HCO formation in the thermal unimolecular decomposition of glyoxal: Rotational and weak collision effects

Article abstract of DOI:10.1039/b809992h

The multi-channel thermal unimolecular decomposition of glyoxal was experimentally investigated in the temperature range 1106 K < T < 2320 K and at total densities of 1.7 × 10^-6 mol cm^-3 < ρ < 1.9 × 10^-5 mol cm^-3 by monitoring HCO (frequency modulation spectroscopy, FMS), (CHO)₂ (UV absorption), and H atom (atom resonance absorption spectroscopy, H-ARAS) concentration-time profiles behind shock waves. With a branching fraction of 48% at T = 2300 K and ρ = 1.6 × 10^-5 mol cm^-3, the so-far-neglected, energetically unfavourable HCO-forming decomposition channel, (CHO) ₂→ 2HCO, was found to play a crucial role and in fact represents the major decomposition pathway at high temperatures and high total densities. A theoretical analysis of the experimental results in terms of Rice-Ramsperger-Kassel-Marcus theory (RRKM), the simplified statistical adiabatic channel model (SACM), and an energy-grained master equation (ME) was based on input parameters from ab initio calculations (G3 and MP2/6-311G(d,p)) and literature data on branching ratios from collision-free photolysis experiments. A consistent description of the temperature and density dependences was achieved, revealing that both rotational and weak collision effects are reflected in the measured branching ratios. Overall, a product channel switching occurs with the CH₂O-forming channel, (CHO)₂→ CH₂O + CO, dominating at low temperatures/densities and the HCO-forming channel dominating at high temperatures/densities. Additionally, the so-called triple-whammy channel, (CHO)₂→ 2CO + H₂, significantly contributes to the total decomposition rate at intermediate temperatures/densities whereas the HCOH-forming pathway, (CHO)₂→ HCOH + CO, is predicted to be the least important one. The temperature and pressure dependences of the different decomposition channels are parametrized in terms of two-dimensional Chebyshev polynomials.

Full text of DOI:10.1039/b809992h

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PAPER
www.rsc.org/pccp | Physical Chemistry Chemical Physics
HCO formation in the thermal unimolecular decomposition of glyoxal:
rotational and weak collision effectsw
Gernot Friedrichs,*a Mark Colberg,a Johannes Dammeier,a Tobias Bentzb and
Matthias Olzmannb
Received 12th June 2008, Accepted 11th August 2008
First published as an Advance Article on the web 29th September 2008
DOI: 10.1039/b809992h
The multi-channel thermal unimolecular decomposition of glyoxal was experimentally investigated
in the temperature range 1106 K o T o 2320 K and at total densities of 1.7 ꢀ 10ꢁ6 mol cmꢁ3
r o 1.9 ꢀ 10ꢁ5 mol cmꢁ3 by monitoring HCO (frequency modulation spectroscopy, FMS),
(CHO)2 (UV absorption), and H atom (atom resonance absorption spectroscopy, H-ARAS)
o
concentration–time profiles behind shock waves. With a branching fraction of 48% at T = 2300 K
and r = 1.6 ꢀ 10ꢁ5 mol cmꢁ3, the so-far-neglected, energetically unfavourable HCO-forming
decomposition channel, (CHO)2 - 2HCO, was found to play a crucial role and in fact represents
the major decomposition pathway at high temperatures and high total densities. A theoretical
analysis of the experimental results in terms of Rice–Ramsperger–Kassel–Marcus theory (RRKM),
the simplified statistical adiabatic channel model (SACM), and an energy-grained master equation
(ME) was based on input parameters from ab initio calculations (G3 and MP2/6-311G(d,p)) and
literature data on branching ratios from collision-free photolysis experiments. A consistent
description of the temperature and density dependences was achieved, revealing that both rotational
and weak collision effects are reflected in the measured branching ratios. Overall, a product channel
switching occurs with the CH2O-forming channel, (CHO)2 - CH2O + CO, dominating at low
temperatures/densities and the HCO-forming channel dominating at high temperatures/densities.
Additionally, the so-called triple-whammy channel, (CHO)2 - 2CO + H2, significantly contributes
to the total decomposition rate at intermediate temperatures/densities whereas the HCOH-forming
pathway, (CHO)2 - HCOH + CO, is predicted to be the least important one. The temperature
and pressure dependences of the different decomposition channels are parametrized in terms of
two-dimensional Chebyshev polynomials.
different regimes of photodissociation can be distinguished.
1. Introduction
At wavelengths of 340 nm o l o 480 nm, glyoxal is
predominantly excited into the S1 state. At l 4 390 nm, the
initial excitation is followed by internal conversion to the
ground state S0 and the subsequent dissociation yields CH2O
(formaldehyde), CO, H2, and HCOH (hydroxymethylene) as
the main products.6 At l o 410 nm, the additional formation
of HCO radicals from S0 becomes energetically accessible.7
However, at still higher excitation energies, 340 nm o l o
390 nm, intersystem crossing into the T1 state starts to
compete with the S1 - S0 pathway resulting in an enhanced,
direct formation of HCO radicals on this triplet surface.7,8
Finally, coinciding with the onset of a broad and diffuse UV
absorption band at l o 340 nm, additional H atom forming
photolysis pathways open up and cause the HCO yield to
decrease again.8,9 For example, at l = 193 nm H atom
quantum yields up to f = 1.26 have been reported.10 In
contrast to the well-studied photochemistry, less attention was
paid to the thermal decomposition of glyoxal. Fig. 1 depicts
the energetics of the four lowest decomposition channels.
Energies of the reactants, transition states, and products are
specified relative to the energy of the trans-(CHO)2 isomer of
glyoxal. The values are based on the Gaussian-3 method12
(G3) and are mainly taken from the work of Koch et al.11 The
The recognition of the importance of glyoxal, (CHO)2, in both
tropospheric and combustion chemistry has led to a renewed
interest in the photochemistry and unimolecular reaction
dynamics of this prototype molecule. Glyoxal is an important
ring-cleavage product in the OH-initiated oxidation of
aromatic hydrocarbons in air1 and has been detected in
engine-2 and wood-combustion emissions.3 Its tropospheric
fate is dominated by an HCO-forming photolysis channel,4
which acts via the consecutive reaction HCO + O2 - HO2 +
CO as an effective source of atmospheric HO2. Many studies
have been performed to clarify the complex photophysics and
photochemistry of the strongly wavelength and pressure-
dependent glyoxal photolysis. A summary of the correspond-
ing literature can be found in the recent publication of Li
et al.5 Depending on the photolysis wavelength, several
a Institut fur Physikalische Chemie, Olshausenstr. 40,
¨
Christian-Albrechts-Universitat zu Kiel, 24098 Kiel, Germany.
¨
E-mail: friedrichs@phc.uni-kiel.de
¨
b Institut fur Physikalische Chemie, Universitat Karlsruhe (TH),
Kaiserstr. 12, 76128 Karlsruhe, Germany
¨
w Electronic supplementary information (ESI) available: Experimental
data and RRKM/SACM/ME input. See DOI: 10.1039/b809992h
ꢂc
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that no distinctive barrier exists for dissociation pathway (1d)
and thus the HCO-forming channel can be considered a simple
C–C bond fission. With E0 = 291 kJ molꢁ1, this channel lies
59 kJ molꢁ1 higher than the CH2O channel and therefore should
not play a significant role. Note that an alternative C–H bond
fission channel, (CHO)2 + M - CHO–CO + H + M, which is
suggested as being responsible for H atom formation observed
in the short wavelength photolysis experiments,5 can be
definitively ruled out for the thermal process due to its exceed-
ingly high dissociation energy of E0 = 370 kJ molꢁ1. However,
care has to be taken when predicting the dominating
decomposition channels based on the critical energies alone.
It is well known from the quite similar formaldehyde decom-
position system:
CH2O + M - H2 + CO + M
E0 = 344 kJ molꢁ1
(2a)
(2b)
Fig. 1 Potential-energy diagram based on G3 energies mainly taken
from Koch et al.11 The numbers in brackets are the scaled critical
energies used in our final kinetic model.
- H + HCO + M
E0 = 363 kJ molꢁ1
that the energetically high-lying bond fission channel with a
loose transition state can compete with the low-lying elimina-
tion channel (2a) with a tight transition state. For example, at
T = 2000 K and p = 1 bar, the loose channel (2b) contributes
15–20% to the total decomposition rate.17–19 This relatively
large contribution of the energetically unfavourable bond
fission channel can be understood in view of the generally
higher sum of states and the much stronger decrease of E0(J)
with increasing rotational excitation for loose transition states
(J is the total angular momentum quantum number). Of
course, with an energy difference of DE = 19 kJ molꢁ1
between channels (2a) and (2b), the effect is likely to be
observed much easier for formaldehyde decomposition than
for glyoxal decomposition [DE = 59 kJ molꢁ1 between
channels (1a) and (1d)]. Consequently, the HCO-forming
channel of glyoxal was assumed to be negligible in thermal
experiments.
cis-isomer of glyoxal is less stable by 20.5 kJ molꢁ1 and the low
isomerization barrier of 23 kJ molꢁ1 allows for a fast inter-
conversion and equilibration—at least at elevated tempera-
tures. Four decomposition channels termed CH2O channel
(1a), triple-whammy channel [(1b), TW], HCOH channel (1c),
and HCO channel (1d)have to be considered:
(CHO)2 + M - CH2O + CO +M
E0 = 232 kJ molꢁ1
(1a)
(1b)
(1c)
(1d)
- CO + CO + H2 + M
E0 = 256 kJ molꢁ1
- HCOH + CO + M
E0 = 254 kJ molꢁ1
- HCO + HCO + M
E0 = 291 kJ molꢁ1
Lowden20 studied the thermal decomposition of glyoxal at
temperatures of 703 K o T o 783 K in a static system, where
glyoxal concentration–time profiles were recorded by means of
mass spectrometry. Based on product analysis, a branching
ratio of 5.25 : 1 for channels (1a) : (1b) was reported. Other
data originating from Troe are mentioned in ref. 6. These
apparently still unpublished data are probably based on shock
tube experiments at temperatures above 1000 K and indicate
that channels (1a) and (1b) are of approximately equal im-
portance. A more comprehensive high-temperature shock tube
work was reported by Saito et al.21 These authors investigated
the temperature and density dependence of the unimolecular
glyoxal decomposition at temperatures of 1100 K o T o
1540 K and total densities of 2.8 ꢀ 10ꢁ6 mol cmꢁ3 o r o 3.4
ꢀ 10ꢁ5 mol cmꢁ3. (CHO)2 absorption and CO emission
signals were monitored simultaneously. The reaction was
found to be strongly density-dependent and detailed fall-off
curves were given. From auxiliary emission experiments at a
wavelength of 3.37 mm (CH emission), Saito et al.21 concluded
that essentially no CH2O is generated and that the triple-
whammy channel (1b) constitutes the main decomposition
route (490%). No indications were found for the involvement
According to theoretical studies of Schaefer III and co-
workers13,14 the unusual three-body fragmentation channel
(1b) proceeds through a planar transition state and the
reaction coordinate suggests a concerted formation of the
three product molecules CO, CO, and H2. More recent work
predicts a slightly twisted transition state but confirms the
three-body fragmentation character of the process.11,15 Since a
simultaneous and symmetric approach of three fragments, as
would be necessary for the reverse association reaction, is very
unlikely, we suspect a certain degree of asymmetry such that
the overall triple-whammy dissociation pathway can be
described by two fast consecutive dissociation steps as well.
For the purpose of this paper, however, a description of
channel (1b) as a three-body fragmentation or, alternatively,
as a two-body fragmentation with a subsequent fast disso-
ciation of a loosely bound intermediate, e.g. a van-der-Waals
complex OC–CO or H2–CO,16 does not make any difference.
At a first glance, reaction channels (1a)–(1c) exhibit the lowest
critical energies E0 and it is tempting to assume that these
channels dominate the thermal unimolecular decomposition.
High-level CASSCF ab initio calculations by Li et al.5 showed
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of the radical-forming channel (1d). From the thermal experi-
ments reported by Lowden, Troe, and Saito et al., it can be
concluded that reactions (1a) and (1b) are the only important
decomposition channels where the relative contributions of the
CH2O channel (dominating at low temperatures) and the
triple-whammy channel (dominating at high temperatures)
change with temperature. This apparent trend is also consis-
tent with the results of an ab initio study of Koch et al.11 These
authors explored the free-energy surface of glyoxal dissocia-
tion by means of G3 methodology. According to their calcula-
tions, the different vibrational structures of the corresponding
transition states give rise to an inversion of the free energy
barriers for channels (1a) and (1b) at high temperatures.
Unlike the HCO-forming channel, which was not considered
by Koch et al., the hydroxymethylene channel (1c) was treated in
some detail.11 At high temperatures, the free energy of activation
was found to be significantly higher for this channel than for
channels (1a) and (1b). Therefore, HCOH formation can be
assumed to be less important for the thermal reaction. In fact,
experimental evidence for the hydroxymethylene-forming channel
is scarce. Hepburn et al.6 studied the photochemistry of glyoxal
by means of molecular beam photofragment translational
We measured concentration–time profiles of HCO, (CHO)2,
and H atoms over a wide range of temperatures and in two
different total density ranges. It will be shown in this paper that
channel (1d) contributes with 440% to the total glyoxal
decomposition rate at T 4 2300 K. The generated HCO
radicals immediately decompose:
HCO + M - H + CO + M
(4)
and initiate a fast chain decomposition of glyoxal via reaction
(3). Hence the HCO-forming channel constitutes the most
important high-temperature decomposition channel of glyoxal.
2. Experimental
2.1 Shock tubes and gas mixtures
Two different stainless steel shock tubes were used, a 81 mm
inner diameter tube located in Kiel for HCO radical and
(CHO)2 detection10,23 and a 98.5 mm tube located in
Karlsruhe for H atom detection.24,25 Both shock tubes were
driven with hydrogen or hydrogen–nitrogen mixtures by
pressure bursting of thin aluminium diaphragms. Experimen-
tal conditions behind the shock waves were obtained from the
initial conditions of the test gas and the shock wave velocity,
which was measured by four fast piezo-electric sensors. Shock
wave parameters were calculated from a 1-dimensional frozen
chemistry code. For the Kiel experiments, high initial glyoxal
mole fractions of 40.5% were used and real gas effects had to
be taken into account. Additionally, a small independent
correction has been applied to allow for boundary layer
effects.10
spectroscopy. Glyoxal was excited at l = 440 nm (272 kJ molꢁ1
)
into the S1 state. Energetically allowed fragmentation channels
(after internal conversion into the S0 state) are reactions (1a), (1b)
and (1c). Translational energy distributions measured at the
masses m/z = 29 and 30 (CH2O or HCOH) showed a low
translational energy component, which could be attributed to
HCOH formation. HCOH fragments are formed with lower
translational energy because the enthalpy of formation of HCOH
is 218 kJ molꢁ1 higher than that of CH2O.22 The reported channel
ratios (1c) : (1b) : (1a) = 1 : 4 : 9 reflect the ratios of the corres-
Glyoxal was prepared by dehydration of the trimer dihy-
drate. A mixture of 15 g (1 equiv.) ((CHO)2)3ꢃ2H2O, 30 g
(3 equiv.) of phosphoric anhydrate (P2O5) and a small amount
of silica sand was slowly heated under vacuum to a tempera-
ture of 155 1C. Gaseous products were passed through an ice-
water-cooled trap to remove impurities. The product was
isolated in form of yellow crystals in a dry ice–isopropanol-
cooled trap and stored at liquid–nitrogen temperature.
No H2O or CO2 impurities could be detected by FTIR
spectroscopy.
ponding specific rate constants at
E E
272 kJ molꢁ1
(22 730 cmꢁ1). This ratio corresponds to a branching fraction of
merely 7% for reaction (1c) and confirms the minor role
of HCOH formation for the overall decomposition process.
In recent shock tube studies on high-temperature HCO
kinetics, we employed the 193 nm photolysis of glyoxal as
an efficient HCO source.10,23 HCO concentration–time profiles
were followed by means of frequency modulation spectro-
scopy. The photolysis generates H atoms and HCO radicals in
high yields, where the H atoms are nearly quantitatively
converted to HCO by a fast subsequent reaction with excess
glyoxal:
Gas mixtures of glyoxal in Ar were prepared manometri-
cally in stainless steel mixing vessels and were used within a
few days after preparation. No noticeable change in the
experimental signals for HCO, (CHO)2 and H atoms was
discernible with increasing mixture age. For the high-
concentration experiments, mixtures of typically 2–3% were
further diluted with Ar by using a flow system with calibrated
flow controllers. Low concentration mixtures used for the H
atom experiments with glyoxal mole fractionsof 7.4–39.9 ppm
were prepared directly in a large 100 dm3 mixing vessel and
were allowed to homogenize for at least 20 h. Prior to each
experiment, the shock tubes were evacuated to pressures below
5 ꢀ 10ꢁ6 mbar, and the cleanliness of the Hatom detection
tube was regularly tested by performing shots with neat argon
at temperatures above 2000 K. To avoid concentration errors
due to wall adsorption, the shock tube was flushed once before
each experiment with the particular reaction mixture
(H-ARAS experiments) or the reaction mixture was slowly
H + (CHO)2 - H2 + HCO + CO
(3)
Initially formed (CHO)CO rapidly decomposes via (CHO)CO
- HCO + CO.10 In these experiments, the upper temperature
limit (E1050 K) was governed by the onset of the thermal
decomposition of glyoxal. Surprisingly, a direct, obviously
thermal formation of HCO radicals was observed behind the
shock waves causing distinctive background signals in the HCO
concentration–time profiles.23 Preliminary experiments at high-
er temperatures clearly showed that reaction (1d) significantly
contributes to the total decomposition of glyoxal. This unex-
pected result in view of the large energy difference (59 kJ molꢁ1
)
between the threshold energies was our motivation to investi-
gate the so-far-ignored role of the HCO-forming decomposition
channel in the thermal unimolecular decomposition of glyoxal.
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pumped through the tube for about 3 min (HCO and (CHO)2
experiments). The purity of the gases and chemicals used were
spectrum reported by Volkamer et al.30 With minimum
detectable (CHO)2 concentrations of approximately 1.5 ꢀ
10ꢁ8 mol cmꢁ3, the detection limit was 75 times higher than
for HCO.
Ar: 99.999% (99.9999% for
H
atom detection),
H2–N2: 499.8% (as driver gas), and glyoxal trimeric
dihydrate: 497%.
H atoms. H atoms were detected by means of atom resonance
absorption spectroscopy (ARAS) at the Lyman-a line at l =
121.6 nm (H-ARAS) with a time resolution of 20–30 ms. The
vacuum ultraviolet (VUV) radiation was produced by a
microwave-discharge lamp using a gas mixture of B1% hydro-
gen in helium at a constant pressure of p = 7 mbar. The VUV
light was transmitted via MgF2 windows through the shock tube
and was detected by a combination of a monochromator (Acton
2.2 Quantitative detection
HCO radicals. HCO was detected by means of frequency
modulation (FM) spectroscopy. FM spectroscopy has been
proven to provide outstanding sensitivity for the time-resolved
detection of small radicals behind shock waves.26 A detailed
description of the FM setup used can be found elsewhere.10,27,28
Briefly, the output of a Nd : YVO4 solid-state laser (Coherent
Verdi-V10) pumped cw ring-dye laser (Coherent 899-21) was
modulated at a frequency of 1.0 GHz using a resonant electro-
optic modulator (New Focus 4421). The modulation depth was
set to a modulation index M = 1.6 and the demodulation phase
angle was chosen by a voltage-controlled phase shifter (Lorch)
to result in a purely absorption-induced signal. The intensity of
the demodulated FM signal, IFM, is proportional to the
concentration c of the absorbing species according to
Research VM 504) with
a solar-blind photomultiplier
(Hamamatsu R1259). Calibration experiments using a well-
characterized H atom source under similar conditions (T and
p) as in the experiments were performed in order to be able to
convert the non-Beer–Lambert absorption signals into H atom
concentration-time profiles. We have chosen a procedure based
on N2O–H2 mixtures31,32 and refer for details to a recent
publication from our laboratory.25 With a minimum detectable
H atom concentration of approximately 5 ꢀ 10ꢁ13 mol cmꢁ3
,
the detection limit was 40 times lower than for HCO. At too
high H atom concentrations, [H] 4 1 ꢀ 10ꢁ10 mol cmꢁ3, the
H-ARAS signal became saturated and the determined H atom
concentrations were less reliable. Consequently, the initial
glyoxal concentrations were kept low enough to avoid satura-
tion. Based on the uncertainties associated with the calibration
procedure, the relative uncertainty of the determined H
concentrations are estimated to be 30%.
I0
IFM
¼
DfsclG
ðE1Þ
2
Here, I0 is the total light intensity, s the narrow-bandwidth
absorption cross section, l the absorption path length and G the
electronic gain of the FM spectrometer. Whereas Df, the FM
factor, was calculated from linewidth data, the gain factor G was
determined experimentally.10 HCO radicals were detected at a
wavelength of
l
=
614.752 nm, corresponding to the
(0,90,0)
overlapping Q(6)P(1) line of the A2A00
’
’
2.3 Modelling
X2A0(0,01,0) transition. Absolute concentrations were calculated
on the basis of accurate line shape data and differential absorp-
tion cross sections determined previously for the Q(9)P(2) line at
l = 614.872 nm.28 The absorption cross section used is in
excellent agreement (ꢄ2%) with recent accurate cavity-ring-
down data from Flad et al.29 Allowance was made for a small
pressure broadening effect according to an estimated pressure-
Numerical simulations. For all numerical simulations the
Chemkin-II package33 was used. Rate constants for reverse
reactions were calculated automatically on the basis of
thermodynamic data.34 Starting with the experimental condi-
tions calculated from the shock tube code, simulations were
performed under the constraint of a constant volume such that
the pressure and temperature were allowed to slightly increase
over the reaction time. At the highest initial glyoxal concen-
trations used, the change of the temperature was 3–4%. For
sensitivity analysis, the sensitivity coefficient s(i,j,t) for
reaction i of species j at time t was normalized with respect
to the maximum concentration cmax of the species j over the
broadening coefficient Dnp = 2.0 ꢀ (T/298 K)ꢁ0.75 GHz barꢁ1
.
The relative error of the determined HCO concentrations
can be estimated to be r20% on the basis of the uncertainty
associated with the temperature dependence of the absorption
cross section, the FM factor, and the gain factor. With the
time resolution of the FM spectrometer set to approximately
1 ms, the minimum detectable HCO concentration was
approximately 2 ꢀ 10ꢁ10 mol cmꢁ3 at T = 1300 K.
time history, s(i,j,t) = (qc(j,t)/qln ki)/cmax
.
Statistical rate theory. The overall rate constant of the
glyoxal decomposition, k(T,p), was computed as the lowest
(CHO)2. Glyoxal was detected by means of UV absorption at
a wavelength of l = 440 nm. The longpass-filtered (4345 nm)
output of a mercury high-pressure lamp was confined by
two 1.5 mm wide slits placed in front of and behind the shock
tube. In this way, an experimental time resolution of
approximately 3 ms was achieved. The light was detected
by a monochromator–photomultiplier combination (Acton
Research VM 502 and SMT MEA30FV6DA) with a spectral
resolution of Dl = 2 nm. The measured room-temperature
absorption cross section of s = 8.3 ꢀ 104 cm2 molꢁ1 is
in very good agreement with a literature value of s = 7.8 ꢀ
104 cm2 molꢁ1 deduced for Dl = 2 nm from a high-resolution
eigenvalue of the matrix
equation:35–37
J of a four-channel master
[o(I ꢁ P) + K]NS ꢅ JNS = 0
(E2)
Here, o denotes the Lennard-Jones collision frequency, I is the
unit matrix, P is the matrix of the collisional transition
probabilities P(,E), and K is a diagonal matrix containing
the sum of the specific rate constants k(E,J) = k1a(E,J) +
k1b(E,J) + k1c(E,J) + k1d(E,J). The vector NS represents the
steady-state population ns(E;T,p) of glyoxal at a given
temperature and pressure. The specific rate constants of
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reactions (1a), (1b) and (1c) were obtained from RRKM
theory35–39 and those of reaction (1d) from the statistical
adiabatic channel model (SACM):35–37,40–42
however, that the actual choice (harmonic oscillator/free
rotator) is not important because the interpolated eigenvalue
spectrum of this disappearing oscillator is extremely product
(rotator)-like and its anharmonicity does hardly influence the
number of open reaction channels. Nevertheless, a hindered
internal rotator treatment is important for the reactant density
of states, which is increased by a factor of B2 over the relevant
energy range.
WiðE0 ꢁ E0ðiÞðJÞ; JÞ
kiðE; JÞ ¼
ðE3Þ
hrðE; JÞ
with Wi(E ꢁ E0(i)(J),J) being the sum of states of the transition
state for i = 1a, 1b and 1c and the number of open adiabatic
reaction channels for i = 1d; r(E,J) is the density of states of
glyoxal. The thermal rate constant for a specific channel then
follows by averaging ki(E,J) over the normalized steady-state
distribution n˜S:
Rotational constants and harmonic vibrational wavenumbers,
which were slightly scaled by a factor of 0.9496 according to
Scott and Radom,47 were adopted from the MP2/6-311G(d,p)
calculations reported by Li et al.15 As a starting point, G3
energies were taken from the work of Koch et al.11 The
Gaussian-3 compound method12 is known to yield reliable
energy barriers and reaction energies. A Table with all
parameters is given in the ESI.w
1
Z
kiðT; pÞ ¼
kiðE; hJiTÞ n~SðE; T; pÞdE
ðE4Þ
0
where the thermal average of the total angular momentum
quantum number for glyoxal, hJTi, was used to approximately
account for the angular momentum dependence of ki(E,J).
In our practical calculations, we set
For the transition probabilities in eqn (E2), a stepladder model
obeying detailed balancing was used.35,36 The step size DESL
(corresponding to the average energy transferred per down
collision, hDEdowni) was treated as an adjustable parameter.
Eqn (E2) is set up with a bin size of 10 cmꢁ1, and the lowest
eigenvalue and the associated eigenvector were determined by
standard routines for tridiagonal matrices.48 Energy zero is the
rovibrational ground state of glyoxal. More technical details of
our master equation approach can be found in ref. 49.
WiðE ꢁ E0ðiÞðhJiTÞ; J ¼ 70Þ
kiðE; hJiTÞ ¼
ðE5Þ
hrðE; J ¼ 70Þ
that is, we calculated all numbers and densities of states for
J = 70, which is the average J for glyoxal at T E 1400 K
corresponding to the middle of our experimental temperature
range. In this way, the J dependence of ki(E,J) is reduced to the J
dependence of the threshold energy E0(i)(J) (see Table 1), which is
by far the dominating effect. The approximation Wi(E,J)/r(E,J)
E Wi(E,J = 70)/r(E,J = 70) holds with an accuracy of better
than 6% at the relevant energies and for varying J in our range
from J = hJi800 K = 54 to J = hJi2500 K = 96.
3. Results and discussion
Two independent rate constant data sets were obtained—the
first one based on measured HCO and (CHO)2 profiles and the
other one based on the H atom profiles. Moreover, for both
data sets the experiments were conducted at two, by a factor of
5 different total density ranges of r E 1.6 ꢀ 10ꢁ5 mol cmꢁ3
and r E 3.2 ꢀ 10ꢁ6 mol cmꢁ3. A previously validated high-
temperature mechanism including HCO, formaldehyde and
glyoxal chemistry was used to numerically simulate the experi-
mental concentration-time profiles.10,17,23 The most important
reactions are summarized in Table 2. Additionally, the GRI
Mech 3.0 natural gas mechanism50 has been applied as a base
mechanism in order to include potential secondary chemistry.
The mechanism is capable of a reliable prediction of almost all
formaldehyde pyrolysis literature data, including CH2O, CO,
and H atom measurements at temperatures of 1200–3200 K,
with mole fractions of 7 ppm to 5% formaldehyde, and
pressures up to 15 bar.17 The rate expression of the important
reaction (3), H + (CHO)2, was taken from our previous study
on glyoxal photolysis.10
The sums of states were calculated by a direct counting
procedure42–44 in the rigid rotor/harmonic oscillator (RRHO)
approximation. The number of open adiabatic reaction
channels was determined from the simplified statistical adia-
batic channel model,40–42 where channel states are interpolated
between reactant and product eigenvalues by using a simple
exponential switch function with
a standard parameter
a/b = 0.5.45 The correlation scheme of conserved and
disappearing oscillators is given in the ESI.w The density of
states of glyoxal was also directly counted in the RRHO
approximation except for the hindered internal rotator, whose
energy levels were determined by solving the one-dimensional
Schrodinger equation with a torsional potential obtained from
¨
quantum chemical calculations at the MP2/6-311G(d,p) level.
More details are given in ref. 46, and a representation of the
torsional potential as well as a Table collecting the eigenvalues
can be found in the ESI.w
3.1 HCO profiles
In the SACM interpolation for W1d(E,J), this hindered
internal rotator was assumed to be harmonic. We note,
HCO concentration–time profiles were measured at tempera-
tures of 1106 K o T o 1630 K at total densities of r E 1.4 ꢀ
Table 1 Temperature dependence of effective critical energies. hJiT is the thermally averaged rotational quantum number
T/K
hJiT
E0(1a)(hJiT)/cmꢁ1
E0(1b)(hJiT)/cmꢁ1
E0(1c)(hJiT)/cmꢁ1
E0(1d)(hJiT)/cmꢁ1
(G3)
(Scaled)
800
1500
2500
0
0
54
74
96
19 376
19 376
19 373
19 370
19 367
21 370
20 500
20 393
20 300
20 165
21 232
20 500
20 447
20 400
20 332
24 319
24 258
23 857
23 512
23 015
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Table 2 Important reactions. Rate constants are given as ki = ATn exp(ꢁEa/RT) (units are cm, mol, K, s and kJ). Additionally, the GRI Mech
3.050 mechanism has been used as a base mechanism in order to include potential secondary chemistry
No.
Reaction
A
n
Ea
Ref.
(1a)
(1b)
(1c)
(1d)
(2a)
(2b)
(3)
(4)
(5)
(6)
(7)
(CHO)2(+M)
" CH2O + CO(+M)
" CO + CO + H2(+M)
" HCOH + CO(+M)
" HCO + HCO(+M)
" H2 + CO + M
" H + HCO + M
" H2 + HCO + CO
" H + CO + M
" H2 + CO
This work, see Table 3
This work, see Table 3
This work, see Table 3
This work, see Table 3
ꢁ6.1
CH2O + M
4.4 ꢀ 1038
1.3 ꢀ 1036
5.4 ꢀ 1013
4.0 ꢀ 1013
1.1 ꢀ 1014
2.7 ꢀ 1013
5.7 ꢀ 107
1.4 ꢀ 1012
393
393
18
19
19
10
28
ꢁ5.5
H + (CHO)2
HCO + M
HCO + H
HCO + HCO
H + CH2O
HCO +
65
17
" CH2O + CO
" H2 + HCO
- Products
17, 51
52, 53
10a
1.9
11.5
18
(8)
(CHO)2
a
Estimated.
Table 3 Parametrization of rate constant data in the temperature range 800 K o T o 2500 K and the pressure range 1 mbar o p o 100 bar.
Extended Arrhenius parameters, k = ATbexp(ꢁEa/RT), and [4 ꢀ 4] Chebyshev polynomial coefficients anm.a All rate constants are given in units of sꢁ1
Rate constant
r/mol cmꢁ3
A/sꢁ1
b
Ea/kJ molꢁ1
kN,total
ktotal
k1a+1b+1c
k1d
ktotal
k1a+1b+1c
k1d
N
6.15 ꢀ 1015
6.11 ꢀ 1047
1.15 ꢀ 1052
2.85 ꢀ 1053
1.22 ꢀ 1049
1.38 ꢀ 1052
2.39 ꢀ 1050
263
310
318
352
305
312
343
1.6 ꢀ 10ꢁ5
1.6 ꢀ 10ꢁ5
1.6 ꢀ 10ꢁ5
3.2 ꢀ 10ꢁ6
3.2 ꢀ 10ꢁ6
3.2 ꢀ 10ꢁ6
ꢁ10.0
ꢁ11.3
ꢁ11.5
ꢁ10.6
ꢁ11.5
ꢁ10.9
a
anm
ꢁ1.8226 ꢀꢁ120ꢁ1
1.820 ꢀ 10
1.643 ꢀ 10ꢁ2
ꢁ6.206 ꢀ 10ꢁ3
7.470 ꢀ 10ꢁ3
3.457 ꢀ 10ꢁ3
4.544 ꢀ 10ꢁ2
ꢁ4.904 ꢀ 10ꢁ3
9.066 ꢀ 10ꢁ3
2.635 ꢀ 10ꢁ3
4.624 ꢀ 10ꢁ2
ꢁ4.933 ꢀ 10ꢁ3
9.274 ꢀ 10ꢁ3
2.765 ꢀ 10ꢁ3
1.412 ꢀ 10ꢁ1
ꢁ1.119 ꢀ 10ꢁ2
4.738 ꢀ 10ꢁ3
1.716 ꢀ 10ꢁ3
˜
log k1a(T,p˜)
2.448
3.971
1.014
6.341 ꢀ 10ꢁ1
4.486 ꢀ 10ꢁ2
ꢁ2.928 ꢀ 10ꢁ2
1.564
ꢁ3.926 ꢀ 10ꢁ1
ꢁ9.117 ꢀ 10ꢁ2
1.934
2.783 ꢀ 10ꢁ2
9.074 ꢀ 10ꢁ4
ꢁ3.222 ꢀ 10ꢁ1
5.283 ꢀ 10ꢁ2
3.032 ꢀ 10ꢁ2
5.520 ꢀ 10ꢁ4
ꢁ3.101 ꢀ 10ꢁ1
3.840 ꢀ 10ꢁ2
2.811 ꢀ 10ꢁ2
8.627 ꢀ 10ꢁ4
ꢁ1.080
˜
log k1b(T,p˜)
4.196
6.773 ꢀ 10ꢁ1
1.327 ꢀ 10ꢁ2
ꢁ3.386 ꢀ 10ꢁ2
1.456
ꢁ4.010 ꢀ 10ꢁ1
ꢁ8.817 ꢀ 10ꢁ2
1.358
˜
log k1c(T,p˜)
4.123
6.779 ꢀ 10ꢁ1
2.746 ꢀ 10ꢁ2
ꢁ3.268 ꢀ 10ꢁ2
3.936
ꢁ4.105 ꢀ 10ꢁ1
ꢁ8.727 ꢀ 10ꢁ2
4.903 ꢀ 10ꢁ1
4.818
˜
log k1d(T,p˜)
4.349 ꢀ 10ꢁ1
ꢁ7.146 ꢀ 10ꢁ2
ꢁ5.084 ꢀ 10ꢁ2
1.747 ꢀ 10ꢁ1
4.338 ꢀ 10ꢁ2
7.064 ꢀ 10ꢁ3
ꢁ3.698 ꢀ 10ꢁ1
ꢁ6.307 ꢀ 10ꢁ2
P
P
a
N M
n=1 m=1
˜
˜
log k (T,p˜) =
anmfn(T)fm(p˜); N = 4 and M = 4 denote the number of basis functions along the normalized temperature and
pressure axis respectively. The sixteen anm values are listed in the order of a11,a12,. . .,a1M,a21,. . .,aNM. fi(x) = cos((i ꢁ 1)cosꢁ1(x)) with i = 1,2,3,4;
ꢁ1
ꢁ1
ꢁ1
T = (2T ꢁ Tmin ꢁ Tmaxꢁ1)/(Tmax ꢁ Tminꢁ1); p˜ = (2 log p ꢁ log pmin ꢁ log pmax)/(log pmax ꢁ log pmin). Tmin = 800 K, Tmax = 2500 K,
˜
pmin = 9.87 ꢀ 10ꢁ4 atm, and pmax = 98.7 atm. A Chemkin58 input matrix is given in the ESI.w
10ꢁ5 mol cmꢁ3 and r E 2.2 ꢀ 10ꢁ6 mol cmꢁ3 respectively.
High initial mole fractions of 1–2% glyoxal in Ar had to be
used to generate detectable HCO concentration levels. Fig. 2
illustrates two experimental HCO profiles at temperatures of
T = 1282 and 1440 K. Following a strong schlieren signal at
t = 0, a fast direct formation of HCO radicals is observed. The
HCO profiles were fitted by adjusting the rate constants of the
glyoxal decomposition channels. Since the channel branching
ratio between the molecular channels (1a) + (1b) + (1c) and
the radical channel (1d) is not known, we performed two
separate evaluations assuming (i) channels (1a) and (1d) as the
sole decomposition channels (scenario I) or (ii) channels (1b)
and (1d) as the sole decomposition channels (scenario II). As it
is elucidated in the following, scenarios I and II formally yield
the upper and lower limit, respectively, for the sum of the rate
constants of the molecular channels, that is, kI ꢅ k1a(I) 4
k1a+1b+1c 4 kII ꢅ k1b(II).
In the lower plot of Fig. 2, the sensitivity analysis of the
T = 1440 K experiment is shown assuming scenario I.
Whereas the initial increase and the modelled HCO maximum
is dominated by reactions (1d) and (4), HCO + M - H +
CO + M, many other reactions [including reaction (1a)]
significantly influence the simulated HCO concentration
profile at later times. Assuming that the kinetic data of these
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Fig. 2 HCO concentration–time profile (upper) and sensitivity analysis (lower plot) of two experiments with 0.98% glyoxal in Ar. Experimental
conditions are T = 1282 K, r = 1.52 ꢀ 10ꢁ5 mol cmꢁ3 (1.81 bar) and T = 1440 K, r = 1.51 ꢀ 10ꢁ5 mol cmꢁ3 (1.61 bar). The mole fraction
axis, due to the different experimental conditions, is approximate.
secondary reactions [except those for reaction (1a)] are
sufficiently well known from literature, it was possible to
deduce the rate constants k1d(I) and k1a(I) by fitting the
simulated HCO profile to the experimental curve. Here, the
rate constant kd(I) is essentially governed by the initial increase
and the rate constant k1a(I) by the long-term consumption of
HCO. The same approach was used to deduce the rate
constants k1d(II) and k1b(II). It turned out that the rate
constants for reaction 1d were largely independent of
the assumed scenario, that is, k1d(I) E k1d(II). In contrast,
we generally obtained k1a(I) 4 k1b(II) with ratios kI/kII in the
order of 3–4, which means that a reliable determination of
k1a+1b+1c and accordingly ktotal = k1d + k1a+1b+1c was not
possible from these experiments alone. In case of scenario I,
the formaldehyde formation triggers an additional
HCO-forming chain reaction sequence:
the generally negative sensitivity coefficent s(HCO) for reac-
tion (1a) (see Fig. 2), an increase of k1a(I) causes a decrease of
the HCO concentration at later times.
All experimental conditions and determined rate constant
values are listed in the ESI.w No systematic variation of the
extracted rate constants with the used initial glyoxal concen-
tration was discernible. The determined rate constant values
for channel (1d) are plotted as function of temperature in
Fig. 3 as filled squares (high-density range) and filled stars
(low-density range). The data, which are best represented in
Arrhenius form
k1d = 1.2 ꢀ 1013 exp(ꢁ240 kJ molꢁ1/RT) sꢁ1
(r E 1.4 ꢀ 10ꢁ5 mol cmꢁ3, Dlog k1d = ꢄ0.26)
k1d = 3.6 ꢀ 1010 exp(ꢁ193 kJ molꢁ1/RT) sꢁ1
(r E 2.2 ꢀ 10ꢁ6 mol cmꢁ3, Dlog k1d = ꢄ0.13)
(CHO)2 + M - CH2O + CO + M
CH2O + H - H2 + HCO
(1a)
(7)
reveal a strong dependence on the total density and thus
clearly show that channel (1d) proceeds close to its low-
pressure limiting value.
HCO + M - H + CO + M
(4)
For a reasonable error estimate, next to the 1s standard error
of the mean, systematic errors arising from uncertainties of the
absolute HCO concentration (ꢄ15%) and the assumed rate
constant expressions are also taken into account. In particular,
for reaction (4) an error of ꢄ20% and for reaction (3) an error of
which has no counterpart in scenario II. Consequently, higher
HCO levels at long reaction times are predicted under scenario
I. In the fit procedure, this had to be compensated for by
choosing kI values higher than kII. As it can be deduced from
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Fig. 3 Arrhenius plot for reaction (1d), (CHO)2 - 2HCO. Filled
symbols refer to HCO and open symbols to H atom measurements.
Squares refer to experiments at high total density (r = 1.6 ꢀ
10ꢁ5 mol cmꢁ3), stars to experiments at low total density (r = 3.2
ꢀ 10ꢁ6 mol cmꢁ3), and the solid curves represent the results of our
RRKM/SACM/ME model. The exact total densities for each single
data point are given in the ESI.w
Fig. 4 (CHO)2 concentration–time profile (upper) and sensitivity
analysis (lower plot) of two experiments with 1.11% glyoxal in Ar.
Experimental conditions are T = 1309 K, r = 1.55 ꢀ 10ꢁ5 mol cmꢁ3
(1.69 bar) and T = 1393 K, r = 1.38 ꢀ 10ꢁ5 mol cmꢁ3 (1.60 bar). The
mole fraction axis, due to the different experimental conditions, is
approximate.
ꢄ50% was assumed. The total error stated above was derived
from simulations with a combined variation of all error sources.
It is more difficult to assess the consequences of neglecting the
HCOH-forming channel (1c). As already mentioned in the
Introduction, a branching fraction o10% can be assumed for
this channel. The question arises, however, whether channel (1c)
acts as a chain-enhancing radical channel [like channel (1d)]or as
a molecular channel [like channels (1a) and (1b)]. Surely,
hydroxymethylene as a singlet species can be assumed to be
quite reactive. For example, HCOH may react with excess
glyoxal or formaldehyde yielding, via C–H insertion or 5-center
addition, a glycolaldehyde product.54 Alternatively, via a unique
hydrogenation of the CQO bond (similar to a diimide
reduction), CO and an alcohol can be formed as well.55 The
corresponding products may subsequently decompose.
Moreover, according to ab initio calculations reported by Koch
et al., a thermal isomerization of HCOH to formaldehyde
shock wave (t o 0) glyoxal absorbs but is thermally stable. The
signal step at t = 0 is due to the increased density behind the
reflected shock wave. At long reaction times the signal reduces to
a zero absorption level indicating that no absorption of possible
long-lived reaction products distorted the measurements.
However, signal contributions from short-lived intermediates,
e.g. by the products of the reactions HCO/HCOH + (CHO)2,
cannot be completely ruled out but can be assumed to be
insignificant for the approximate data evaluation procedure.
The solid curves in the upper plot of Fig. 4 correspond to a
numerical fit using the mechanism outlined in Table 2. Short
induction times can be seen in the simulations due to the chain
decomposition character induced by the HCO-channel (1d).
Unfortunately, these induction times are obscured by the rather
strong schlieren signal present in the experimental profiles.
Again, two separate evaluations based on scenarios I and II
were performed (see section 3.1). The lower plot illustrates the
sensitivity analysis of the T = 1309 K experiment based on
scenario I. Although other HCO radical and H atom reactions
are also important, the most sensitive reactions are the
decomposition channels (1a) and (1d) indeed. Both channels
exhibit comparable sensitivity profiles. Keeping the rate constant
of the HCO-forming channel,k1d, fixed at the value determined
from the HCO experiments, it was possible to extract rate
constant values kI (or kII in case of scenario II). Unlike in the
modelling of the HCO profiles, the choice of the scenario had
(E0
E ) or dissociation to H2 and CO
121 kJ molꢁ1
(E0 E 126 kJ molꢁ1) is also feasible.11 However, none of these
reactions is a direct source of atoms or radicals. Therefore, it is
reasonable to assume that the HCOH channel acts similar to the
molecular channels and that its contribution is comprised in the
rate constants of channels (1a) and (1b). Also note that
dissociation to CH and OH is strongly endothermic
(E0 E 556 kJ molꢁ1).
3.2 (CHO)2 profiles
(CHO)2 conccentration–time profiles were measured at tempera-
tures of 1198 K o T o 1461 K at total densities of r E 1.6 ꢀ
10ꢁ5 mol cmꢁ3 and r E 2.6 ꢀ 10ꢁ6 mol cmꢁ3. High initial mole
fractions of 0.5–2% glyoxal in Ar were used to ensure (CHO)2
concentration profiles yielding sufficient signal-to-noise ratio.
Fig. 4 illustrates two experimental (CHO)2 profiles at tempera-
tures of T = 1309 and 1393 K. Already behind the incident
little influence on the determined rate constants. With kI/kII
E
1.3 for the high-density experiments and kI/kII E 1.14 for the
low-density experiments, which were performed at significantly
lower initial glyoxal concentrations, a more or less direct
determination of k1a+1b+1c was possible.
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The average values of kI and kII, which were taken as the final
results for k1a+1b+1c, are plotted as function of temperature in
Fig. 5 as filled squares (high-density range) and filled stars
(low-density range). All experimental conditions and
determined rate constant values are listed in the ESI.w The
data, which are best represented in Arrhenius form
k1a+1b+1c = 4.8 ꢀ 1012 exp(ꢁ215 kJ molꢁ1/RT) sꢁ1
(r E 1.6 ꢀ 10ꢁ5 mol cmꢁ3, Dlog k1a+1b+1c = ꢄ0.20)
k1a+1b+1c = 3.1 ꢀ 1010 exp(ꢁ166 kJ molꢁ1/RT) sꢁ1
(r E 2.6 ꢀ 10ꢁ6 mol cmꢁ3, Dlog k1a+1b+1c = ꢄ0.06)
reveal a weak dependence on the total density. Whereas the
density was changed by a factor of 6, the rate constants are
lower by only a factor of 2. This is typical for a unimolecular
reaction in the fall-off range.
The rate expressions obtained from the (CHO)2 measure-
ments can be compared to the rate constant data obtained for
kI and kII from the HCO measurements (see ESI).w For the
high-density range better agreement is found with the scenario
II data, for the low-density range better agreement is found
with the scenario I data. This implies that the branching ratios
of channels (1a) and (1b) switch or, at least, the
triple-whammy channel (1b) gains importance with increasing
density.
Fig. 6 Temperature dependence of the branching fraction k1d/ktotal at
total densities of r = 3.2 ꢀ 10ꢁ6 mol cmꢁ3 (upper plot) and r = 1.6 ꢀ
10ꢁ5 mol cmꢁ3 (lower plot). Filled symbols refer to experimental
results based on the HCO and (CHO)2 measurements, and open
symbols to the results of the H atom measurements. Solid curves
corresponds to the RRKM/SACM/ME model predictions. The short
arrows drawn along with some high temperature data points indicate
the necessary small corrections associated with the H-atom-forming
reaction (2b), CH2O - HCO + H (see text).
Branching fractions k1d/ktotal calculated by using experi-
mental k1d values from the HCO measurements and using the
stated Arrhenius expressions for k1a+1b+1c from the (CHO)2
measurements are shown in Fig. 6 as filled symbols. The
indicated error bars are based on the uncertainty of k1d and
thus assume a partial error compensation for ktotal. In spite of
the large scatter of the data, a pronounced temperature and
density dependence is discernible, which will be discussed in
more detail below.
3.3 H atom profiles
H atom concentration-time profiles were measured at tem-
peratures of 1032 K o T o 2320 K and at total densities of
7.0 ꢀ 10ꢁ6 mol cmꢁ3 o r o 1.9 ꢀ 10ꢁ5 mol cmꢁ3 and
2.1 ꢀ 10ꢁ6 mol cmꢁ3 o r o 4.9 ꢀ 10ꢁ6 mol cmꢁ3. Because of
the high sensitivity of the H-ARAS detection method, very low
initial mole fractions of 7.4–39.9 ppm glyoxal in Ar could be
used. At these low concentrations, secondary chemistry is
almost completely suppressed, and a direct determination of
the HCO branching fraction becomes possible. Generated
HCO radicals are almost instantaneously (lifetime: 70 ns
oto 6 ms) converted into H atoms via reaction (4),
HCO + M - H + CO + M.
(4)
At not too high temperatures, no other H atom source is
present in the reaction system and the measured H atom profiles
directly reflect the HCO formation. Two H atoms are generated
for each dissociating (CHO)2 molecule. Fig. 7 illustrates two
experimental H atom profiles at temperatures of T = 1136 and
1206 K. A fast direct formation of H atoms is observed, and a
H atom concentration plateau is reached at long reaction times.
The sensitivity analysis of the T = 1206 K experiment shown in
the lower plot of Fig. 7 reveals that the H atom profile is only
Fig. 5 Arrhenius plot of the sum of the rate constants of the CH2O,
TW, and HCOH channels (1a), (1b) and (1c). Filled symbols refer to
(CHO)2 and open symbols to H atom measurements. Squares refer
to experiments at high total density (r = 1.6 ꢀ 10ꢁ5 mol cmꢁ3), stars
to experiments at low total density (r = 3.2 ꢀ 10ꢁ6 mol cmꢁ3), and the
solid curves correspond to the results of the RRKM/SACM/ME
model. Exact total densities of the four different data sets are given
in the text and for each single data point in the ESI.w
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up to a temperature of T = 2320 K. Detailed simulations
showed that at these high temperatures the unimolecular
decomposition of CH2O cannot be neglected. Small amounts
of H atoms are formed through reaction (2b):
CH2O + M - H + HCO + M
(2b)
causing a slight overestimation of the branching fractions.
However, the H atom yield from formaldehyde decomposition
is well known from literature17–19 and can be taken quantitatively
into account. The short arrows associated with the high
temperature data points in Fig. 6 indicate the necessary minor
corrections.
The experimental rate constants are best represented in
Arrhenius form:
k1d = 2.0 ꢀ 1013 exp(ꢁ246 kJ molꢁ1/RT) sꢁ1
(r E 1.7 ꢀ 10ꢁ5 mol cmꢁ3, Dlog k1d = ꢄ0.16)
k1d = 4.2 ꢀ 1011 exp(ꢁ223 kJ molꢁ1/RT) sꢁ1
(r E 4.2 ꢀ 10ꢁ6 mol cmꢁ3, Dlog k1d = ꢄ0.17)
k1a+1b+1c = 5.7 ꢀ 1012 exp(ꢁ212 kJ molꢁ1/RT) sꢁ1
(r E 1.7 ꢀ 10ꢁ5 mol cmꢁ3, Dlog k1a+1b+1c = ꢄ0.16)
Fig. 7 Experimental and numerically simulated H atom concentration-
time profile (upper plot) and sensitivity analysis (lower plot) of two
experiments with 12.2 ppm glyoxal in Ar. Experimental conditions are
T = 1136 K, r = 1.84 ꢀ 10ꢁ5 mol cmꢁ3 (1.76 bar) and T = 1206 K,
r = 1.68 ꢀ 10ꢁ5 mol cmꢁ3 (1.69 bar). The mole fraction axis, due to
the different experimental conditions, is approximate.
k1a+1b+1c = 1.7 ꢀ 1010 exp(ꢁ158 kJ molꢁ1/RT) sꢁ1
(r E 4.2 ꢀ 10ꢁ6 mol cmꢁ3, Dlog k1a+1b+1c = ꢄ0.15)
The stated errors, next to the 1s standard error of the mean,
are mainly associated with the uncertainty of the absolute
H atom concentration, which is roughly ꢄ30%. Also the
uncertainty of the branching fractions as indicated by
the error bars in Fig. 6 was assumed to be ꢄ30%.
sensitive to the glyoxal decomposition channels. At not too high
temperatures, scenarios I and II (see section 3.1) yielded
indistinguishable H atom concentration-time profiles. Again,
the HCOH channel (1c) was neglected in the numerical
simulations and, for the reasons discussed above, can be
assumed to be unimportant for the overall model. The signal
can be approximated analytically according to a simple
first-order decay to different products,
3.4 Modelling by statistical rate theory
Specific rate constants ki(E,J) for the tight channels (1a), (1b) and
(1c) were calculated from RRKM theory whereas the loose bond
fission channel (1d) was described by SACM. Thermal rate
constants were obtained by solving the master equation as
described in section 2.3. First of all, the G3 energies were slightly
scaled to reproduce the channel branching ratios (1c) : (1b) : (1a)
= 1 : 4 : 9 found by Hepburn et al.6 in their molecular beam study
of the photodissociation of glyoxal at an excitation wavelength of
l = 440 nm (272 kJ molꢁ1). Under collision-free conditions these
ratios directly reflect the ratios of the corresponding low-J specific
rate constants at E = 272 kJ molꢁ1 (22 730 cmꢁ1). Using the
original G3 energies from ref. 11 and MP2 structural data,
channel branching ratios of 1 : 2.3 : 36 were obtained for J = 0
thus slightly underestimating the contributions of the HCOH and
TW channels. A small adjustment by lowering the critical energies
of channels (1b) and (1c) from E0 = 256 and 254 kJ molꢁ1
respectively, to E0 = 245 kJ molꢁ1 was sufficient to reproduce the
experimental ratio of 1 : 4 : 9. This 9–11 kJ molꢁ1 change is within
the expected uncertainty of barrier heights taken from G3
calculations. Of course, also an increase of the critical energy of
the CH2O-forming channel (1a) would have been possible, how-
ever, an increase of this barrier was found to result in too low
total thermal rate constants. In the next step, the experimental
data were fitted treating the critical energy of the HCO-forming
2k1d½ðCHOÞ2ꢆ0
½Hꢆ ¼
ð1 ꢁ expðꢁktotaltÞÞ
ðE6Þ
ktotal
and thus the initial increase is given by (d[H]/dt)t=0
2k1d[(CHO)2/ktotal 0 whereas the plateau concentration is
[H]t-N = 2 ꢀ k1d[(CHO)2]0. Both k1d and k1a+1b+1c
=
]
=
ktotal ꢁ k1d were extracted from the profiles using eqn (E6).
The determined rate constant values are plotted as function of
temperature in Fig. 3 and 5, and the corresponding branching
fractions are given in Fig. 6 as open squares (high-density
range) and open stars (low-density range). All experimental
conditions and data are also listed in the ESI.w Alternatively,
k1d values were directly determined from the initial slope of the
H atom profile. At not too high temperatures, these data were
found to agree well with the results of the full numerical
simulation using the mechanism outlined in Table 2. However,
probably due to the limited time resolution of the H-ARAS
experiment, this simple analysis yielded rate constants which
were increasingly too low at temperatures above 1200 K.
Finally, at temperatures T 4 1370 K the initial increase of
the H atom profiles was too fast and no reasonable k1d values
could be extracted at all. Nevertheless, a determination of the
branching fraction from the plateau concentrations was feasible
channel (1d) and the average energy removal parameter hDEdown
i
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as the adjustable parameters. Alternatively, instead of adjusting
the critical energy, also a slight variation of the anisotropy ratio
a/b would have been possible. The anisotropy ratio, however, was
kept at its ‘‘standard’’ value a/b = 0.5 to avoid the introduction
of an additional parameter.45 In order to reproduce the experi-
mental HCO yields, the G3 bond dissociation energy was slightly
lowered by 0.7 kJ molꢁ1 and the average energy removal para-
meter was set to hDEdowni = 1200 cmꢁ1. Whereas the resulting
C–C bond dissociation energy of 290 kJ molꢁ1 is in very good
agreement with the value of 295 kJ molꢁ1 calculated from
thermodynamic data,34 the value of the average energy removal
parameter is comparatively high. This may be partly explained by
an actual rather effective energy transfer which may occur for
collisions of species with comparable masses, but can be also
partly due to the J-averaging model applied to solve the energy
grained master equation. As can be seen from Table 1, the
rotational effect causes a considerable lowering of the effective
critical energy in case of channel (1d). Lower effective critical
energies for high-J values cause an asymmetry of the reaction
probability of different J-states favouring high-J states. This
asymmetry is not accounted for by our simple J-averaging
procedure and probably has to be compensated by using higher
hDEdowni values.56 Full J-resolved 2D ME calculations should be
capable to account for these effects,35,57 but are still in their
infancy and beyond the scope of this article.
depleted at energies above the critical energy of the loose HCO
channel. A comparison of the specific rate constants with the
Lennard-Jones collision number (dotted line) reveals that for
molecules at energies higher than E0(1d) the dissociation
successfully competes with the collisional deactivation such
that the HCO channel is close to the low-pressure limit. In
contrast, the tight channels are still close to their high-pressure
limit. Pronounced temperature and pressure (or density)
dependences of the branching fractions can be expected from
the complex interplay between the ki(E) curves and the colli-
sional activation/deactivation processes as can be realized from
Fig. 8. A more detailed discussion and comparison with
experimental data is given in the next section.
The rate constants finally obtained for all four reaction
channels resulting from the theoretical model were parame-
trized in terms of Chebyshev polynomials. Chebyshev
polynomials were shown to yield a reliable and accurate
representation of the complex pressure and temperature
dependences experienced in multi-channel unimolecular
reactions.59 This type of formal parametrization, although less
intuitive, is more flexible than those starting from modified
Lindemann expressions and slowly emerges to be used in
common reaction mechanism simulation software.58 Care
has to be taken, however, not to use these approximations
outside their defined domain. In our case, a [4ꢀ4] representa-
tion with four basis functions along each of the normalized
temperature and pressure axes was found to yield an excellent
fit of the fall-off surfaces (B5% accuracy over the whole fit
range). Chebyshev polynomial coefficients anm are given
together with the parameters of three extended Arrhenius fits
at selected total densities in Table 3.
Fig. 8 illustrates k(E) curves for J = hJiT = 74 and steady-
state populations ns(E) for a temperature of T = 1500 K. As
expected for a loose reaction channel, the energy dependence of
k1d is much morepronounced than those for the tight channels
and therefore the k1d curve intersects the others. In general, at
high temperatures and high pressures, higher energy states get
populated such that the HCO channel gains importance.
Interestingly, another intersect of k1a and k1b (CH2O and
TW channels respectively) occurs indicating that the relative
importance of the TW channel also increases with temperature
and pressure. Steady-state populations ns(E) are shown for the
high-pressure limit and a pressure of p = 1 bar. At 1 bar, which
is close to our experimental conditions, the population is still
close to the high-pressure limit at energies close to the energy
barriers of the tight channels whereas the population is strongly
3.5 Data analysis
Experimental values of the rate constants, the determined
branching fractions, and their dependences on temperature and
total density are compared with the model predictions in Fig. 3, 5
and 6. The experimental data can be divided into a group
measured at high total densities, 7.0 ꢀ 10ꢁ6 mol cmꢁ3 o r o
1.9 ꢀ 10ꢁ5 mol cmꢁ3, with an average density of r = 1.6 ꢀ
ꢀ
10ꢁ5 mol cmꢁ3 (squares), and a group measured at lower total
densities, 1.7 ꢀ 10ꢁ6 mol cmꢁ3 o r o 4.9 ꢀ 10ꢁ6 mol cmꢁ3, with
ꢁ6
a five times lower average density of r = 3.2 ꢀ 10 mol cmꢁ3
ꢀ
(stars). The solid curves in the Figures correspond to the results of
our RRKM/SACM/ME model at these two average densities.
The two independent sets of experimental k1d and k1a+1b+1c
rate constant values extracted from the HCO and (CHO)2
measurements on the one hand (filled symbols) and the H
atom measurements on the other hand (open symbols) agree
very well. Both the accuracy of the HCO radical and the H
atom measurements heavily rely on the absorption cross
section of HCO and on the absolute calibration of the H atom
concentration, respectively. Therefore, the good agreement of
the measurements nicely underlines the reliability of the FM
and H-ARAS detection schemes.
A comparison of Fig. 3 and 5 reveals that the energetically
high-lying loose HCO-forming channel, in contrast to the
energetically low-lying tight channels, is strongly density
dependent. This overall density dependence is nicely captured
Fig. 8 Specific rate constants k(E) (solid curves, right axis) and
steady-state populations n(E) (dashed curves, left axis) calculated for
a temperature of T = 1500 K (J = hJiT = 74). ZLJ is the Lennard-
Jones collision frequency at p = 1 bar.
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by our ME model. For the HCO-forming channel, with a
factor of 6–7, the model predicts a density dependence that is
even more pronounced than the proportionality expected for a
simple unimolecular decomposition at its low-pressure limit
(ratio of densities, factor 5). This excessive density dependence
is a clear indication of a population depletion effect associated
with the weak-collision activation of the glyoxal molecule. The
highly excited glyoxal molecules, which predominantly dis-
sociate through the HCO channel, are mainly activated from
energy states lying above the critical energies of the tight
channels. With decreasing total density, the population of
these (populating) states is increasingly depleted via the tight
channels. This leads to an activation bottleneck for the HCO
channel resulting in a stronger density dependence than in the
case of a simple one-channel unimolecular reaction. In
contrast to the HCO-forming channel, the moderate density
dependence of the tight channels (see Fig. 5) reveals that these
channels are in the fall-off range indeed. Thus the experimental
densities have just the right magnitude to provide insight into
this subtle effect. Also note that a successful modelling of this
population depletion effect requires a weak-collision ME
approach and would not have been captured by a simpler
strong-collision model.
HCO channel branching fractions are as low as o4% at 1100 K
and increase to 440% at a temperature of 2300 K. This strong
temperature dependence can be partly traced back to the
generally observed increase of branching ratios for high-lying
channels at higher temperatures but is influenced by rotational
effects as well. As can be seen from Table 1, changing the
temperature from T = 800 K to 2500 K decreases the effective
critical energy E0(hJiT) of channel (1d) by as much as 842 cmꢁ1
(10 kJ molꢁ1). Accordingly, the tight channels (1a) (ꢁ6 cmꢁ1),
(1b) (ꢁ228 cmꢁ1) and (1c) (ꢁ115 cmꢁ1) become less important.
In our master equation modelling, we find an increase of the
HCO yield from 3.6 to 36.6% at 1 bar and from 11.6 to 62.4%
at 10 bar if the temperature is increased from 800 to 2500 K. If
the J-dependence of the threshold energies is neglected and the
values for E0(i)(J = 70) are used throughout, this temperature
dependence is distinctively less pronounced (5.6 to 20.2% and
13.3 to 47.3% respectively).
The predicted temperature and density trends for all
four channels are summarized in Fig. 9 for temperatures of
800 K o T o 2500 K and total densities of 1 ꢀ 10ꢁ8 mol cmꢁ3
4 r o 1 ꢀ 10ꢁ3 mol cmꢁ3 (1.1 mbar–110 bar at T = 1300 K).
With branching fractions o7% the HCOH-forming channel
remains unimportant over the whole range of parameters. The
CH2O channel is dominant at low temperatures and low total
densities. In accordance with the aforementioned literature
findings, the triple-whammy channel gains importance with
increasing temperature. Also the qualitative trend deduced
from the HCO/(CHO)2 data indicating a gain of the TW
channel (1b) relative to channel (1a) at higher densities is
reproduced by the theoretical model. At high temperatures
and densities both channels contribute about 20% each. In
contrast to all previous literature assumptions, the HCO
channel is an important decomposition channel and becomes
For a detailed comparison of the modeled curves with the
experimental data points shown in Fig. 3, the slightly different
experimental densities have to be taken into account. Exact total
densities for each single data point are given in the ESI.w Based
on the Arrhenius expressions for channel (1d) (see sections 3.1
and 3.3) and the respective average densities, the rate constants
from the HCO measurements exhibit an approximate density
dependence of factor 5.9 (ratio of densities = 6.4, T = 1400 K)
and the rate constants from the H atom measurements show an
approximate density dependence of factor 4.8 (ratio of densities
= 4.1, T = 1200 K). Thus the predicted population depletion
effect is hardly to detect within experimental error, however, the
very good overall agreement between theoretical calculation and
experimental data is still convincing.
A further inspection of the rate constant data sets reveals
minor inconsistencies. For example, the high-density range
H-ARAS data points (open squares), whichꢁw5 ere measured at
an average total density of r = 1.7 ꢀ 10 mol cmꢁ3 and,
~
therefore, should more or less coincide with the theoretical curve
~
ꢁ5
for r = 1.6 ꢀ 10 mol cmꢁ3, are systematically lower for the
HCO channel and systematically higher for the sum of the other
channels (Fig. 3 and 5 respectively). Though all deviations are
well within the uncertainty of the measurements, they result in a
systematic shift of the determined HCO branching fractions
extracted from the H-ARAS measurements relative to the results
extracted from the HCO/(CHO)2 experiments (see Fig. 6). But
keeping in mind the general difficulties associated with the
measurement of accurate branching fractions, the agreement
between the two data sets and the theoretical model is still very
good. Note that the five high-temperature data points from the
H-ARAS experiments at high-density were actually measured at
r E 8.0 ꢀ 10ꢁ6 mol cmꢁ3 and that the corresponding prediction
ꢀ
(Fig. 6, dashed curve, based on Chebyshev polynomial fit from
Table 3) reproduces the experimental data as well.
Clearly, the HCO yield increases with increasing pressure and,
more pronounced, with increasing temperature. Experimental
Fig. 9 Temperature and density dependence of the channel branching
fractions calculated from the Chebyshev polynomials given in Table 3.
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behind shock waves. The experiments, which were performed
at two different total densities of r = 1.6 ꢀ 10ꢁ5 and r = 3.2
ꢀ 10ꢁ6 mol cmꢁ3, revealed a strong temperature and density
dependence of the absolute HCO yield. With a branching
fraction of 48% at T = 2300 K and r = 1.6 ꢀ 10ꢁ5 mol cmꢁ3
,
the so-far-neglected HCO-forming channel turned out to be
the most important thermal decomposition channel at high
temperatures and densities. A theoretical analysis in the frame-
work of unimolecular rate theory based on a detailed
RRKM/SACM/ME model allowed for a consistent descrip-
tion of the observed temperature and density dependences.
Both rotational effects and weak collision effects are reflected
in the measured branching ratios and thus make the glyoxal
thermal decomposition an ideal test system for unimolecular
rate theory. Finally, in order to facilitate the implementation
in reaction mechanism simulation software, the multi-channel
unimolecular decomposition rate constants were parametrized
using Chebyshev polynomials.
Fig. 10 Arrhenius plot of total (CHO)2 decomposition rate constant
ktotal. Solid curves: this work, dashed curves: uncorrected data from
Saito et al. (see text).21
Acknowledgements
the dominating pathway at high temperatures and densities.
The distinctive channel switching behaviour of glyoxal takes
place at easily accessible experimental conditions and thus the
investigation of its thermal decomposition represents an ideal
test system for unimolecular rate theory.
We would like to thank Oliver Welz, Karlsruhe, for calculating
the glyoxal internal rotor eigenstates and the Deutsche
Forschungsgemeinschaft (FR1529/2-3 and SFB 606—Unsteady
Combustion: Transport Phenomena, Chemical Reactions,
Technical Systems) for the support of this work.
Our results can be compared with the study of Saito et al.21
As already outlined above, these authors investigated the
temperature and density dependence of the unimolecular
glyoxal decomposition by measuring (CHO)2 absorption and
CO emission signals. No indications were found for the
involvement of the HCO channel and, based on additional
CH emission experiments, it was concluded that essentially no
CH2O was generated and that the TW channel contributes
with 490%. All these findings are in conflict with our study.
Reported total rate constants from Saito et al.21 for two
selected total densities of r = 2.8 ꢀ 10ꢁ6 mol cmꢁ3 and
r = 1.2 ꢀ 10ꢁ6 mol cmꢁ3 (dashed lines) are shown in
comparison with our data (solid lines) in Fig. 10. Whereas
the overall dependence on temperature and total density is
similar, the reported rate constants from Saito et al. are lower
by a factor of 1.4–1.7. Moreover, since the neglected HCO
channel induces an accelerated chain decomposition of
glyoxal, the reported total rate constants can be assumed to
be systematically too high. A simulation of the experiments
performed by Saito et al. using our mechanism showed that a
neglect of the HCO channel induces about two times larger
rate constant values. Therefore, with a factor of about 3, the
discrepancy between our measurements and the reported data
of Saito et al. is considerably higher than deduced from
Fig. 10. The reason for this disagreement remains unclear;
however, most probably the neglect of the HCO channel
caused a misinterpretation of the measured signals in ref. 21.
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