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DSpace at VNU: Mechanism and kinetics of low-temperature oxidation of a biodiesel surrogate-methyl acetate radicals with...
Struct Chem DOI 10.1007/s11224-014-0495-2 ORIGINAL RESEARCH 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 Ó 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 modeling 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 products The accurate composite CBS-QB3 level of theory was used to explore potential energy surfaces for MA radicals ? O2 system Using the electronic structure calculation results under the framework of canonical statistical 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 Furthermore, pressure- and temperature-dependent rate constants were then computed using the Quantum Rice– Ramsperger–Kassel and the modified strong collision theories 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 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 Á X T Le Á 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 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 Á Oxygenated hydrocarbon Á Alkyl peroxy radical Á Detailed kinetic model Á 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 uncertain 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 component 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., 123 Struct Chem the 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 molecules 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 Therefore, 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 chemistry/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 intermediate 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 biodiesels [15] In this paper, we concentrate our efforts on characterizing 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-constructed 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 radicals ? 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 123 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?O2 systems [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 CBSQB3 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)/631?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 species 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 frequencies 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 thermodynamics calculations by an explicit evaluation of the hindered rotations in the most accurate manner as Struct Chem described hereafter The 1-D Schroădinger equation for a hindered internal rotor (HIR) is given as d2 Whir ỵ VhịWhir ẳ EWhir ; 2Ired dh2 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 torsional 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, P V hị ẳ LlẳL cl eilh , in which L is some cut-off number depending on the nature of the potential The wave function was expanded as a harmonic series, jmi ¼ p1ffiffiffiffi eimh ; 2p and plugged into HIR equation The matrix elements for the Hamiltonian are then given by Hmn hmjH jni ¼ 2p Z2p eÀimh  ¼ ! L X : o2 ilh ỵ Cl e einh dh 2Ired oh lẳL 2ị m2 dmn ỵ cmn 2Ired 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 tunneling 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 Transition 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 constants for the barrierless recombination of MA radicals with O2 were not calculated in this work but derived from similar alkyl?O2 systems [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 unimolecular rate coefficients k(E) were computed using the Quantum Rice–Ramsperger–Kassel (QRRK) theory Collisional 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 ˚ and well depths (rLJ) of 669.8 K were estimated 5.94 A 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 hEall i ¼ 440 cal/mol ˚ LJ ¼ 71:4 K) for the bath gas collider of N2 (rLJ ¼ 3:80 A,e [36] We also run calculations with the bath gas of He ˚ LJ ¼ 10:0 K) [36], and the simulation (rLJ ¼ 2:55 A,e 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 CH3C(=O)OC•H2 and •CH2C(=O)OCH3 These two radicals can isomerize to each other through the hydrogen migration reactions via five-membered ring transition 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 products 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 (a) (b) Fig 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 123 Struct Chem Fig Simplified potential energy diagram for the reactions between MA radicals with molecular oxygen at K: (a) •CH2C and (b) CH3C(=O)OC•H2 ? O2 For (= O)OCH3 ? O2 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 functional group) and to play a central role in low-temperature combustion of the title fuel [39] methyl acetate radicals and molecular oxygen were intensively explored at the CBS-QB3 level of theory, given in Fig Even though both isomers react on the same surface, 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 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 123 Struct Chem Fig Singly occupied molecular orbitals (SOMO) for the two initially formed adducts: (a) •OOCH2C(= O)OCH3 (I1) and (b) CH3C(=O)OCH2OO• (I3) practical 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)OCH2OO• (I3), to form bimolecular products as well as highenergy 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 importance of the collisional stabilization channel and the temperature 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 combination 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 significant 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 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 lowered its energy of 7.5 kcal/mol compared to I1 at 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)OCH2O] ? 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 CO2 via 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 (compared 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 significant on this site compared to the alkyl ones In addition to 123 Struct Chem dissociation 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 comparable to the entrance channel (0.3 and 0.5 kcal/mol at 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-membered 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 addition, 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 backbone 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 Table in an attempt to evaluate the reliability of our numbers The thermodynamic 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 for 4fH, S and Cp The average differK ences in 4fH298 K, S298 K, and C298 between our numbers p 123 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 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?O2 systems [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 computing 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 reactions 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 O2 to MA radicals whose rate constants were adopted from the analogous propyl ? O2 system [19], high-pressure rate coefficients for all important reaction pathways were calculated using unadjusted CBS-QB3 results, following the procedure described earlier Calculated high-pressure rate constants for all individual channels for MA systems over the temperature range 300–1,500 K are given in Table 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 and Rxn in Table 2) 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 justification 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 Section), 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 Struct Chem Table 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 4fH298c S298 C300 p C400 p C500 p C600 p C800 p C1000 p C1500 p CH3COOCH3 This workb -100.26 77.20 20.13 24.73 29.09 32.90 38.94 43.39 50.23 ATcT -99.22 76.84 20.47 24.66 28.85 32.66 38.60 43.08 49.75 NIST -98.00 [46] – 20.64 25.17 29.49 33.28 39.31 43.75 50.51 [47] This work -11.75 57.67 12.28 14.09 15.55 16.76 18.66 20.11 22.44 ATcT -11.61 60.09 12.40 14.20 15.68 16.90 18.79 20.25 22.48 NIST -11.40 [48] – 12.41 14.22 15.68 16.89 18.80 20.25 22.55 [49] This work ATcT -27.34 -26.09 52.23 52.28 8.44 8.47 9.31 9.36 10.35 10.44 11.40 11.52 13.24 13.37 14.68 14.82 16.92 16.93 NIST -27.70 [50] 52.33 [50] 8.47 9.38 10.45 11.52 13.37 14.81 17.01 [49] This work -140.62 74.19 20.43 25.20 29.17 32.21 36.26 38.79 42.39 ATcT -139.33 76.14 20.90 25.74 29.81 32.99 36.92 39.53 43.12 CH2=C=O HCHO HOCH2COOH CH3C(=O)OC•H2 • CH2C(=O)OCH3 NIST – – 20.34 24.87 28.83 32.02 36.44 39.24 43.13 [51] This work -52.06 80.19 22.06 26.21 29.88 32.95 37.67 41.10 46.35 ATcTd -52.97 75.75 20.46 24.94 28.95 32.35 37.32 40.89 46.05 NIST – – – – – – – – – This work -53.17 77.91 21.10 25.46 29.36 32.64 37.69 41.31 46.69 ATcTd -52.97 75.75 20.46 24.94 28.95 32.35 37.32 40.89 46.05 NIST – – – – – – – – – 298 Units: kcal/mol for 4fH 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 4fH298 was calculated by atomization method d The radical position cannot be identified In this section, we investigate the effect of pressure on rate constants, thus affecting the product distribution The calculated 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 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 ? O2 and CH3C(=O)OC•H2 ? O2 systems are presented in Figs and The effect of temperature at different pressures (e.g., 0.1, 1, and 10 atm) for all channels for the two systems is also presented in Figs and For both radicals, the dominant reaction is formation of the corresponding stabilized peroxy adducts The importance of this channel is expected to be more profound for the CH3C(=O)OC•H2 ? O2 system 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 ? O2 system, rate constants to the adduct decrease from 300 to 800 K (4 10?12 and 10?11 at atm, respectively, cf Fig 4a, c), while rate constants to other channels increase (e.g., 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 atm are 10?8 and 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 atm are 10?5 and 10?2 at 300 and 800 K, respectively (cf Fig 6a, c) Therefore, for the chemically activated channels, the formation of the adducts is the dominant ones (e.g., 123 Struct Chem Table High-pressure rate constants for reactions of MA radicals with O2 and comparison with available literature data Aa No Reaction CC(=O)OC• ? O2 =[ CC(=O)OCOO• 0.00 -0.61 (see Huynh et al [19]) 1.38 1015 0.00 32.64 – CC(=O)OCOO• =[ CC(=O)OC = O ? OH 5.48 102 3.18 36.61 – • 3.33 10 3.32 71.35 – 6.03 103 2.48 26.71 1.25 105b (2.30 105) CC(=O)OC = O ? OH =[ CC(=O)OCOO • 4.39 10 -0.14 19.38 – • CC(=O)OCOOH =[ C=C(OH)OCOO• 2.35 106 2.13 38.82 – C=C(OH)OCOO• =[ •CC(=O)OCOOH 7.34 1010 0.45 12.21 – • 1.09 109 1.11 22.35 – 11 CC(=O)OCOOH =[ CC(=O)OCOO• Literature data for ka at 1,000 K CC(=O)OCOO =[ CC(=O)OC ? O2 • CC(=O)OCOO• =[ •CC(=O)OCOOH Ea (kcal/mol) 1.48 1012 • n CC(=O)OCOOH =[ CC(=O)OC=O ? OH • -2 CC(=O)OC = O ? OH =[ CC(=O)OCOOH 8.62 10 3.88 64.41 – • CC(=O)OCOOH =[ HOCC(=O)OCO• HOCC(=O)OCO• =[ •CC(=O)OCOOH 1.16 1013 5.89 1010 -0.40 0.64 36.01 80.96 – – • 2.23 1014 CC(=O)OCOOH =[ cy[CC(= O)OCO] ? OH -0.72 25.06 – cy[CC(=O)OCO] ? OH =[ CC(= O)OCOOH 1.15 103 3.04 51.95 – • 1.48 1012 0.00 -0.61 (see Huynh et al [19]) 1.92 1014 0.00 24.23 – 1.18 103 2.52 25.97 3.46 105b (8.62 104) • CC(=O)OC ? O2 =[ •OOCC(=O)OC • • OOCC(=O)OC =[ CC(= O)OC ? O2 • OOCC(=O)OC =[ HOOCC(=O)OC• • 10 11 • HOOCC(=O)OC =[ OOCC(=O)OC 13 2.58 10 -0.87 18.25 – HOOCC(=O)OC• =[ O=CC(=O)OC ? OH 3.59 1010 0.36 23.25 – O=CC(=O)OC ? OH =[ HOOCC(=O)OC• 6.12 10-5 4.60 52.20 – HOOCC(=O)OC =[ OCC(= O)OCOH 3.68 1014 -0.97 28.20 – • 5.29 1010 0.65 80.94 – 3.92 1016 -1.34 19.36 – 2.99 54.05 – • • OCC(=O)OCOH =[ HOOCC(=O)OC• 12 HOOCC(=O)OC• =[ cy[CC(=O)OCO] ? OH cy[CC(=O)OCO] ? OH =[ HOOCC(=O)OC • 6.03 103 Rate constants are given as k(T) = A Tn 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 Tn 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 [cm3 mol-1 s-1] for second-order reactions b From the work of Hakka et al [22] at the same temperature accounting for more than 99 % of the reactant consumption in the temperature of 300–1,500 K and pressure of larger than 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 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 increases 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 Fig 4c), the rate constant of the cyclization channel is higher than that of the isomerization even though the highpressure rate coefficient for the former is much lower due to the multiple reaction pathways The cyclization pathway becomes more competitive as temperature increases and 123 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, isomerization), it plays a role up to 1,000 K (accounting for larger than 99 % at P [ atm) Again, the formation of cyclic channel becomes more competitive as temperature increased; however, it does not compete to the isomerization reaction to form I2 up to 800 K at low pressure of Struct Chem Fig 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 0.05 atm (cf Fig 4f) All of the major pathways are near their high-pressure limiting rate constants at about 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 which 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 temperature (about 400 and 500 K at 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 generally 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 increasing pressure compared to the remaining 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 123 Struct Chem Fig 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 the re-dissociation to the reactants, which becomes much more important with increasing pressure at lower temperature Other pathways are less competitive again in this system For the •CH2C(=O)OCH3 system, the important channels 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, 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, 123 600, and 800 K are presented in Fig For the chemicalactivated channels, the dominant reaction is the formation of the corresponding stabilized adduct, CH3C(= O)OCH2OO• (I3) The different pressure dependencies observed in this figure are consistent with the earlier discussion The stabilization channels appear to be approaching the highpressure limit near 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 stabilized 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 Struct Chem Fig Rate coefficients for CH3C(=O)OC•H2 ? O2 ? products (a–c) and CH3C(=O)OCH2OO• ? products (d–f) as a function of pressure at 300, 600, and 800 K Only the most important reaction pathways are shown conditions due to their lower barrier height The pathway via OH migration is much slower because of its higher barrier Again, all major channels are near their high-pressure limiting rate constants at *1 atm at 600 K In conclusion, the pressure behavior of the CH3C(=O)OC•H2 ? O2 system is similar to that of •CH2C(=O)OCH3 ? O2, except for the increasing importance of the concerted elimination channel The most dominant channel is the adduct stabilization which is more competitive than other channels at low temperature and high pressure Therefore, it is necessary to investigate the pressure effects for an accurate description of its kinetics The effect of the pre-exponential factor plays a more and more important role with the temperature This is shown in Fig which presents the temperature dependence of the apparent rate constants for CH3C(=O)OC•H2 ? O2 ? products (cf Fig 7a–c) and CH3C(=O)OCH2OO• ? products (cf Fig 7d–f), where the most dominant channel is still re-dissociation to the reactants The increasing importance of the concerted elimination reactions to form aldehyde ? OH at higher temperature (cf Fig 7a–c) is due to its higher A-factor relative to the cyclic ether ? OH channel and its lower 123 Struct Chem Fig Rate coefficients for CH3C(=O)OC•H2 ? O2 ? products (a–c) and CH3C(=O)OCH2OO• ? 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 barrier height (0.3 and 0.5 kcal/mol above the entrance channel, respectively) The higher A-factor value for the concerted elimination can be explained by the fact that the transition state of this pathway ties up one more hindered rotor than the transition state for the 1,5-H shift isomerization reaction to form the cyclic ether compound Important channels According to the pressure analysis above, it is noticed that at common low-temperature combustion conditions in engine (e.g., 300 K \ T \ 1,000 K and P [[ atm), the most 123 important reactions are Rxns 1–4 (cf Table 3) whose rate constants sum up to 99 % or more of the overall rate constant for each of the two MA radicals ? O2 systems The other channels such as isomerization, cyclic ether formation, and concerted HO2 elimination are less important at the same conditions The OH migration reactions discussed earlier are even less important Thus, in spite of the complexity of the full potential energy surface, only two chemically activated reactions and two thermally activated reactions are found to be important at practical low-temperature combustion conditions Note that for larger systems which allow faster isomerization reactions (due to larger TS Struct Chem Table Simplified MA radicals ? O2 submechanism at low-temperature combustion conditions Radicals ? O2 channels • CH2C(=O)OCH3 ? O2 ? •OOCH2C(=O)OCH3 (Rxn 1) CH3C(=O)OC•H2 ? O2 ? CH3C(=O)OCH2OO• (Rxn 2) ROO dissociation channels • OOCH2C(=O)OCH3 ? C•H2C(=O)OCH3 ? O2 CH3C(=O)OCH2OO• ? CH3C(=O)OC•H2 ? O2 (Rxn 3) (Rxn 4) Valid in the temperature range of 300–1,000 K and P [ atm ring size), different subsequent reactions of the isomerization products such as beta-scission, cyclic ether formation, and OH migration can compete with the dominant channels observed in the MA ? O2 systems The competition makes the behaviors of larger systems more complicated, especially the pressure dependence of the rate coefficients Conclusions We have constructed accurate potential energy surfaces for methyl acetate radicals ? O2 reactions at the CBS-QB3 level of theory Thermodynamic properties of all species were calculated with explicit corrections for hindered internal rotations Pressure- and temperature-dependent rate constants for the various channels of this system were derived under the QRRK/MSC framework with high-pressure rate constants obtained from the transition state theory with explicit Eckart tunneling treatment A thermodynamically consistent detailed kinetic mechanism, consisting of all elementary reactions together with their thermodynamic and kinetic data (given in the accompanied Supplementary Table S7), was constructed for low-temperature oxidation and auto-ignition of the title fuel The simplified mechanism, consisting of reactions (cf Table 3), was also composed specifically for the engine-liked conditions The mechanism, either full or simplified, can be used as a solid building block to construct detailed kinetic mechanisms for low-temperature combustion of real fuel molecules In addition, since MA is the smallest biodiesel surrogate, the several unimportant reactions existing in the system such as isomerization, cyclization, and concerted HO2 elimination can play an important role in larger systems; thus, MA is not a good surrogate model for investigation of the lowtemperature oxidation of real methyl ester For this purpose, larger methyl ester molecules such as methyl propanoate and methyl butanoate should be considered Supporting Information Available (1) Conventional names, short notations, and 2-D structures for all species; (2) Tabulated values for electronic structure calculations (geometries, energies, frequencies) for the MA radicals ? O2; (3) Calculated reaction barrier and reaction energy at the CBS-QB3 level comparing with other methods for several important channels; (4) Tabulated calculated thermodynamic properties of species are formed from reactions in system; (5) Tabulated values for the pressure-dependent apparent rate constants for the various reactions as a function of temperatures at 0.1, 1.0, and 10.0 atm; (6) Potential energy surfaces for the internal rotations for some stable species; (7) Detailed kinetic submechanism in Chemkin format for MA radicals ? O2 ? 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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... 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... kcal/mol for 4fH 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