭ 0.0519 cm
3
Ϫ1
active: B ϭ 0.2588 cm
1
Vibrational frequencies:
677 i, 3376, 3306, 3290, 3266, 3264, 3250, 3248, 3182,
3
1
1
4
177, 3162, 2970, 1752, 1603, 1596, 1589, 1575, 1572,
564, 1493, 1491, 1464, 1410, 1355, 1301, 1229, 1183,
149, 1100, 1071, 1009, 944, 930, 892, 843, 709, 536,
Ϫ1
68, 292, 269, 248, 198, 165, 89, 80 cm
Reaction path degeneracy:
Critical energy barrier:
Bathgas interaction:
2
E
0
ϭ 12.046 kcal/mol (incl. zero point energies)
Lennard-Jones-parameters
σ ϭ 5.003 A, ε ϭ 150.4 K ([M] ϭ N )
˚
2
6
-31G(d) level of theory and the use of spin-projected (PMP2) energies
which remove the largest spin-contaminant throughout the single point cal-
culations in all steps of these additive model chemistries. As a consequence,
we take into account the open shell nature of the molecular configurations
involved as well as the insufficient reliability of Hartree-Fock (HF) derived
structures and frequencies at positions far from equilibrium. Details of the
calculation together with a validation of the aforementioned methods have
been presented elsewhere [6].
3
.2 RRKM/ME calculations
The most important data derived from the ab initio calculation and which
are used in the statistical dynamical RRKM calculations are summarized in
Table 2. These data include scaled MP2-frequencies, the critical energy bar-
†
rier (E ) as well as rotational constants (B,B ) of the relevant molecular
0
configurations. Also included in Table 2 is the information on the interac-
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H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
Fig. 3. Detailed mechanism used for numerical simulations of the 3-pentoxy oxidation.
3
Ϫ1 Ϫ1
Second order rate coefficients in cm molecule
s
and first order rate coefficients in
Ϫ1
18
s
are taken from the literature. The major fluxes predicted for [O ] ϭ 1.2ϫ10 mol-
2
Ϫ3
14
Ϫ3
14
ecules cm , [NO] ϭ 1.0ϫ10 molecules cm , and [3-bromobutane] ϭ 1.0ϫ10 mol-
Ϫ3
ecules cm are indicated by the size of the arrows.
tion (Lennard-Jones potential) with the bath gas N . From these data we
2
calculate densities and sums of states to determine energy specific rate coef-
ficients k(E) for the decomposition reaction by statistical means and make
use of the standard RRKM expression, viz. [12, 13].
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E−E
0
Ϫ1
†
k(E) ϭ [hÆ(E)]
P (E
ϩ
)
Eq. (1)
͚
0
Because the reaction proceeds across a significant barrier as well as a tight
transition state along the intrinsic reaction path, the J-dependence of Eq. (1)
which in the general case has to be taken into account, has been neglected.
As a consequence, the best position of the diving surface, corresponding to
the point of no return in transition state theory, is sufficiently determined
by the saddlepoint on the potential energy surface as calculated by ab initio
methods. Because of the similar rotational constants of the equilibrium and
transition state configurations the release of additional rotational energy in
the reaction coordinate due to the conservation of angular momentum is
small. Nevertheless, the effect of conservation of angular momentum is†
taken into account correctly in the high pressure limit by the ratio B23/B23
of the rotational constants for the adiabatic external rotations.
In order to derive thermal rate coefficients we have made use of the
one-dimensional master equation [12], viz.
ϱ
λn(E) ϭ Ϫ ki(E) ϩ ω 0
͐
(PE′→En(E′) Ϫ PE→E′n(E))dE′
Eq. (2)
͚i
which relates the microscopic rate coefficients k (E) to thermal values of
i
ki(p,T). In the case of i ϭ 1, i.e. a single channel reaction the largest eigen-
value of Eq. (2) is identified as the thermal rate coefficient via λ ϭ Ϫkuni
which corresponds to the eigenfunction n(E) denoting the population of the
microcanonical ensemble with energy E. ω denotes the collision frequency
and PE→E′ is the probability of collisional energy transfer from a state with
internal energy E to one with energy E′. For PE→E′ we used a displaced
Gaussian arising from Biased Random Walk theory [14]. It was also used
to estimate the characteristics of this distribution such as the energy transfer
parameter ͗∆Edown͘ for this reaction with N as a collider. The details of the
2
complete treatment have been described elsewhere [7].
In the current treatment we are able to derive rate constants solely based
on theoretical calculations and without the use of experimental data. In fact
these calculations were carried out prior to experiment and hence must be
regarded as an independent and unbiased source for comparison of experi-
ment and theory. This is contrary to approaches where fitting reproduction
and/or extension of experimental data by theory is partly identified with a
theoretical validation.
4. Results
4
.1 Experimental investigations
4
.1.1 Sensitivity analysis
Sensitivity of the profiles towards k 2
O
The sensitivity of the concentration profiles for NO
2
and OH towards k 2
O
has been tested using the mechanism presented in Table 1 and in Fig. 3. For
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58
H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
Fig. 4. Computed variation of the NO
2
(top) and OH (bottom) profiles for different k
O
2
1
8
Ϫ3
14
Ϫ3
values. ([O ] ϭ 1.2ϫ10 molecules cm , [NO] ϭ 1.0ϫ10 molecules cm ).
2
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A Combined Experimental and Theoretical Investigation of the Reactions .. .
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Fig. 5. Computed sensitivity of the NO
left ordinate) and of the maximum OH concentration, [OH]max, (right ordinate) on k 2
The error bars shown represent a 10% uncertainty of the NO
2
concentration at infinite reaction time, [NO
2
]
O
ϱ
,
.
(
2
and OH detection systems.
18
Ϫ3
the sensitivity tests the concentrations [O ] ϭ 1.2ϫ10 molecules cm ,
14
2
1
4
Ϫ3
[
NO] ϭ 1.0ϫ10 molecules cm , and [3-bromopentane] ϭ 1.0ϫ10
Ϫ3
molecules cm , as used later in the experiments, were used. Since the
sensitivity tests also require rate constants for the reactions under investi-
Ϫ15
3
Ϫ1
3
Ϫ1
gation, the values kO2 ϭ 8ϫ10 cm s [15] and kdecomp ϭ 6.6ϫ10 s
this work, theoretical analysis) have been adopted.
The computed profiles including changes in temporal behavior as well
as absolute yields for different kO2 values are displayed in Fig. 4. This figure
reveals that significant changes upon a variation of k 2 only occur in the
(
O
OH profile, whereas changes in the NO profile are too small to be con-
2
sidered significant. This is because OH is formed in the reaction sequence
CH
3
CH
CH
ϩ NO → OH ϩ NO
for which the rate of formation of HO
contrast, the weak dependence of [NO
2
CH(O
2
)CH
2
CH
3
ϩ NO → CH
3
CH
2
CH(O)CH
2
CH
3
ϩ NO
2
(3)
(5)
CH
3
2
CH(O)CH
2
CH
3
ϩ O
2
→ 3-pentanone ϩ HO
2
HO
2
2
(13)
2
and hence OH depends on k 2
O
. In
2
](t) on k 2 is explained by its domi-
O
nant generation in reaction (3) rather than be the sequence of reactions (5)
and (13).
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H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
Fig. 6. Computed variation of the NO (top) and OH (bottom) profiles for different kdecomp
2
1
8
Ϫ3 14 Ϫ3
values. ([O ] ϭ 1.2ϫ10 molecules cm , [NO] ϭ 1.0ϫ10 molecules cm ).
2
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The main features of the profiles of Fig. 4, the NO
infinite reaction time, [NO , and the maximum OH concentration,
OH]max, are plotted as function of k 2 in Fig. 5. This figure allows to esti-
mate the relative error with which kO2 can be determined in the present
work, viz. ∆k 2/∆[NO and ∆k 2/∆[OH]max. The error bars shown in Fig. 5
2
concentration at
]
2 ϱ
[
O
O
2
]
ϱ
O
represent the 10% uncertainty of the experimental detection systems. The
variations occurring in the OH profile are large enough to be discernible in
an experimental OH profile (cf. Fig. 8). However, the relative sensitivity
Ϫ15
3
∆
k /∆[OH] , if kO2 is varied around its expected value of 8ϫ10 cm
max
Ϫ1 Ϫ1
O
2
molecule s , is of the order of the experimental uncertainties of the OH
detection system. Therefore, the accuracy of k 2 determined using this me-
O
thod is ϳ50%. As indicated by the behaviour of [NO ] , these data cannot
2
ϱ
be used to derive kO2 with sufficient accuracy.
Sensitivity of the profiles towards kdecomp
In the same manner as described above for k 2
towards kdecomp was tested. The resulting profiles are shown in Fig. 6. In
contrast to the k 2 variation, the sensitivity of the NO profile towards kdecomp
is much larger. Although some sensitivity also appears in the OH profile, it
O
, the sensitivity of the profiles
O
2
4
Ϫ1
cannot be considered sufficient if kdecomp is smaller than 1.0ϫ10 s , a
value expected from theory. As a consequence, only the NO profile can be
2
used to derive the rate coefficient kdecomp
.
The sensitivity of the NO profile towards the decomposition rate coef-
2
ficient can easily be understood. With the decomposition channel of 3-pen-
toxy (reaction (6))
CH CH CH(O)CH CH ϩ M → propanal ϩ C H ϩ M
(6)
3
2
2
3
2
5
becoming increasingly important, an additional NO
2
source opens and the
total amount of NO generated is enhanced. NO now originates jointly
2
2
from reactions (3), (9) and (11), where reaction (11) is followed by reaction
13), viz.
(
CH CH CH(O )CH CH ϩ NO → CH CH CH(O)CH CH ϩ NO (3)
3
2
2
2
3
3
2
2
3
2
CH CH O ϩ NO → CH CH O ϩ NO
(9)
(11)
(13)
3
2
2
3
2
2
CH CH O ϩ O → acetaldehyde ϩ HO
3
2
2
2
HO
2
ϩ NO → OH ϩ NO
2
.
As can be seen, in the case of decomposition of 3-pentoxy there are three
NO forming processes whereas in the course of the O reaction channel
there are only two NO/NO conversions. Therefore, the decomposition
channel must be expected to have a stronger impact on the NO profile than
2
2
2
2
the O
2
reaction.
The exact dependence of [NO ] and of [OH] upon kdecomp can be
2
ϱ
max
seen from Fig. 7. Since the sensitivity of [OH]max upon kdecomp is much
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H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
Fig. 7. Computed sensitivity of the NO
left ordinate) and of the maximum OH concentration, [OH]max, (right ordinate) on kdecomp
The error bars shown represent a 10% uncertainty of the NO and OH detection systems.
2
concentration at infinite reaction time, [NO
2
ϱ
] ,
(
.
2
smaller than the experimental uncertainties, no information about kdecomp can
be drawn from the OH profile. In the case of the NO profile, however, the
changes in [NO are significant and larger or equal to the experimental
uncertainties. We determine ∆[NO ] /∆k
2
]
2 ϱ
6
Ϫ3
2
ϱ
decomp
ϭ 4.9ϫ10 cm s which
with our experimental uncertainty transfers into an accuracy of ϳ50%.
4
.1.2 Determination of rate coefficients
After the sensitivity of the profiles towards the rate coefficients of interest
had been demonstrated, experiments with a variety of different reactant con-
centrations at 293 K and 50 mbar total pressure were carried out. Sub-
sequently, the experimentally obtained concentration profiles of OH and
NO were simulated with the FACSIMILE code using the mechanism pre-
2
sented in detail in Table 1. As opposed to the sensitivity analysis, in the
FACSIMILE simulations the rate constants for reaction of 3-pentoxy rad-
icals with O and for its unimolecular decomposition were varied until best
2
fits to the experimental profiles were obtained. A typical example for the
comparison between experiment and simulation is shown in Fig. 8. From
the best fits the following rate coefficients could be derived: k
ϭ
O
3
2
Ϫ15
3
Ϫ1 Ϫ1
Ϫ1
(7.2Ϯ3.5)ϫ10
cm molecule
s
and kdecomp ϭ (5.0Ϯ2.5)ϫ10 s .
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463
Fig. 8. Comparison between experimentally obtained and simulated OH and NO
2
concen-
tration-time profiles in the oxidation of 3-pentoxy radicals. k02 and kdecomp have been
18
varied until the best fit was obtained. Experimental conditions: [O ] ϭ 1.2ϫ10 mol-
2
Ϫ3
14
Ϫ3
14
ecules cm , [NO] ϭ 1.0ϫ10 molecules cm , and [3-bromopentane] ϭ 1.0ϫ10 mol-
Ϫ3
ecules cm , T ϭ 293 K, p ϭ 50 mbar, photolysis wavelength λ ϭ 248 nm.
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4
64
H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
Fig. 9. Ab initio/RRKM derived fall off curves for the decomposition of the 3-pentoxy
radical at different temperatures (M ϭ N ).
2
The error limits correspond to those derived in the detailed sensitivity analy-
sis as described in the previous section.
4
.2 Theoretical results
The quantum chemically derived molecular data in Table 2 have been used
as input data for the RRKM calculations. The existence of two equivalent
decomposition transition states is accounted for by an explicit reaction path
degeneracy of two. The resulting energy specific rate coefficients are used
in the subsequent solution of the master equation. These calculations have
been performed for nine temperatures in the range of 220 K to 300 K, ap-
propriate for the conditions found in the troposphere. In order to assure that
the low and high pressure limiting regions are encompassed, a pressure
7
range from 1 to 10 mbar was covered. Nevertheless, by the use of our
input data rate constants can easily be obtained at arbitrary temperatures
and pressures and for a wide variety of bath gases.
We have solved the master equation for sufficient discrete pressures to
produce fall-off curves of continuous shape. The results for the pressure
and temperature regions covered in our calculations are shown in Fig. 9.
In order to derive from these curves temperature dependent rate constant
expressions for the high and low pressure limiting regions we have adopted
both conventional and modified Arrhenius interpolations. For the high
pressure rate coefficient (220 K Յ T Յ 300 K) we obtain in conventional
Arrhenius form:
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465
1
4
Ϫ1
k
ϱ
(T) ϭ 1.18ϫ10 · exp(Ϫ6451 K/T) s .
Eq. (3)
14
Ϫ1
The preexponential factor in the order of 10 s is in agreement with struc-
tural and thermodynamic considerations since the entropy of activation is
‡
positive (∆S Ͼ0) but small. The corresponding analysis of the temperature
dependent low pressure rate constants yields an Arrhenius expression of
Ϫ6
3
Ϫ1 Ϫ1
k0(T) ϭ 2.31ϫ10 · exp(Ϫ5123 K/T) cm molecule s .
Eq. (4)
Numerically more accurate representations of our calculated rate con-
stants are obtained by the use of slightly modified Arrhenius expressions,
viz.
1
3
1.28
Ϫ1
k (T) ϭ 3.08ϫ10 · (T/300 K) · exp(Ϫ6095 K/T)s
Eq. (3′)
Eq. (4′)
ϱ
Ϫ3
Ϫ9.39
k
0
(T) ϭ 6.54ϫ10 · (T/300 K)
exp(Ϫ7526 K/T) cm molecule
3
Ϫ1 Ϫ1
·
s
The difference between our numerically derived data and the modified
Arrhenius form (Eqs. (3′) and (4′)) amounts to less than 2% in the “low”
(
220 K) and “high” (300 K) temperature limit covered by our calculation,
whereas a slightly larger deviation (Ͻ10%) is produced by the standard
Arrhenius form, especially in case of the low pressure limiting rate constant
(
Eq. (4)).
In addition we have fitted our “exact” fall-off curve at 300 K to the
semi-empirical Troe-formalism [16, 17],
k
k
0
[M]/k
ϱ
ϭ
F
Eq. (5)
k
ϱ
1 ϩ k [M]/k
0
ϱ
where the pressure dependent weak collision broadening factor F is param-
eterized by its central value Fcent in the middle of the fall-off curve at the
pressure where k [M] ϭ k :
0
ϱ
log(Fcent
)
log (F) ϭ
κ ϭ log(k
Eq. (6a)
2
1
ϩ {κ/(N Ϫ 0.14 κ)}
0
[M]/k ) Ϫ 0.4 Ϫ 0.67 log (Fcent
ϱ
)
Eq. (6b)
Eq. (6c)
N ϭ 0.75 Ϫ 1.27 log (Fcent).
From these fits a broadening parameter of about Fcent (300 K) ϭ 0.36 in the
center of the fall-off curve (pcent (300 K) ϭ 23 mbar) is determined. We do
not analyze the temperature dependence of Fcent because this form of ana-
lytical representation is only an approximation and errors of about 20% are
possible, partially masking the effect of Fcent(T).
In order to compare our theoretically derived rate coefficients with the
experimental data we have tabulated our calculated decomposition rate con-
stants arising from the full RRKM/ME treatment for pressures of 50 and
1
000 mbar in Table 3.
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66
H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
Table 3. Rate constants for the decomposition reaction of 3-pentoxy radicals calculated
at different temperatures for pressures of 50 and 1000 mbar using the RRKM/ME treat-
ment. All calculations assumed N
2
as collision partner.
Ϫ1
Ϫ1
T/K
k (50 mbar)/s
k (1000 mbar)/s
1
1
2
2
2
2
2
2
2
2
3
20
30
40
50
60
70
80
90
00
1.12ϫ101
1.78ϫ101
3.64ϫ10
6.15ϫ10
2
2
1.92ϫ102
1.06ϫ102
2.84ϫ10
5.46ϫ10
2
3
6.88ϫ103
1.42ϫ103
1.55ϫ10
3.44ϫ10
3
3
3.28ϫ103
7.78ϫ104
6.57ϫ10
1.21ϫ10
1.66ϫ10
4
4
3.32ϫ10
5. Discussion
5
.1 Rate coefficient k 2
O
The kinetics of the reaction of 3-pentoxy radicals with O
2
has never before
been directly investigated. Nevertheless structure activity relationships
SARs) are available which are commonly used to predict rate coefficients
for oxygen reactions of alkoxy radicals. Moreover, k 2 as derived in the
(
O
present work may be compared to rate constants of other secondary alkoxy
radicals which are available from the literature.
The most frequently adopted SARs for alkoxy radical reactions were
summarized by Atkinson [15] in his recent review paper. In this article two
different SARs for O reactions are suggested. The more simple one applies
2
to all secondary alkoxy radicals and does not account for differences be-
tween different organic substituents, viz.
Ϫ14
3
Ϫ1 Ϫ1
k 2
O
ϭ 1.5ϫ10 · exp(Ϫ200/T) cm molecule s .
Eq. (7)
Ϫ15
At T ϭ 293 K the rate coefficient kO2 derived from Eq. (7) is 7.6ϫ10
3
Ϫ1 Ϫ1
cm molecule s , in excellent agreement with kO2 obtained in the present
work.
The more extended SAR given by Atkinson [15] accounts for statistical
factors as well as for thermodynamical differences but is restricted to 300 K,
viz.
Ϫ19
3
Ϫ1 Ϫ1
k ϭ 4.0ϫ10 · n · exp(Ϫ0.28 · ∆H ) cm molecule s .
Eq. (8)
O
2
R
In here n is the number of abstractable H-atoms and ∆H
R
Ϫ14
is the enthalpy of
Ϫ1
3
Ϫ1
reaction given in kcal mol . Eq. (8) yields k ϭ 1.0ϫ10 cm molecule
O
2
Ϫ1
Ϫ1
s
at 300 K if the enthalpy of formation of ∆Hf,300(HO ) ϭ 14.6 kJ mol
2
as given in the most recent IUPAC recommendation [3] is used and the
Ϫ1
unknown enthalpies of formation of ∆Hf,300(3-pentoxy) ϭ Ϫ94 kJ mol
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A Combined Experimental and Theoretical Investigation of the Reactions .. .
467
Ϫ1
and ∆Hf,300(3-pentanone) ϭ Ϫ260 kJ mol are calculated using Benson’s
incremental method [18]. Again the agreement between prediction and
experiment is very satisfactory.
The agreement between k 2 predicted by Eqs. (7) and (8) and the exper-
O
imentally determined value is somewhat surprising since only a small num-
ber of alkoxy radicals were used to derive the SARs. Whereas Eq. (7) is
almost entirely based on kinetic data of ethoxy radicals, only methoxy,
ethoxy and 2-propoxy radicals were considered in the derivation of Eq. (8).
Alkoxy radicals for which absolute rate constants for reaction with O
2
are available are methoxy [19Ϫ25], ethoxy [23, 26, 27], 1- [28] and 2-
propoxy [28, 29], as well as 1- [9] and 2-butoxy [8]. The IUPAC re-
Ϫ1 Ϫ1
Ϫ15
3
commended [3] rate constants at 298 K are: 1.9ϫ10 cm molecule
s
Ϫ15
3
Ϫ1 Ϫ1
Ϫ15
3
for methoxy, 9.5ϫ10 cm molecule
s
for ethoxy, and 8ϫ10 cm
for 2-propoxy. Mund et al. [28] recently determined kO2
and (6.0Ϯ1.0)ϫ10 cm molecule
for 1-propoxy and 2-propoxy, respectively, using a direct LiF technique
Ϫ1 Ϫ1
molecule
s
ϭ
Ϫ15
3
Ϫ1 Ϫ1
Ϫ15
3
Ϫ1
(
8.7Ϯ1.4)ϫ10 cm molecule
s
Ϫ1
s
for the detection of the alkoxy radicals. In an independent study from our
group using the same technique as in the pesent work, Hein et al. measured
Ϫ14
3
Ϫ1 Ϫ1
kO2 ϭ (1.5Ϯ0.8)ϫ10
2
cm molecule
s
for 1-butoxy [9] and (6.5Ϯ
Ϫ15
3
Ϫ1 Ϫ1
.0)ϫ10 cm molecule
s
for 2-butoxy radicals [8], both at 298 K.
The available kinetic data on alkoxy radical reactions with O , therefore,
2
indicate that primary alkoxy radicals have rate coefficients of approximately
Ϫ14
3
Ϫ1 Ϫ1
1
ϫ10 cm molecule s , whereas rate constants of their secondary ana-
Ϫ15 3 Ϫ1 Ϫ1
logues tend to be in the range (7Ϯ1)ϫ10 cm molecule s . This reac-
tivity trend is fully confirmed by the findings of the present work. It needs
to be borne in mind though that the difference between the rate constants
of primary and secondary alkoxy radicals is relatively small. Therefore,
future work on even larger alkoxy radicals is needed to verify if the reactiv-
ity trend can be extrapolated to even larger alkoxy radicals.
5
.2 Rate coefficient kdecomp
A discussion of the decomposition rate coefficient kdecomp for 3-pentoxy rad-
icals is more complicated for several reasons. Firstly, the data base for al-
koxy radical decompositions is much poorer than that for the reaction with
O . To our knowledge only one study in which the reactions of 3-pentoxy
2
radicals have been investigated has been reported previously. Atkinson et
al. [30] investigated the products of the OH initiated gas phase oxidation of
1
8
n-pentane and derived a rate constant ratio kdecomp/k 2
O
of 3.3ϫ10 mol-
Ϫ3
ecule cm at 296Ϯ2 K and atmospheric pressure with an estimated overall
uncertainty of a factor of two. If k is assumed to be 7ϫ10 cm molecu-
le s , as indicated by the available kinetic data on secondary alkoxy rad-
icals, kdecomp can be calculated to be 2.3ϫ10 s . It needs to be borne in
Ϫ15
3
O
2
Ϫ1 Ϫ1
4
Ϫ1
mind though that because of the experimental procedure chosen by Atkin-
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68
H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
Table 4. Summary of available decomposition rate constants for 3-pentoxy radicals at
95Ϯ3 K.
2
decomp Ϫ1
/s
p/mbar
000
k
Method
Ref.
4
a
1
2.3ϫ10
RRS
[27]
This work
[9]
4
3
3
.3ϫ10
RRKM calculation
4
b
.0ϫ10
SAR
3
50
6.6ϫ10
5.0Ϯ2.5)ϫ10
RRKM calculation
LPO
This work
This work
3
c
(
a
Relative Rate Study. kdecomp determined relative to reaction with O
2
for which a
Ϫ15
3
Ϫ1 Ϫ1
rate constant of 7ϫ10 cm molecule
s
has been adopted.
b
c
Ϫ1
Structure Activity Relationship. E
a
(kcal mol ) ϭ 11.4ϩ0.36 · ∆Hdecomp and A ϭ
1
4
Ϫ1
4
ϫ10 s .
Laser Pulse initiated Oxidation.
son et al. [30] all types of alkoxy radicals (1-pentoxy, 2-pentoy, and 3-
pentoxy) are formed simultaneously and the result obtained must be con-
sidered as a weighted average of all individual O reactions and unimolecul-
2
ar processes, respectively.
The decomposition rate coefficient for 3-pentoxy can also be derived
from an SAR for the Arrhenius parameters as given by Atkinson in his
1
997 review and valid for atmospheric pressure [15], viz.
Ϫ1
E
a
ϭ A ϩ 0.36 · ∆Hdecomp/kcal mol
Eq. (9)
1
4
Ϫ1
A ϭ β ·2 ϫ 10 s .
Eq. (10)
In here the constant A takes into account the nature of the alkyl product,
Ϫ1
∆H
decomp is the enthalpy of the decomposition reaction in units of kcal mol ,
and β is the reaction path degeneracy. With the thermochemical data given
Ϫ1
elsewhere [3, 18], A ϭ 11.4 kcal mol , and β ϭ 2, k
can be estimated
decomp
4
Ϫ1
to be 3.0ϫ10 s at 298 K and atmospheric pressure, a factor of 6 larger
than the present experimental result at 50 mbar.
The values for kdecomp at 1000 mbar can be compared with the results of
4
Ϫ1
our ab initio/RRKM/ME calculations which indicate kdecomp ϭ 3.3ϫ10 s
at 300 K and 1000 mbar. Considering the uncertainties of the different
methods the agreement between experiment, SAR prediction, and RRKM
calculation is satisfactory. The same ab initio/RRKM treatment yields
3
Ϫ1
k
decomp ϭ 6.57ϫ10 s at 293 K and 50 mbar, the conditions of the exper-
imental investigation of the present work. Compared to the experimentally
3
Ϫ1
obtained value of (5.0Ϯ2.5)ϫ10 s the agreement is again very satisfac-
tory. The available rate coefficients for the decomposition of 3-pentoxy rad-
icals are listed in Table 4 and, combined with the theoretically determined
fall-off curves at 290 and 300 K, presented graphically in Fig. 10.
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A Combined Experimental and Theoretical Investigation of the Reactions .. .
469
Fig. 10. Fall-off curves for the decomposition of 3-pentoxy radicals obtained from ab
initio/RRKM calculations (T ϭ 290 and 300 K) and comparison with experimental rate
constants as derived in this work and previous studies.
6. Summary and conclusions
The rate coefficient for the reaction of 3-pentoxy radicals with O
2
O
(k 2) and
their unimolecular decomposition (kdecomp) were investigated by different
approaches. The experimental set-up utilizes the technique of time-resolved
and simultaneous detection of NO and OH with subsequent numerical
2
simulation of the experimentally obtained concentration profiles. From best
fits absolute values of rate coefficients were obtained which are in good
agreement with previous studies. Moreover, in the case of k , the kinetic
O
2
data measured in the present work confirms the reactivity trend for the
oxygen reactions of primary and secondary alkoxy radicals.
Theoretical calculations using a combined ab initio/RRKM/ME treat-
ment were applied to the decomposition reaction. Independent of experi-
ment, a rate constant was predicted which matches favourably with the
present experimental result and the known literature data and hence lends
credibility to the theoretical approach. This should also allow us to predict
decomposition rate constants at arbitrary temperatures and pressures.
In summary, the theoretical approach as well as the experimental me-
thods using the technique of laser pulse initiated oxidation combined with
numerical simulation of measured concentration-time profiles proved its
usefulness for investigations of alkoxy radical reactions.
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70
H. Hein, H. Somnitz, A. Hoffmann and R. Zellner
Acknowledgements
Financial support of the present work by BMBF within the German Tropo-
sphere Research Program (contract LT3/C.2-54799/35), Fonds der Chemi-
schen Industrie and by European Commission with the SARBVOC project
(contract ENV4-CT95-0031) is gratefully acknowledged.
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