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Trang 1O R I G I N A L R E S E A R C H
Mechanism and kinetics of low-temperature oxidation
of a biodiesel surrogate2methyl acetate radicals with molecular
oxygen
Tam V.-T Mai•Xuan T Le•Lam K Huynh
Received: 24 May 2014 / Accepted: 11 August 2014
Springer Science+Business Media New York 2014
Abstract Accurate description of reactions between
methyl acetate (MA) radicals and molecular oxygen is an
essential prerequisite for understanding as well as
model-ing low-temperature oxidation and/or ignition of MA, a
small biodiesel surrogate, because their multiple reaction
pathways either accelerate the oxidation process via chain
branching or inhibit it by forming relatively stable
pro-ducts The accurate composite CBS-QB3 level of theory
was used to explore potential energy surfaces for MA
radicals ? O2 system Using the electronic structure
cal-culation results under the framework of canonical
statisti-cal mechanics and transition state theory, thermodynamic
properties of all species as well as high-pressure rate
constants of all reaction channels were derived with
explicit corrections for tunneling and hindered internal
rotations Our calculated results are in good agreement with
a limited number of scattered data in the literature
Fur-thermore, pressure- and temperature-dependent rate
con-stants were then computed using the Quantum Rice–
Ramsperger–Kassel and the modified strong collision
the-ories This procedure resulted in a thermodynamically
consistent detailed kinetic mechanism for low-temperature
oxidation of the title fuel We also demonstrated that even
the detailed mechanism consists of several reactions of
different reaction types, only the addition of the reactants and the re-dissociation of the initially formed adducts are important for low-temperature combustion at engine-liked conditions
Keywords Biodiesel surrogate Oxygenated hydrocarbon Alkyl peroxy radical Detailed kinetic model Low-temperature oxidation and ignition
Introduction
Biodiesel fuels (or biologically derived fuels in general) have been emerging as one of most promising candidates to meet the continually increasing demands on internal combustion engine development for higher combustion efficiency, reduced pollutant emissions, the depletion of fossil fuels, and higher performance Biodiesel is a renewable and environmentally friendly fuel with low emission of pollutants such as carbon monoxide, carbon dioxide, sulfur compounds, and particulate matter [1], while its effects on nitrogen oxides (NOx) remain uncer-tain Such NOx emissions have been experimentally observed either increasingly [2,3] or decreasingly [4] with the use of biodiesel as an alternative fuel or a blend com-ponent Therefore, there is a need for further investigation
to shed more light on benefits, drawbacks of biodiesel fuels
as well as its influence on operational conditions of engines
Biodiesel fuels are often produced from mono-alkyl esters
of long-chain fatty acids derived from vegetable oils and animal fats [1,5,6] Typically, they have the structure of a methyl ester group attached to a long hydrocarbon chain of about 16–19 carbon atoms (C16–19Hx–C(=O)O–CH3) Due to their large size and their chemical/physical complexity (e.g.,
Electronic supplementary material The online version of this
article (doi: 10.1007/s11224-014-0495-2 ) contains supplementary
material, which is available to authorized users.
T V.-T Mai X T Le L K Huynh (&)
Institute for Computational Science and Technology at Ho Chi
Minh City, Ho Chi Minh City, Vietnam
e-mail: lamhuynh.us@gmail.com
L K Huynh
International University, Vietnam National University-HCMC,
Ho Chi Minh City, Vietnam
DOI 10.1007/s11224-014-0495-2
Trang 2the introduction of the heterogeneous O atom compared to
hydrocarbon fuels), detailed kinetic study on these biodiesel
molecules is challenging both experimentally and
theoretically
In terms of detailed kinetic modeling, surrogate
mole-cules are widely used to study the chemistry/physics of real
fuels Surrogates are simple molecules used to emulate the
physical and chemical properties of real conventional fuels
that are too complicated for detailed investigation
There-fore, it is necessary to determine optimal surrogate models
which are small enough to be investigated using accurate
calculations but also large enough to represent the
chem-istry/physics of real molecules Such good surrogate
models will allow us to investigate the oxidation of real
methyl esters in internal combustion engine [7 12] In this
context, because methyl acetate (MA) is the simplest
methyl ester molecule with a chain of only one carbon
atom connected to the methyl ester group, the chemistry as
well as the role of the methyl ester group can be explicitly
investigated Importantly, because MA radical is an
inter-mediate with relatively high concentrations in the pyrolysis
of larger surrogates (e.g., methyl propanoate [13]) as well
as real biodiesel molecules such as the rapeseed methyl
ester (RME) [14], understanding of mechanisms and
kinetics of MA will contribute to the development of
reliable kinetic models for larger methyl esters and
bio-diesels [15]
In this paper, we concentrate our efforts on
character-izing detailed kinetics of MA radicals ? O2 reactions
which is believed, similar to the analogous alkyl systems,
to play a very important role in low-temperature oxidation
and auto-ignition processes [7] Based on the
well-con-structed potential energy surfaces (PESs) explored at the
high level composite method CBS-QB3, the detailed
kinetic analysis is then carried out to investigate the
structural effects on the kinetic behavior of this system at
low-temperature conditions under the framework of the
Quantum Rice–Ramsperger–Kassel (QRRK) and the
modified strong collision (MSC) theories The detailed
kinetic mechanism for the title reaction, MA
radi-cals ? O2, was also compiled in the Chemkin format for a
wide range of temperatures and pressures A simplified
mechanism, which consists of important reactions, is also
suggested for low-temperature combustion at engine-liked
conditions
Computational details
Electronic structure calculations
The electronic structure calculations were carried out using
the Gaussian 09 program [16] The composite CBS-QB3
method by Petersson and coworkers [17] was selected because of its capability of predicting thermodynamic properties to ‘‘chemical accuracy’’, which is normally defined as within *1 kcal/mol of experimental data It is worth mentioning that the method has shown to be the effective method for analogous alkyl?O2systems [18,19] Moreover, the method was also intensively used to study thermodynamics and kinetics of similar and/or larger oxygenated systems For example, CBS-QB3 numbers were used to derive group additive values for different oxygenated compounds [20]; bond dissociation energies and enthalpies of formation of methyl/ethyl butanoate [21]; oxidation of methyl and ethyl butanoates [22]; and abstraction reaction between MA and hydroxyl radical [23]
in which CBS-QB3 is the method of choice to refine the energy for the use of other methods such as BH&HLYP and MP2 A good agreement on calculated reaction barriers and energies for several important reactions were also observed with those by other methods, namely G3, G3B3, and G4 (see supplementary Table S3 for details) The CBS-QB3 method calculates geometries and frequencies at the B3LYP/6-311G(2d,d,p) level of theory The energy is calculated at several levels of theory including CCSD(T)/6-31?G(d0) and then extrapolated to the complete basis set limit All reported results for stable molecules as well as transition states (first-order saddle points on the PESs) were obtained for the lowest-energy conformer of a given spe-cies Normal-mode analysis was performed to verify the nature of each of these stationary points For complicated reaction pathways, in order to confirm the correct transition state, the minimum energy paths (MEP) from the transition state to both the reactants to products were calculated using the intrinsic reaction path (IRC) following method [24,25]
Thermodynamic property calculations
The atomization method was employed to calculate the heats of formation of all species, and standard statistical mechanics methods were used to calculate thermodynamic properties such as entropies and heat capacities Because only relative energies are required in this work, no attempts were made to improve the heats of formation using, for example, bond additivity corrections All harmonic fre-quencies were scaled by a factor of 0.99 as recommended
by Petersson and coworkers [17] prior to their use Using the experimental vibrational frequencies of methyl acetate [26], the calculated scale factor is 0.98 ± 0.01 Therefore, the use of scale factor of 0.99 is expected to give reliable results for both enthalpy and entropy Some low-frequency vibrational modes, which are better treated as internal rotations around single bonds, were replaced in the ther-modynamics calculations by an explicit evaluation of the hindered rotations in the most accurate manner as
Trang 3described hereafter The 1-D Schro¨dinger equation for a
hindered internal rotor (HIR) is given as
1
2Ired
d
2
Whir
dh2 þ VðhÞWhir¼ EWhir; ð1Þ
where E is the energy and Ired is the reduced moment of
inertia for the considered rotation and is calculated as I(2,3)
according to East and Radom [27] on the basis of the
original work by Kilpatrick and Pitzer [28] The hindrance
potential, V(h), is directly computed as a function of
tor-sional angle, h, with a step of 10 Specifically for this
system, it was obtained at the B3LYP/6-31G(d) level via
relaxed surface scans with the step size of 10 for dihedral
angles that correspond to the rotations In order to solve the
HIR equation, we cast it into a Mathieu-type equation by
representing the hindrance potential as a Fourier series,
Vð Þ ¼h PL
l¼Lcleilh , in which L is some cut-off number
depending on the nature of the potential The wave
func-tion was expanded as a harmonic series, mj i ¼p 1ffiffiffiffi2peimh;
and plugged into HIR equation The matrix elements for
the Hamiltonian are then given by
Hmn mh jH nj i ¼ 1
2p
Z2p
0
eimh
2Ired
o2
oh2þXL l¼L
Cleilh
!
einhdh
2Iredm
2
dmnþ cmn
The matrix can be diagonalized to obtain its eigenvalue
spectra which are the energy levels of the considered rotor
These information are used to calculate the partition
function and the contributions to the thermodynamic
functions
Rate constant calculations
High-pressure rate constant calculations were carried out
using canonical transition state theory (TST) with
tunnel-ing corrections based on asymmetric Eckart potentials [29]
Note that other empirical and/or ab initio-based methods
(e.g., Group Additivity [30,31] and Reaction Class
Tran-sition State Theory [32]) to obtain reliable high-pressure
rate constants on the fly were extended to the kinetics of the
oxygenated species [33, 34] The high-pressure rate
con-stants for the barrierless recombination of MA radicals
with O2were not calculated in this work but derived from
similar alkyl?O2systems [18,19]
Pressure- and temperature-dependent rate constants for
the multiwell-multichannel PES were calculated based on a
steady state analysis in which the energy-dependent
uni-molecular rate coefficients k(E) were computed using the
Quantum Rice–Ramsperger–Kassel (QRRK) theory Col-lisional stabilization rate constants were calculated using the modified strong collision assumption (MSC) More details of the methodology can be found in the work of Chang and coworkers [35] In addition to the high-pressure rate constants, Lennard-Jones collision diameters (rLJ) of 5.94 A˚ and well depths (rLJ) of 669.8 K were estimated from similar systems [36], thus used for all adducts and isomers The MSC model further requires a value for the average energy transferred per collision hEalli to calculate stabilization rate constants We used Eh alli ¼ 440 cal/mol for the bath gas collider of N2(rLJ¼ 3:80 ˚A,eLJ¼ 71:4 K) [36] We also run calculations with the bath gas of He (rLJ ¼ 2:55 ˚A,eLJ ¼ 10:0 K) [36], and the simulation results were generally found to be rather insensitive to the nature of the collider, at least for the conditions considered
in this study The results are provided in the accompanied Supplementary material
Results and discussion
Due to breaking of different bond types, MA molecule produces several fragments (e.g., CH3C(=O)O, CH3C=O,
CH3O, CH3, CO, etc.) [21, 37] which are too many to include this study; therefore, we limit ourselves on the main fragments having the same carbon–oxygen backbone
of MA due to the breaking of C–H bond, namely CH 3-C(=O)OC•H2 and •CH2C(=O)OCH3 These two radicals can isomerize to each other through the hydrogen migra-tion reacmigra-tions via five-membered ring transimigra-tion states (cf Fig.1) These radicals can react with molecular oxygen to form chemically activated peroxy radicals which can undergo the stabilization, isomerization, and dissociation reactions to form back reactants and/or bimolecular pro-ducts Similar to the analogous alkyl systems [18,19,38], these systems are expected to be more complicated (due to the presence of heterogeneous O atom in the ester
Fig 1 Two MA radicals, namely (a) 2-methoxy-2-oxoethyl and (b) (acetyloxy)methyl, can isomerize through hydrogen migration reactions via five-membered ring transition states given below and above the reversible arrows
Trang 4functional group) and to play a central role in
low-tem-perature combustion of the title fuel [39]
Potential energy surface
Potential energy surfaces (PESs) play the central role in
computational chemistry, especially in detailed kinetic
modeling analysis The PESs for the reactions between
methyl acetate radicals and molecular oxygen were inten-sively explored at the CBS-QB3 level of theory, given in Fig.2 Even though both isomers react on the same sur-face, we artificially separate the surface in two parts, one for 2-methoxy-2-oxoethyl (cf Fig.2a) and the other for (acetyloxy)methyl (cf Fig.2b) This separation is feasible because—as we will discuss later—the reaction pathways connecting these parts are sufficiently slow that for all
Fig 2 Simplified potential energy diagram for the reactions between
MA radicals with molecular oxygen at 0 K: (a) •CH2C
(= O)OCH3? O2 and (b) CH3C(=O)OC•H2? O2 For
simplification, channels with barrier higher than 15.0 kcal/mol (e.g., beta-scission reaction from I2 and I4) are not included Calculations were carried out at the composite CBS-QB3 level of theory
Trang 5practical purposes both parts are, from a kinetic point of
view, independent To simplify the figure, dissociation
channels originating from the two initially formed adducts,
namely •OOCH2C(=O)OCH3 (I1) and CH3C(=O)OCH
2-OO• (I3), to form bimolecular products as well as
high-energy pathways (e.g., having the barrier higher than
15 kcal/mol above the entrance channel) are omitted
Formation/stabilization of initially formed adduct ROO•
The strength of the formed C-OO bond in the alkyl peroxy
radicals (or the ROO• well depth) determines the
impor-tance of the collisional stabilization channel and the
tem-perature and pressure at which this reaction plays a role
Re-dissociation of ROO•is believed to be the main cause
for negative-temperature coefficient (NTC) behavior [39];
thus, it is expected the behavior of biodiesel surrogates due
to the ester group –C(=O)O–, at least for this system, and is
different from the analogous alkyl systems The
combina-tion of both MA radicals and molecular oxygen produces
the adducts via a barrierless reaction (cf Fig.2)
The C-OO bond energy at 298 K of •OOCH2C(=O)
OCH3 (I1) is about 8.4 kcal/mol smaller than that of
CH3C(=O)OCH2OO• (I3) (25.5 and 33.9 kcal/mol for I1
and I3, respectively) The latter value is closer to those of
alkyl systems (35.6, 37.4, and 38.7 kcal/mol for primary,
secondary, and tertiary carbon sites, respectively) [40,41]
suggesting that the effect of –C(=O)O– group is less
sig-nificant on this site Note that the stabilization trend of the
adducts is opposite to that of the corresponding radicals
before adding O2 This can be explained in terms of
hyperconjugation effects as discussed for similar alkyl
systems by Villano et al [40, 41] and Porter et al [42]
This can be clearly seen by looking at the adducts’ singly
occupied molecular orbitals (SOMO), given in Fig.3 The
SOMO of intermediate I3 occupies more space than that of
I1 makes I3 more stable Specifically, the SOMO of I3
includes the two O atom of –C(=O)O– group while only
one O atom of –C(=O)O– group for I1 This leads to the
more sufficient hyperconjugation effect in I3, which low-ered its energy of 7.5 kcal/mol compared to I1 at 0 K
•CH2C(=O)OCH3? O2 system The initially formed adduct, •OOCH2C(= O)OCH3 (I1), can isomerize to HOOCH2C(= O)OC•H2(I2) involving a seven-membered ring TS with the energy barrier of 29.8 kcal/mol (*4.7 kcal/mol above the entrance channel); thus, the isomerization is not comparable to the re-dissociation of I1
at low temperature, making the consequent reactions of I2 less important Intermediate I2 having the relative energy
of -15.7 kcal/mol can undergo the OH-group immigration reaction with the rather high barrier of 28.5 kcal/mol (12.8 kcal/mol above the reactant channel) to form
•OCH2C(=O)OCH2OH This channel is expected not to play a role here (at least at the conditions that we are interested in) even the product has the lowest relative energy (-68.4 kcal/mol) This is confirmed in the rate constant analysis session (cf Rate Constant Calculations) Alternatively, I2 can dissociate to form two bi-molecular products: (1) aldehyde channel, CHO–C(=O)OCH3? OH, and (2) cyclic ether channel, cy[CH2C(=O)OCH 2-O] ? OH The latter goes through a five-membered ring
TS involving O–O bond breaking and C–O bond forming, with the lower barrier energy compared to the other channel (*2.9 vs 9.9 kcal/mol), identified as one of the important reaction pathways from an alkyl–ester radical to formation of CO2via the radical OCHO [7] In summary, the energetically important channels are the formation and re-dissociation of the adduct I1 and due to the narrower of the well-depth, the formation of the adduct plays a less important role compared to the alkyl systems A more detailed picture can be seen in the rate constant analysis
CH3C(=O)OC•H2? O2 system Similarly, radical CH3 C(= O)OCH2OO•(I3) is formed via a barrierless reaction but with a deeper well-depth of 33.9 kcal/mol at 298 K (com-pared to 25.5 kcal/mol of I1) This value is closer to those of the alkyl systems (* 35.6 kcal/mol for primary carbon site) suggesting that the effect of –C(= O)O– group is less signif-icant on this site compared to the alkyl ones In addition to
Fig 3 Singly occupied
molecular orbitals (SOMO) for
the two initially formed adducts:
(a)•OOCH2C(= O)OCH3(I1)
and (b) CH3C(=O)OCH2OO•
(I3)
Trang 6dissociation back to the reactants, this adduct can isomerize to
form •CH2C(=O)OCH2OOH (I4) (through 1,6 hydrogen
migration) and CH3C(=O)OC•HOOH (through 1,3 hydrogen
migration) with the barrier height of 30.5 and 41.3 kcal/mol,
respectively The latter radical is unstable; thus, it, once
formed, easily dissociates to form CH3C(=O)OCHO and OH
The barrier difference between the two hydrogen migration
reactions is mainly due to the ring strain energy of different
ring sizes (7-membered vs 4-membered ring) This leads to
the dominance of the formation of•CH2C(= O)OCH2OOH
(cf rate constant calculations for detailed analysis) which can
dissociate to form several bi-molecular products among which
the formation of aldehyde (CH3C(=O)OCHO) and cyclic
(cy[CH2C(=O)OCH2O]) compounds has the barriers
com-parable to the entrance channel (0.3 and 0.5 kcal/mol at 0 K
above the entrance channel, respectively); thus, these two
channels are expected to be energetically important even at
low temperature Note that the lower-energy conformers are
considered if there are more than two conformers including
the cyclic transition states (e.g., chair and boat for
6-mem-bered ring conformers)
For the considered systems, the unimolecular degradation
due to beta-scission reaction will occur at intermediates I2
and I4, which are the products of the isomerization reaction
Since the isomerization is not important in this system, the
consequent beta-scission does not play a role here In
addi-tion, the barrier for these channels is high; specifically, the
barriers of the I2? HOOCC(=O) ? CH2O and
I4? CH2C=O ? OCH2OOH are 32.1 and 45.1 kcal/mol,
respectively (16.4 and 20.3 above the entrance channel,
respectively) For larger systems where isomerization can
dominate (i.e., molecules with longer carbon/oxygen
back-bone chains which allow faster isomerization due to the
larger ring size of the TS), the beta-scission reaction is
expected to play a more important role, especially in high
temperature regime
Thermodynamic properties
Thermodynamic properties including heat of formation
(4fH), entropy (S), and heat capacity at constant pressure
(Cp) were calculated, following the procedure described in
the ‘‘Thermodynamic Property Calculations’’ session
above The calculated numbers as well as literature values
for selected species are provided in Table1in an attempt
to evaluate the reliability of our numbers The
thermody-namic data for all species involved in the system can be
found in the accompanied Supplementary material The
available experimental/calculated data (from NIST [43]
and Active Thermochemical Tables (ATcT) [44, 45])
confirm that our calculated values are within expected
uncertainty range for4fH, S and Cp The average
differ-ences in4fH298 K, S298 K, and Cp298 Kbetween our numbers
and ATcT approach are 0.8 kcal/mol, 1.9 cal/mol-K, and 0.5 cal/mol-K, respectively The difference in 4fH is normally less than 1 kcal/mol which is normally defined as
‘‘chemical accuracy’’ This excellent agreement gives us more confidence on our calculations
The good agreement with the literature data, together with the previous success of this method for analogous alkyl?O2systems [18,19,40,41], provides evidence that the CBS-QB3 level of theory is adequate for calculating accurate thermodynamic data for the title reactions This theory is a good compromise between accuracy and com-puting time, especially in the context of extending this type
of analysis to larger biodiesel methyl ester radical reactions (perhaps up to the C8 level) in an attempt to derive the rate rules for real biodiesel molecules We anticipate that these results can be generalized in the form of rate rules that could then be applied confidently to ester alkyl?O2 reac-tions involving even larger ester alkyl radicals generated from realistic biodiesel fuels
Rate constant calculations
Calculation of the pressure-dependent rate coefficients using QRRK theory requires specification of the high-pressure rate coefficients for each reaction pathway With the exception
of the addition of O2to MA radicals whose rate constants were adopted from the analogous propyl ? O2system [19], high-pressure rate coefficients for all important reaction pathways were calculated using unadjusted CBS-QB3 results, following the procedure described earlier Calcu-lated high-pressure rate constants for all individual channels for MA systems over the temperature range 300–1,500 K are given in Table 2 The rate constants for the reverse reactions, calculated from the corresponding equilibrium constants and the forward rate constants, are also provided in the table The literature data for those reactions are limited For example, there are only two reactions (Rxn 3 and Rxn 9
in Table2) whose rate constants were suggested by Hakka and coworkers [22] The ratios of our values to Hakka’s data for these two reactions at 1,000 K are 1.8 and 0.25, respectively Since Hakka et al reported no detail or justi-fication for their suggested rate constants, we strongly believed that our values, which are rigorously derived from the accurate CBS-QB3 level under the solid statistical mechanic framework (see Thermodynamic Property Sec-tion), are more reliable and thus should be confidently used for analyzing the effect of pressure in the next section as well
as for other related applications
Pressure dependence analysis
We have calculated high-pressure rate constants for the reactions between two MA radicals with molecular oxygen
Trang 7In this section, we investigate the effect of pressure on rate
constants, thus affecting the product distribution The
cal-culated high-pressure rate constants were used to compute
the pressure- and temperature-dependent rate constants
This QRRK analysis included all the pathways shown in
Fig.2 as well as several low-barrier dissociation channels
from all isomers A complete list of the calculated rate
constants for all channels over the temperature range
300–1,500 K at 0.1, 1.0, and 10 atm was included in the
Supplementary Table S5
Some representative results on the effect of pressure at
different temperatures (e.g., 300, 600, and 800 K) for both
chemically and thermally activated reactions for
•CH2C(=O)OCH3? O2and CH3C(=O)OC•H2? O2
sys-tems are presented in Figs.4 and 6 The effect of
tem-perature at different pressures (e.g., 0.1, 1, and 10 atm) for
all channels for the two systems is also presented in Figs.5
and7
For both radicals, the dominant reaction is formation of
the corresponding stabilized peroxy adducts The
impor-tance of this channel is expected to be more profound for
the CH3C(=O)OC•H2? O2system at the same condition
(cf Fig.6) due to the deeper well depth as discussed above
The re-dissociation of the adduct to the reactants is less
profound for this system due to relatively low barrier of the competing isomerization channel (2.9 kcal/mol lower than the re-dissociation, cf Fig 2) The different pressure dependencies observed for the two systems (cf Figs.4,5,
6, 7) are consistent with the general pressure-dependent features of the analogous alkyl?O2 reactions [18, 19], which will be described in the following session
The most important chemically activated channel (reactants ? intermediates/products) is the stabilization but its importance decreases with temperature (or the other competing reactions become more and more important) For example, for the •CH2C(=O)OCH3? O2system, rate constants to the adduct decrease from 300 to 800 K (4 9 10?12 and 3 9 10?11 at 1 atm, respectively, cf Fig.4a, c), while rate constants to other channels increase (e.g., 4 9 10?4 and 7x10?7 for HOOCH2C(= O)OC•H2
(I2) formation) The ratios of the two most dominant reactions (e.g., R ? I1 and R ? I2) at 1 atm are
1 9 10?8 and 4 9 10?3 at 300 and 800 K, respectively For the CH3C(= O)OC•H2? O2 system, the ratios of
R? I3 to R ? I4 channels at 1 atm are 3 9 10?5 and
3 9 10?2 at 300 and 800 K, respectively (cf Fig.6a, c) Therefore, for the chemically activated channels, the for-mation of the adducts is the dominant ones (e.g.,
Table 1 Comparison of calculated thermodynamic properties of selected stable species involved in the system with experimental/calculated data (ATcT = active thermochemical tables [ 44 , 45 ] a , NIST Webbook NIST [ 43 ])
Species Method 4 f H298c S298 Cp300 Cp400 Cp500 Cp600 Cp800 Cp1000 Cp1500
NIST -27.70 [ 50 ] 52.33 [ 50 ] 8.47 9.38 10.45 11.52 13.37 14.81 17.01 [ 49 ]
• CH2C(=O)OCH3 This work -53.17 77.91 21.10 25.46 29.36 32.64 37.69 41.31 46.69
Units: kcal/mol for 4 f H 298 and cal/mol-K for S and Cp
a Values collected from Burcat’s online database, http://garfield.chem.elte.hu/Burcat/burcat.html (access date: Dec 2013)
b Data were calculated at CBS-QB3 level of theory
c 4 f H298was calculated by atomization method
d The radical position cannot be identified
Trang 8accounting for more than 99 % of the reactant consumption
in the temperature of 300–1,500 K and pressure of larger
than 1 atm)
•CH2C(=O)OCH3? O2 system As the temperature
increases, the stabilization channel appears to approach the
high-pressure limit at higher pressures (e.g., 0.1 atm and
1 atm at 300 and 600 K, respectively, cf Fig.4a, b), while
other rate constants for chemically activated bimolecular
product channels continue to decrease as pressure
increa-ses For this reason, it is expected the complexities
involved in chemically activated reaction play a role at a
low pressure For example, at 800 K and below 0.6 atm (cf
Fig4c), the rate constant of the cyclization channel is
higher than that of the isomerization even though the
high-pressure rate coefficient for the former is much lower due
to the multiple reaction pathways The cyclization pathway
becomes more competitive as temperature increases and
pressure decreases because of the arrangement of the transition state via five-membered ring with a high barrier height of 18.6 kcal/mol This process is believed to favor at higher temperature and lower pressure It is expected to be
a sensitive channel to the temperature and pressure For the thermally activated channels of the initially formed adduct, the fastest channel is the dissociation back
to form the reactants as discussed above This channel is believed to be the main cause for NTC behavior for hydrocarbon fuels [39] Because this channel has the lowest barrier (25.1 kcal/mol compared to the barrier of 29.8 kcal/mol for the second lowest reaction, isomeriza-tion), it plays a role up to 1,000 K (accounting for larger than 99 % at P [ 1 atm) Again, the formation of cyclic channel becomes more competitive as temperature increased; however, it does not compete to the isomeriza-tion reacisomeriza-tion to form I2 up to 800 K at low pressure of
Table 2 High-pressure rate constants for reactions of MA radicals with O2and comparison with available literature data
1 CC(=O)OC•? O2=[ CC(=O)OCOO• 1.48 9 1012 0.00 -0.61 (see Huynh et al [ 19 ])
3 CC(=O)OCOO•=[•CC(=O)OCOOH 6.03 9 103 2.48 26.71 1.25 9 105b(2.30 9 105)
•
cy[CC(=O)OCO] ? OH =[•CC(= O)OCOOH 1.15 9 103 3.04 51.95 –
8 •CC(=O)OC ? O2=[•OOCC(=O)OC 1.48 9 1012 0.00 -0.61 (see Huynh et al [ 19 ])
9 •OOCC(=O)OC =[ HOOCC(=O)OC• 1.18 9 103 2.52 25.97 3.46 9 105b(8.62 9 104)
•
Rate constants are given as k(T) = A 9 Tn9 exp(-Ea/RT), Valid for 300–1,500 K Hydrogen is not explicitly given in the molecule formula for simplicity
The maximum error for fitting to k(T) = A 9 T n 9 exp(-Ea/RT) is generally less than 3.5 % but in a very few cases is about 5.0 % The values
in parentheses obtained from this work at 1,000 K
a Units of [s -1 ] for first-order reactions and [cm 3 mol -1 s -1 ] for second-order reactions
b From the work of Hakka et al [ 22 ] at the same temperature
Trang 90.05 atm (cf Fig.4f) All of the major pathways are near
their high-pressure limiting rate constants at about 1 atm at
600 K At higher temperatures, the pre-exponential term of
the rate constant becomes increasingly more important
This is shown in the Fig.5which presents the temperature
dependence at 0.1, 1.0, and 10.0 atm for the most important
reaction pathways As pressure increases, the stabilization
channel approaches the high-pressure limit at higher
tem-perature (about 400 and 500 K at 1 and 10 atm, cf Fig.5b,
c) The stabilization channel is still the most important
one as we expected earlier; especially at high pressure
where the similar trend for n-C3H7 ?O2 system was observed [19] The rate constants of other channels gen-erally decrease with increasing pressure Note that the cyclization channel through the five-membered TS has been more affected by pressure as mentioned before With this reason, its rate constant decreases faster with increas-ing pressure compared to the remainincreas-ing competitive channels These complexities illustrate the necessity of properly accounting for pressure effects The Fig.5d–f presents the pressure effects for the thermally activated channels, I1 ? products The most dominant channel is
Fig 4 Rate coefficients for•CH2C(=O)OCH3? O2? products (a–c) and•OOCH2C(=O)OCH3? products (d–f) as a function of pressure at
300, 600, and 800 K Only the most important reaction pathways are shown
Trang 10the re-dissociation to the reactants, which becomes much
more important with increasing pressure at lower
temper-ature Other pathways are less competitive again in this
system
For the •CH2C(=O)OCH3 system, the important
chan-nels for this radical system are the formation of the initial
adduct and the re-dissociation back to the reactants of the
adduct Other channels, having much higher barrier, do not
play a role for this system at least at low temperature and
the high pressure Therefore, at engine-liked conditions
(e.g., pressure [30 atm), the significance of these two
reactions is expected to be more profound
CH3C(=O)OC•H2? O2 system Some representative
results on the effect of pressure at the temperature of 300,
600, and 800 K are presented in Fig 6 For the chemical-activated channels, the dominant reaction is the formation
of the corresponding stabilized adduct, CH3C(= O)OCH
2-OO•(I3) The different pressure dependencies observed in this figure are consistent with the earlier discussion The stabilization channels appear to be approaching the high-pressure limit near 1 atm at 600 K (cf Fig.6b), while the rate constant for the bimolecular product channels continue
to decrease as pressure increases (cf Fig.6a–c)
With respect to thermally activated reactions of the sta-bilized adducts, the similar trend is observed for this system (cf Fig 7) The isomerization to form I4 (via five-membered TS), the concerted elimination to form the aldehyde channel, and the cyclization channel can play a role at certain
Fig 5 Rate coefficients for •CH2C(= O)OCH3? O2? products (a–c) and •OOCH2C(=O)OCH3? products (d–f) as a function of temperature at 0.1, 1.0, and 10.0 atm Only the most important reaction pathways are shown