st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Calculation of Parameters of O2(a1Δ g) Reactions
for Low-Temperature Mechanism of Methane Oxidation
Maxim Deminsky1,2, Alexander Lebedev2, Andrey Zaitzevsky2 and Boris Potapkin1,2
1
National Research Centre "Kurchatov Institute", Moscow, Russia
2
KintechLab, Moscow, Russia
Abstract: The important for low-temperature oxidation reactions of electronically excited
oxygen O2(a1Δg) with methyl radical are investigated theoretically by state-of-art quantum
chemical methods. It was found that the association reaction has a threshold with energy of
8.5 kcal/mole. The data obtained was used for kinetic analysis of excited oxygen formation
and reaction in non-equilibrium plasma.
Keywords: singlet oxygen, plasma
1. General
Singlet Oxygen O2(a1Δg) has lately become a
subject of intense research because of possible its capability of significantly enhancing the combustion of hydrocarbons. Although some efforts were made in modeling
methane combustion involving singlet oxygen [1], a reliable theoretical model based on first-principles calculations is required. The most interesting effect of O2(a1Δg)
is the involvement of this molecule into the reactions of
chain initiation and chain propagation. The potential efficiency of O2(a1Δg) can be high for chain propagation,
because each excited oxygen molecule could stimulate the
production of a greater number of active radicals. At low
temperatures, the shift of the reaction equilibrium towards
the chain branched mechanism and the acceleration of
chain propagation may provide excited oxygen with an
additional possibility for enhancing HC combustion. This
effect could be achieved using, for example, cold
non-equilibrium plasmas [1]. Simulation of this effect
requires accurate information about the rates of elementary processes involving chain propagation. In fact, an
inaccuracy of 5 kcal mole in the energetic parameters of a
reaction at temperatures below 900 K changes the reaction rate by about one order of magnitude and may become a reason for the incorrect conclusions about the
pathways of oxidation in the mechanism. A kinetic model
of methane-air combustion in the presence of O2(a1Δg)
was proposed in several works. [1,2]. Theses models were
focused on the behavior of ignition time and flame velocity at elevated temperatures (T>1600K) when sensitivity
to accuracy of used rate constants with participation of
O2(a1Δg) is low. Presumably, this is why reactions involving O2(a1Δg) are estimated within a rather rough ”vibronic terms” model. Nevertheless, this model can be
regarded as a basis for the comprehensive theoretical description of combustion process stimulated by O2(a1Δg).
One of the key reactions of singlet oxygen in
an air-methane mixture is the reaction with the methyl
radical:
, which correlate with following channels of reaction of
CH3 with oxygen in the ground state:
Unfortunately, there are no experimental data on the rate
parameters of the process 1a. Only several ab initio calculations of this reaction have been performed so far [3,
4]. However, the difference in approaches used for calculations of the Potential Energy Surface (PES) for CH 3 +
O2(a1Δg) may lead to a contradiction in the conclusions
about the input of this reaction to the total oxidation
mechanism. The difference in conclusions about the absence [4] or presence [3] of a threshold of the reaction
together with the sufficiently great discrepancy for the
excitation energies (26.3 kcal/mole , 24.6 kcal/mole ) with
respect to the table value (22.5 kcal mole ) makes the effect of the error propagation of ab-initio calculations upon
the final value of the oxidation rate at low temperatures
strongly undetermined. Thus, the accuracy of the models
and calculations discussed above is not sufficient for
making an unambiguous conclusion about the role of
O2(a1Δg) in methane oxidation at low temperatures. The
aim of this study was to find out the principal reactions
involving excited oxygen, which provide the maximal
sensitivity with respect to the overall kinetic parameters
(induction time) and to evaluate the microkinetic characteristics of the key elementary reactions using
state-of-the-art computational methods.
2. Ab-initio calculation of rate constants of O2(a1Δg)
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21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
reactions.
The Potential Energy Surface of the system
CH3 + O2(X3Σ; a1Δg) was investigated at the
multireference configuration interaction (MRCI) level of
theory [5] in the triple-zeta basis set of Dunning and Hay.
To obtained accurate data, MRCI level of theory was used
with two different active space spans. The smaller active
space was consisted of 3 electrons on the 4 molecular
orbitals MRCI (3/4), while largest one was MRCI(7/5).
Results achieved with two different active spaces give
notably different values of the energy for reagents CH3
and O2(a1Δg) on the 2A′ term. Application of
size-extensivity corrections (Davidson’s, Pople’s methods) permits to smooth that difference and converges both
results to single energy point. It was concluded that
smaller (MRCI(3/4)) and larger active space (MRCI(7/5))
give regular under and overestimation of the results. Davidson correction was applied to MRCI energies in order
to obtain the correct depth of the well on the ground
term( 2A′′). Finally, the potential energy surface obtained
by the MRCI(7/5) approach was selected for further analysis as the best fit for known thermodynamics data. For
example, calculated energy of the excitation (0.99 eV)
and the well depth of CH3O2 in ground state (1.301 eV)
are in good agreement with experimental values (0.98 and
1.34±0.04 eV respectively). Figure 1 presents the resulting PES. The activation energy of the process (1a) is as
high as 0.28 eV
Fig.1 PES for system CH3 + O2(X3Σ; a1Δg). 1- ground state 2A''
corresponds to reaction with O2(X3Σ), 2- excited state 2A' corresponds to reaction with O2( a1Δg), 3 - tems crossing and transition state (TS).
(0.36 eV taking ZPE energies into account).
The rate parameters of the reactions 1a, 1b, 2a, 2b, 1c, 2c
were computed from the data of quantum chemical calculations. Microcanonical variational Rice – Ramspergen –
Kassel – Marcus (RRKM) calculations were carried out
using the Khimera code [6]. A microcanonical loose variational transition state was used for the rate parameters 2a,
2c, 1c of reactions without a distinctive potential energy
barrier. A rigid transition state was used for the reactions
1a, 2b, 1b. The pressure dependence was computed using
the master equation method. Figure 2 presents the dependence of the rate of association reaction via excited
state 2A’ vs. temperature and the parameters of rate constant approximation in the quasi-Arrhenius form.
Fig. 2. Rate constants of reactions 1a, 2a. P = 1 atm. 1, 2 and
3-reactions through ground state in accordance with the works
[7], this study and [1] respectively, 4- reaction through excited
state in accordance with [1], 5-reaction through excited state in
accordance with this study.
The figure also includes the rate approximation used in
the work [1]. The confidence interval of the calculation
(dashed area) was estimated from the characteristic value
of the error of threshold calculation ±2 kcal/mole. The
reaction for the singlet state is several orders of magnitude slower than the reaction of the triplet state at the
characteristic pressure 1 atm. This effect can be explained
by the appearance of an energy barrier in the reaction path
and by the high probability for CH3 and O2(a1Δg)) reaction directly into CH2O and OH, avoiding stabilization of
the way into the methylperoxy radical (CH3O2). The reaction rate is three orders of magnitude lower than that from
[1], where intuitive suggestions about the PES behavior
were used in calculations within the ‘‘vibronic terms’’
approach.
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Fig. 3. Rate constants of reactions 1b, 2b. P = 1 atm. 1, 2 and
3-reactions through ground state in accordance with the works
[8], this study and [1] 4-reaction through excited state in accordance with the study [1], 5-reaction through excited state in
accordance with this study.
In Fig. 3 the rate constant of reactions 1b, 2b is shown as
a function of temperature at atmospheric pressure. The
results are compared with the data of ab initio calculations
[8] and work [1]. Our calculations demonstrate a strong
effect of the potential energy surface features on the rate
behavior at low temperatures. Comparison of the three
possible channels for the reaction with excited oxygen
shows that the stabilization phenomena of the intermediate complex becomes significant at pressures greater than
300 atm. Therefore channels 1b and 1c are principal reactions in wide range of pressures and temperature. As was
mentioned in the work [8], the production of CH2O and
OH requires PES hopping with a high transition probability between the 2A’ and 2A” states. Using the results of
this study and the parameters of the saddle points from [8],
we came to the conclusion that the rate constant of reaction to CH2O for the excited state is higher than that for
the ground one at low and moderate pressures.
Fig. 4. Rate constants of reactions 1c, 2c. P = 1 atm. 1, 2 and
3-reactions through ground state in accordance with the works
[9], this study and [1] 4-reaction through excited state in accordance with the study [1], 5-reaction through excited state in
accordance with this study.
Figure 4 provides a comparison of the rates of the reactions 1c and 2c. The rate of the reaction 1c is significantly
greater than the reaction through the ground term because
of the difference in the endothermicity of the reactions.
The graphs also present a comparison of the temperature
dependence of the calculated rate parameters with the
corresponding data from other works. The comparison of
the reaction rate of 2c with the corresponding data from
the Ref. [9] shows that the rate for the triplet state is well
reproduced by our model. A comparison of the rate 1c
with the curve from [1] exhibits a coincidence, which
probably indicates that the vibronic term approach is justified in this case. The results of approximation of the rate
constants of the reactions 1-2 (a-c) in quasi-Arenius form
for P=1 atm are presented in the Table 1.
Table 1. Rate constants of the reactions 1-2 (a-c)
The reaction for the singlet state in CH3O2 is several orders of magnitude slower than the reaction of the triplet
state at the characteristic pressure 1 atm. This effect can
be explained by the appearance of an energy barrier in the
reaction path and by the high probability for CH3 and
O2(a1Δg) reaction directly into CH2O and OH, avoiding
stabilization of the way into the methylperoxy radical(CH3O2). The reaction rate is three orders of magnitude
lower than that from paper [1], where intuitive suggestions about the PES behavior were used in calculations
within the ”vibrational term” approach.
3. Application for plasma assisted CH4 oxidation
The developed model was applied for the simulation of
plasma stimulated oxidation of CH4. According to common knowledge the most pronounced effect of plasma
discharge in air on kinetics is produced by generation of
the atomic oxygen [10]. In order to find out the efficiency
of the O2(a1Δg) we compare the influence of both particles
on the ignition delay. Since generation of O2(a1Δg) in air
is not effective [10] the generating this particle was applied to pure oxygen and after that the plasma components were mixed with other part of the mixture. The effect of the atomic oxygen was simulated by the discharge
applied to both full mixture and oxygen alone. In all simulations the generation of the desired particle was promoted by adjustment of the reduced electric field strength
to the conditions optimal for the desired particles. Generation of atomic oxygen is most effective if the reduced
electric field in the discharge is about 150 Td depending
on the composition of the gas processed by the plasma
while generation of singlet oxygen is most effective when
E/N is about 5-10 Td [10]. Since the rate of O2(a1Δg)
quenching is not well established the simulations were
performed both with and without the corresponding processes in the kinetic model. The models of the nanosec-
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
ond pulsed in case of high E/N and nonself-sustained
discharges in case of low E/N in frame work of computational environment Chemical Work Bench [6] were used.
The plasma chemical mechanism includes primary, secondary processes in the discharge volume and chemical
reactions of the heavy particles. Mechanism was validated
for wide range of the temperatures for methane combustion including low temperatures T<1000 K [11]. The
sub-mechanism with participation of O2(a1Δg) was taken
from [1] and modified in accordance with this paper results.
The comparison of following effects was performed:
-discharge in pure oxygen (E/N = 100 Td).
-discharge in air (E/N = 150 Td).
- discharge in pure oxygen (E/N = 10 Td).
- discharge in pure oxygen (E/N = 10 Td) without
quenching.
- input of the energetically equivalent amount of heat
The results of the comparison with different
total plasma energy input are given in Fig. 5.
Fig.5 Ratio of induction time at mixture heating to induction
times at different scenario: solid line – non self-sustained discharge at 10Td in O2, dashed line – discharge in O2 at 100 Td,
dotted line - non self-sustained discharge at 10Td in O2 without
quenching, dash-dotted line - dashed line – discharge in Air at
150 Td
One can see that the efficiency of O2(a1Δg) is
sensitive to the rate of quenching and could potentially be
competitive to the reaction with atomic oxygen. The influence of the O2(a1Δg) is occur due to participation in the
initiation reaction and reaction 1b. It is important to note
principal consequence of the modification of the rate constants of the reactions 1a and 1b. The lowering of rate
parameter of the reaction 1a leads to reducing of ignition
delay time. It is explained by fact that CH3O2 produced in
reaction 1a then mainly dissociates into CH3 + O2(X3∑)
(that is property of the [1] mechanism).So, the overall
effect of this reaction is the dissipation of the excitation
energy into heat O2(a1Δg)=> O2(X3∑)+Q. Since the intermediate states of the excited and ground CH3O2 corre-
sponds to actually different species with different electronic configurations, the correctness of the reaction
pathway CH3+O2(a1Δg)=> CH3O2(2A’)=> CH3O2(2A’’)=>
CH3 + O2(X3∑) seems questionable.
In all simulations application of plasma produced greater impact on the ignition delay than heating of
the mixture. One can see that in the optimal regime (low
E/N value, pure oxygen) the effect of the O2(a1Δg) can be
compatible with effect of the atomic oxygen (discharge in
the air-methane mixture at high E/N).
The results of the kinetic simulations show
high sensitivity of the model results to the rate of
quenching of O2(a1Δg) and peculiarities of the chemical
O2(a1Δg) sub-mechanism. Thus, further development of
the kinetic model should be performed focusing on the
evaluation of the rates of O2(a1Δg) quenching on the variety of particles present in the mixture and analysis of the
reaction pathways with participation of excited oxygen.
4. References
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