Kinetics of Hydrogen Abstraction Reactions of Methyl Palmitate and

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Kinetics of Hydrogen Abstraction Reactions of Methyl Palmitate and Octadecane by Hydrogen Atoms Yawei Chi, and Xiaoqing You J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b08802 • Publication Date (Web): 21 Mar 2019 Downloaded from http://pubs.acs.org on March 21, 2019

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The Journal of Physical Chemistry

Kinetics of Hydrogen Abstraction Reactions of Methyl Palmitate and Octadecane by Hydrogen Atoms Yawei Chia, b and Xiaoqing Youa, b* a

Center for Combustion Energy, Tsinghua University, Beijing, 100084, China

b

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing, 100084, China *Corresponding

Author

E-mail: [email protected]

ACS Paragon Plus Environment

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Abstract: Hydrogen abstractions play a crucial role in the consumption of fuel molecules during fuel pyrolysis and combustion processes. In this study, a generalized energy-based fragmentation approach was used to obtain CCSD(T)-F12a/cc-pVTZ energy barriers of hydrogen abstraction reactions by hydrogen atoms from methyl palmitate (C15H31COOCH3), a key component of biodiesel. The accuracy of M06-2X/6-311++G(d,p) for obtaining the energy barriers was evaluated against the CCSD(T) results. Based on the quantum chemical results, the high-pressurelimit rate constants for C15H31COOCH3 + H were calculated and compared with those of octadecane (n-C18H38) reacting with H. The treatment of hindered internal rotations for such long chain molecules was discussed and the rate rules for different abstraction sites were summarized. The results show that in the C15H31COOCH3 + H system, the α hydrogen abstraction no longer plays a dominant role as in small methyl esters, and the hydrogen atoms of CH2 groups far away from the ester group are more easily abstracted than those near the ester group.


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 INTRODUCTION The sustained depletion of fossil fuels and accelerated environmental degradation are motivating many research efforts to discover alternative fuels.1-3 Known for its environmental friendliness and sustainability, biodiesel has attracted more and more attentions in past few decades.4-8 It is a blend of long-chain fatty acid methyl esters derived from the trans-esterification of vegetable oil or animal fat feedstocks, which makes the combustion behaviors of biodiesel fuels quite different from those of diesel fuels that are mainly consisted of hydrocarbons.7-8 To fully utilize biodiesel fuels in engines, the chemical kinetic studies are crucial for our understanding of their combustion and emission processes. The most common constituents of widely used biodiesel fuels, i.e. soybean oil and rapeseed oil, are saturated or unsaturated fatty acid methyl esters with 17–19 carbon atoms.8 Owing to the relatively large size of the components and their physicochemical complexity, detailed chemical kinetic models of these biodiesel molecules indispensably contain massive amount of species and elementary reactions. In most of the previous research, priority has always been given to important reaction classes, for instance, the hydrogen abstraction reactions.9 Dooley et al.10 have studied the auto-ignition of methyl butanoate in a shock tube and found that majority of methyl butanoate is consumed by hydrogen abstraction reactions with H atoms (58.3%), OH radicals (16.8%), O atoms (5.0%) and CH3 radicals (3.5%) at 1546 K and 1 atm, and the hydrogen abstraction by H atoms inhibits ignition at high temperatures due to its competition with the chain branching reaction of H+O2=OH+O. The simulation by Dayma et al.11 on oxidation of methyl octanoate in opposedflow diffusion flames has shown that at 1052 K about 65%, 25%, and 3% of the fuel is consumed


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by hydrogen abstraction reactions with H, CH3 and OH radicals respectively. The importance of hydrogen abstraction reactions by H can also be reflected from many other studies, such as the kinetic studies of methyl hexanoate,12 methyl heptanoate13 and methyl decanoate,14, 15 because they not only play an important role in fuel consumption but also affect the ignition of fuels at mediumto-high temperatures. Despite the great importance of hydrogen abstraction reactions, the rate constants for biodiesel molecules or large methyl esters have been obtained through estimations by extrapolation from small surrogates in terms of structure-based rate rules, due to a lack of theoretical and experimental studies. In some models, the rate constants of hydrogen abstraction reactions of methyl esters were estimated from the analogy of those on similar sites of alkanes, alkenes and alcohols. Fisher et al.16 constructed a model for the combustion of methyl butanoate, in which rate constants of the hydrogen abstraction reactions followed the rules for n-heptane and iso-octane; for example, the rate constant for the reaction occurring on the tertiary carbon of iso-octane was used for that on the carbon adjacent to the ester group (called α carbon) in methyl butanoate, because the C-H bond energies of the two sites are similar. In the combustion model of methyl heptanoate, Dayma et al.13 referred to the work by Fisher et al.,16 in which the rate constants for the primary and secondary carbons of methyl heptanoate were estimated based on those of n-heptane, respectively. The difference is that, Dayma et al.13 assumed the reactivity of H atoms on the methoxy group be identical to that in methanol,17 and used the rate constant on the vinylic carbon of 1-pentene18 for the reaction on α carbon of methyl heptanoate. The rough estimation of hydrogen abstraction rate constants would significantly affect the reaction flux of fuels. Diévart et al.14 simulated the


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oxidation of methyl butanoate with three models of Dooley et al.,10 Hakka et al.19 and Fisher et al.,16 respectively, and found large discrepancy of the branching ratio for the same hydrogen abstraction reactions among the three models, because the hydrogen abstraction rate constants were estimated from different sources. The inconsistency of the rate constants used in different combustion models suggests an urgent need for a theoretical kinetic study on the hydrogen abstraction reactions of methyl esters. Recently, some progress has been made on the theoretical investigations of hydrogen abstraction reactions of methyl esters, most of which focused on methyl butanoate (MB). Huynh and Violi20 studied the kinetics of methyl butanoate reacting with H, CH3 and OH radicals at the BH&HLYP/cc-pvTZ level of theory. They found that the hydrogen abstraction reactions of MB by H atoms contributed the most to the consumption of MB at 700–1500 K, and the hydrogen abstraction reaction on the secondary site far away from the ester group was the dominant reaction in four MB + H reactions despite of its higher energy barrier. Akih-Kumgeh and Bergthorson21 studied the hydrogen abstractions of C1–C4 alkanoic acid methyl esters with the CBS-QB3 method, and suggested that the rate constants could be optimized to predict better ignition delay times of MB. Liu et al.22 investigated the MB + H reactions with the CCSD(T)/ cc-pV∞Z//MP2/cc-pVTZ method, and reported that the computed rate constants by high-level theoretical methods were significantly different from those by rate rules and low-level ab initio methods. Zhang et al.23 studied hydrogen abstraction reactions of MB with H atoms by QCISD(T)/CBS//B3LYP/6311++G(d,p) and underlined the importance to obtain highly accurate energy barriers and to treat hindered internal rotations.


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Despite all the advances, theoretical investigations on the hydrogen abstraction reactions of methyl esters larger than MB are scarce. The rate constants of large methyl esters were often obtained by analogy from smaller methyl esters. For example, in the oxidation model of methyl decanoate by Diévart et al.,14 the rate constants of hydrogen abstraction reactions on secondary carbons (except for α carbon) were assumed to be the same as those in the methyl butanoate model of Dooley et al.10 This implies that these reactions have similar energy barriers. However, combining the ONIOM method with QCISD(T)/CBS, Zhang and Zhang24 calculated the energy barriers of all secondary hydrogen abstraction reactions of CnH2n+1COOCmH2m+1 (n = 1–5, 9, 15, m = 1, 2), and found that the reaction occurring adjacently to the α site has an energy barrier 0.8 kcal/mol higher than other secondary reactions. Consequently, the secondary hydrogen abstraction rate constants should be reaction-site dependent. For obtaining highly accurate rate constants, it is necessary to perform high-level energy calculations. However, it is infeasible to apply those high-level methods directly on the hydrogen abstraction reactions of biodiesel fuels due to the huge computational costs. Another difficulty lies in the treatment of hindered rotations for large molecules. Xu et al.

25

studied the hydrogen

abstraction from carbon-2 of 2-methyl-1-propanol by HO2 radicals, and found that neglecting multi-structural anharmonicity in rate constants would lead to errors of factors of 1.5–13 at 300– 2400 K. Li et al.26 explored the effect of tunneling, multi-structural torsional anharmonicity on the rate constants of the hydrogen abstraction of methyl butenoate by H atoms, and concluded that the multi-structural torsional anharmonicity affected the rate constants by a factor of 0.5–2.5. The multi-structural torsional anharmonicity effect is more significant in Xu et al. than in Li et al.,


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because the transition state of the abstraction reaction by HO2 radicals has much more conformers than the reactant. To examine the multi-structural torsional anharmonicity effect for large molecules such as biodiesel, it is infeasible to use the same approach for such big molecules with so many internal torsions. Hence, an alternative approach should be adopted. To obtain accurate energy barriers of hydrogen abstraction reactions of large methyl esters, we applied a generalized energy-based fragmentation (GEBF) approach27-30 on energy calculations of C15H31COOCH3 + H (represented by REx as shown in Fig. 1(a)) at the CCSD(T)-F12a/cc-pVTZ level. To balance accuracy and efficiency, a simplified method to treat the hindered internal rotations was proposed. For a better understanding of the difference of the hydrogen abstraction reactions between long-chain esters and alkanes, the kinetics of reactions n-C18H38 + H (represented by RAy as shown in Fig. 1(b)) were also studied.

(a)

(b) Figure 1. Reaction sites of (a) C15H31COOCH3 + H (REx) and (b) n-C18H38 + H (RAy), where ‘x’ and ‘y’ represent the reaction site no., varying from 1 to 16 and 7 to 15, respectively.

 METHODS The geometry optimization and vibrational frequency calculations were performed by a widely used density functional theory method M06-2X/6-311++G(d,p),31,


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proven reliable for barrier height calculations of hydrogen abstraction reactions.27, 33-34 The highlevel single point energies denoted as GEBF[CCSD(T)-F12a/cc-pVTZ] were calculated by combining the GEBF approach27-30 with the CCSD(T)-F12a/cc-pVTZ method.35-37 The GEBF method has been established on the basis of quantum locality (also called chemical locality),38-40 i.e., the interatomic interaction decays rapidly and the interaction between atoms far away from each other can be neglected. Consequently, the target molecule can be divided into small fragments for quantum chemical calculations to reduce the computation cost. This method has been demonstrated to be accurate and efficient in the energy barrier calculations for the hydrogen abstraction reactions CnH2n+1COOCH3 + H (n = 4, 5) in our previous study.41 Especially, when the fragmentation scheme with two atoms in each fragment was applied, more than 90% computational time was saved and less than 0.1 kcal/mol deviations were obtained at the CCSD(T)-F12a/cc-pVTZ level in the energy calculations of large molecules with more than 12 non-hydrogen atoms. Hence, we have taken the same fragmentation scheme in the present study. The zero-point energies from the M06-2X/6-311++G(d,p) calculations were scaled by 0.97.42 The electronic structure calculations were performed using the Gaussian 09 program43 and the GEBF[CCSD(T)-F12a/cc-pVTZ] calculations were performed with the LSQC44,

45

and

MOLPRO46 programs. The rate constants for all hydrogen abstraction reactions were computed by applying the canonical transition state theory using the MESMER program47 in which a projection method based on force-constant matrix by Sharma et al.48 is used for hindered rotations treatment. This method projects out vectors corresponding to the torsional modes from the force-constant matrix,


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and re-diagonalizes the resulting Hessian matrix to produce new harmonic frequencies, avoiding any human error in recognition of torsional modes. It should be emphasized that for large molecules such as C15H31COOCH3, the multi-dimensional internal rotation treatment method is not affordable. Therefore, we chose the one-dimensional method, which has been found in our previous study49 to be able to obtain thermochemical properties effectively and accurately. In addition, the hindrance potentials were obtained via relaxed scan at fixed dihedral angles with 10° increments by M06-2X/6-31G(d). To determine the lowest-energy structure, we examined the stationary points on the potential energy surface for all internal rotational dihedral angles. The structure with the global minimum energy was then optimized as the new lowest-energy conformer. The final lowest-energy structure was ultimately settled after repeating optimization and scan until no structure with lower energy could be found. 23 Lastly, to balance accuracy and efficiency, the one-dimensional Eckart method50 has been applied to account for the tunneling effect in the rate constant calculations. According to Li et al.26, for the hydrogen abstraction reaction from methyl butenoates by H atoms, the computed transmission coefficients using Eckart tunneling approximations were close to the multi-dimensional small-curvature tunneling approximation in the temperature range of interest to combustion chemistry.

 RESULTS AND DISCUSSION i. Energy barriers Figure 2 compares the calculated hydrogen abstraction energy barriers of C15H31COOCH3 and n-C18H38. As shown, for C15H31COOCH3 reacting with H, the agreement in energy barriers at

various

reaction

sites

between

GEBF[CCSD(T)-F12a/cc-pVTZ]


and 9


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ONIOM[QCISD(T)/CBS:DFT] by Zhang and Zhang24 is generally satisfactory, with the maximum discrepancy of 0.6 kcal/mol for RE4. The QCISD(T)/CBS energy barriers for C3H7COOCH3 + H by Zhang et al.23 at the same type of sites deviate no more than 0.2 kcal/mol from our GEBF results for the C15H31COOCH3 + H system. All these comparisons demonstrate the reliability of the GEBF[CCSD(T)-F12a/cc-pVTZ] results.

Figure 2. Energy barriers for H-atom abstraction reactions of C15H31COOCH3 and n-C18H38

Although the GEBF[CCSD(T)-F12a/cc-pVTZ] results are highly accurate, it is much more efficient to use density functional theory methods for large molecules. M06-2X/6-311++G(d,p)31, 32

has been recommended for combustion kinetics studies; however, it has never been validated

for large biodiesel molecules because of no accurate benchmark energies are available. Therefore, in the present work, the GEBF[CCSD(T)-F12a/cc-pVTZ] energy barriers were used as benchmark values for testing the performance of the M06-2X method. As shown in Fig. 2, the M06-2X/6311++G(d,p) barrier heights are commonly higher than those GEBF[CCSD(T)-F12a/cc-pVTZ] values by 0.4–0.5 kcal/mol except for RE4, where the M06-2X/6-311++G(d,p) energy barrier is


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0.7 kcal/mol lower. Since the deviations are generally small, we may use either GEBF[CCSD(T)F12a/cc-pVTZ] or M06-2X/6-311++G(d,p) energy barriers in rate constant calculations. However, the M06-2X method is more efficient for obtaining the internal rotation energy surfaces, therefore we applied the M06-2X/6-311++G(d,p) energies in the detailed kinetics analysis of the hydrogen abstraction reactions of C15H31COOCH3 and n-C18H38. It is worth noting that the energy barriers of RE1–RE14 are very close, ranging from 7.5 to 7.9 kcal/mol, except that the energy barrier of RE2 is slightly higher. The same trend can be found in Zhang and Zhang,24 where the energy barrier of RE2 is higher than the rest secondary hydrogen abstraction reactions by 0.89–1.22 kcal/mol. The α hydrogen abstraction reaction RE1, does not have a distinct lower energy barrier as in the small methyl esters such as methyl propanoate51 and methyl butanoate.23 As expected, abstracting hydrogen atoms from the two methyl groups (RE15 and RE16) have higher energy barriers; especially, the energy barrier of methoxyl hydrogen abstraction (RE16) is the highest for both methyl butanoate and methyl palmitate. By contrast, the characteristics of the hydrogen abstraction reactions of n-C18H38 + H are much simpler; the highest energy barrier (RA15) is 10.9 kcal/mol, and the rest (RA7–RA14) range from 7.7 to 7.8 kcal/mol. In general, the M06-2X/6-311++G(d,p) energy barriers for C15H31COOCH3 + H and n-C18H38+ H systems are quite close at similar reaction sites with the maximum discrepancy of 0.4 kcal/mol on the primary site. ii. Treatment of hindered internal rotations The rotational potential energy surfaces are required for accurate treatment of internal rotations. However, it is very challenging and time-consuming to perform potential energy scans


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of internal rotations for all reactants and transition states of C15H31COOCH3 + H and n-C18H38 + H. In order to get a better trade-off between the efficiency and accuracy, we were obliged to use a simplified treatment of hindered rotations. We found that internal rotation potentials of C-C or C-O bonds near the reaction site of the transition states are different from those in the reactants, while the internal rotation potentials of the rest C-C or C-O bonds far away from the reaction sites in transition states can be replaced by the corresponding ones in the reactants. Take RE7 as an example. Figure 3 shows the denotation of bonds of C15H31COOCH3 and Fig. 4 exhibits the rotational potential energies for the neighboring bonds (b7–b9) of reactant and transition state of RE7. The results of b10–b12 are not shown in Fig. 4, since they are almost coincided with those of b7–b9. The potential energy scan results for all species can be found in the supporting information. As shown in Fig. 4, the potential energy scan results for b7, b8 and b9 in the reactant C15H31COOCH3 are almost identical. The greatest difference in potential energy surfaces between the reactant and the transition state lies in the rotation around bond b9 with the maximum difference of 1.5 kcal/mol, while the differences for b8 and b7 are quite small and almost disappear for bonds far away from the reaction site 7, i.e. b1, b2, b5, b6, b13–b17. The results for other transition states follow a similar pattern. Therefore, the rotational potential energy surfaces for bonds far away from reaction sites in transition states can be replaced by the corresponding ones in the reactant. We call it the simplified treatment of hindered internal rotations. Note that the rotational potential energy surfaces of b3 and b4 in the transition states should not be replaced, because they are quite different from those of the reactant due to the bending structure near the ester group, which can be seen in the supporting information.


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Figure 3. Denotation of C-C and C-O bonds in C15H31COOCH3

Figure 4. Potential energy scan results of internal rotations near the reaction site of RE7 for the reactant (reac) and the transition state (ts7)

To check the accuracy of this simplified treatment of hindered internal rotations, the rate constants of several randomly chosen reactions RE1, RE4, RE7, RE10, RE13, and RA7, RA9, RA11, RA13, RA15 were calculated with the treatment of hindered rotations of varying accuracy. Figure 5 shows the ratios of kpart to kall as a function of Num (the number of internal rotations of transition state using the direct potential energy scan results). kpart mean the rate constants calculated with part transition-state rotational potential energy surfaces from direct scan of the transition state and the rest from the corresponding ones of the reactant, and kall mean the rate constants calculated with all transition-state rotational potential energy surfaces from direct scan of the transition state. Consequently, kpart is closer to kall with increasing Num.


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As shown in Fig. 5(a), only the torsions around b3, b4 and the left and right two bonds of the reaction sites impact greatly on the rate constants, because the potential energies of the internal rotations far away from reactions sites in transition states are nearly identical with those of the corresponding ones in the reactant, which cancels out their effects on the rate constants. When we consider the torsions around b3, b4 and no more than three bonds on each side of the reaction sites of transition states, the largest deviation of kpart from kall is 42.8% at 500 K, and 16.5% at 2000 K. For the n-C18H38 + H system in Fig. 5(b), since the potential energy surfaces for most internal rotations in transition states nearly overlap with those in the reactant, only the neighboring internal rotations on both sides of the reaction sites of the transition states have a significant effect and need to be considered. Consequently, when we take the potential energy surfaces of three internal rotations on each side of the reaction sites from the relaxed scan of transition states (Num = 6 in Fig. 5(b)), kpart deviate from kall by no more than 19.7% at 500 K and 4.7% at 2000 K. Hence, to balance computational costs and accuracy, most of the internal rotation potential energy surfaces of the transition states may be replaced by those of the corresponding ones in the reactants, except for the three internal rotations on each side of the reaction sites for n-C18H38 + H and C15H31COOCH3 + H, and the two additional rotations around b3 and b4 near the ester group for the latter.


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(a)

(b)

Figure 5. The ratio of kpart to kall as a function of the number of internal rotations scanned directly for the transition state for (a) C15H31COOCH3 + H and (b) n-C18H38+ H. (The words “left 1”, “left 2”, and “left 3” mean the first, second, and third C-C or C-O bond on the left of the reaction site, respectively. And “right 1”, “right 2”, and “right 3” mean the first, second, and third C-C or C-O bond on the right of the reaction site, respectively. )


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iii. Rate constants Figure 6 presents the rate constants calculated with the simplified treatment of hindered rotors for all hydrogen abstraction reactions of C15H31COOCH3 by H atoms. We can see that RE6 and RE13 are tied for the first place. As expected, it is more difficult to abstract hydrogen atoms from two methyl groups (RE15 and RE16) due to the higher energy barriers, especially at low temperatures. RE15 occurring on the methyl group far away from the ester group is 1–3 times faster than RE16 at 500–2000 K, although the energy barrier gap of RE15 and RE16 is only 0.4 kcal/mol. RE2 is relatively slower than most secondary hydrogen abstractions of C15H31COOCH3 at low temperatures because of the higher energy barrier. The distinctions of rate constants between RE1–RE3, RE5–RE14 are not substantial, and the ratio of rate constant of RE13 to that of RE1, k(RE13)/k(RE1) is 2.6–3.1 at 500–2000 K. It is believed that α-hydrogen atoms in methyl esters are more readily to be abstracted than all other hydrogen atoms, as shown in the theoretical studies of Zhang et al.23 and Tan et al.51, and it is also a widely used rate rule in several combustion models of methyl esters. Contrary to this accepted conclusion, RE1 is not the dominant reaction but the slowest one in all secondary hydrogen abstraction reactions except RE4. Another interesting finding is about RE4. Its energy barrier is very similar to most other secondary hydrogen abstraction reactions, but its rate constants are far smaller than all other reactions. For instance, the rate constants of RE6 are 4.8–24.8 times as big as those of RE4 at 500–2000 K.


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Figure 6. Rate constants of H-atom abstraction reactions at different sites of C15H31COOCH3

To understand why the rate constants of RE6 are much larger than those of RE4, we examined each term of the high-pressure-limit rate constant expression Eq. (1) 52 as follows, 𝑘𝑇𝑆𝑇(𝑇) = 𝜎𝜅

𝑘𝐵𝑇 𝑅𝑇 ∆𝑛 ℎ

( ) 𝑃0

≠ 𝑒𝑥𝑝( ― ∆𝐺 (𝑇) 𝑘𝐵𝑇)

(1)

where σ is the reaction path symmetry number, κ the tunneling factor, 𝑘B Boltzmann’s constant, T the temperature, ℎ Planck’s constant, R the universal gas constant, 𝑃0 the standard pressure, ∆𝑛 the difference between forward and reverse stoichiometric coefficients; Δ𝐺 ≠ (𝑇) is the Gibbs free energy of activation given by Eq. (2), ∆𝐺 ≠ (𝑇) = 𝐺TS(𝑇) ― 𝐺Reactant(𝑇)

(2)

where ‘Reactant’ and ‘TS’ represent the reactants and transition state, respectively. The Gibbs free energy G can be calculated with Eq. (3), 𝐺(𝑇) = 𝐻(𝑇) ―𝑇 ∗ 𝑆(𝑇) = 𝜀𝑒𝑙𝑒𝑐 +𝑍𝑃𝐸 + 𝐻0→𝑇 ―𝑇 ∗ 𝑆(𝑇)

(3)

where 𝜀𝑒𝑙𝑒𝑐 is the electronic energy; ZPE represents the zero-point energy; 𝐻0→𝑇 is the sensible enthalpy, i.e. the energy needed to heat the species from temperature 0 K to a certain temperature T; 𝑆(𝑇) is the entropy. The energy barrier of RE4, i.e. the difference of ZPE corrected electronic


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energy (𝜀𝑒𝑙𝑒𝑐 +𝑍𝑃𝐸) between the transition state and reactant, is only 0.13 kcal/mol lower than that of RE6. Consequently, the tunneling factors of RE4 and RE6 are almost the same. Thus, the big differences of rate constants between RE4 and RE6 lie in the differences of 𝐺TS4 and 𝐺TS6, which are 3.3–6.3 kcal/mol at 500–2000 K as shown in Fig. 7. Both the sensible enthalpy (𝐻0→𝑇) and the entropy term ( ― 𝑇 ∗ 𝑆(𝑇)) contribute to the differences of Gibbs free energy. Similarly, the differences of rate constants between RE1 and RE6 also result from the difference between 𝐺TS1 and 𝐺TS6, as shown in Fig. 7; however, the entropy term ( ― 𝑇 ∗ 𝑆) is bigger than the sensible enthalpy (𝐻0→𝑇) below 1400 K. Examining molecular structures in these reactions, we found that the differences in G lie in the change of structure of transition states. Affected by the ester group, the molecular structure bends near the ester group, and the degree of bending varies with reaction sites. As an example, Fig. 8 exhibits the lowest-energy structures of C15H31COOCH3, TS4 and TS6. The structure of TS6 is similar to that of the reactant, while TS4 is more curved. The degree of bending does not cause much difference in energy barriers, but affects greatly the sensible enthalpy (𝐻0→𝑇) and the entropy term ( ― 𝑇 ∗ 𝑆(𝑇)) by changing slightly the vibrational frequencies.


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Figure 7. Gibbs free energy differences among TS4, TS6 and TS1

(a) C15H31COOCH3

(b) Transition state of RE4, TS4

(c) Transition state of RE6, TS6

Figure 8. Structures of C15H31COOCH3, TS4 and TS6

To sum it up, in the C15H31COOCH3 + H system, the hydrogen atoms on sites 6, 13 are more readily to be abstracted than the rest secondary sites. The α-hydrogen abstraction no longer has the absolute advantage in all hydrogen abstraction reactions as we had assumed. It is difficult to abstract hydrogen atoms from 4 site and the two methyl groups, especially at low temperatures. As for the n-C18H38 + H system in Fig. 9, the rate constants of those secondary hydrogen abstraction reactions distribute within a factor of 4 at 500–2000 K with RA14 and RA7 being the fastest and the slowest, respectively. The differences of the rate constants between RA7 and RA14 are mainly caused by the differences in the entropy of the transition states. RA15, where the hydrogen atom is abstracted from the methyl group, is slower than other reactions at low temperatures, but more competitive with increasing temperatures.


19


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Figure 9. Rate constants of H-atom abstraction reactions at different sites of n-C18H38

iv. Implications on kinetic model improvement After the investigation of the kinetics of hydrogen abstraction reactions of C15H31COOCH3 and n-C18H38 by H atoms, it is necessary to examine their implications on kinetic model development for long-chain methyl esters and alkanes. In Fig. 10 and Fig. 11, we compared the calculated rate constants with those in previous studies. In nearly all combustion models of longchain methyl esters, including the methyl decanoate model of Herbinet et al.,53 the methyl decanoate model of Sarathy et al.,54 the methyl heptanoate model of Dayma et al.,13 and the methyl octanoate model of Dayma et al.,11 the rate constants of hydrogen abstraction reactions were usually estimated based on the C-H bond strengths of different groups, i.e. CH3, CH2, the CH2 group adjacent to the ester group, and the -O-CH3 group, each represented as “p”, “s”, “α”, “m” in Fig. 10, respectively. Since the rate constants of most hydrogen reactions of CH2 groups in the C15H31COOCH3 + H system are distributed between those of RE13 and RE2 except for RE4, only the calculated rate constants of RE2, RE4, RE13 are shown in Fig. 10(a). Their rate constants in


20

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most models of various methyl esters are identical, as represented by the black dashed line in Fig. 10(a); they are visibly included in the range of the rate constants from RE2 to RE13. What this implies is that there is no difference between most hydrogen abstraction reactions of CH2 groups. However, hydrogen abstraction reactions on the fourth carbon away from the ester groups (RE4) should be given extra attention. It caught our attention that there were great variances on the rate constants of α hydrogen abstraction reactions in different models. First of all, having considered the kinetic studies for the hydrogen abstraction reactions of various methyl esters in both our study and previous studies, we believe that the difference of the energy barriers between secondary hydrogen abstractions and α hydrogen abstraction is not significant enough to lead to the any big gaps among the slopes in Fig. 10(a). Secondly, the estimated rate constants for α hydrogen abstraction reactions (three red lines in Fig 10(a)) are always thought to be larger than those of secondary hydrogen abstraction reactions (black dashes line in Fig. 10(a)), while our studies reveal that this rate rule might fail for large methyl esters. Therefore the rate constants for α hydrogen abstraction reactions in most models of methyl esters may be lowered, to 1/3–1/2 of those of secondary hydrogen abstraction reactions. Commonly, the primary hydrogen abstractions are usually thought to share the same rate constants with the methoxyl hydrogen abstraction reactions, which are usually estimated by analogy with the primary hydrogen abstraction reactions of alkanes. As shown in Fig. 10(b), the estimated rate constants for the primary hydrogen abstractions are quite close to our results. However, the rate constants for methoxyl hydrogen abstractions seem to have been overestimated, especially those in Dayma et al.13, which were derived from the kinetic study of the hydrogen


21


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abstraction reactions of methanol. Thus, based on the results in this study, the rate constants of methoxyl hydrogen abstractions should be decreased to 1/4–1/2 of that of primary hydrogen abstraction reactions.

(a)

(b)

Figure 10. The H-atom abstraction reaction rate constants at several representative sites of methyl esters

There are normally two types of hydrogen abstraction reactions for the straight-chain alkanes: the primary and secondary hydrogen abstraction reactions, represented by “p” and “s” respectively in Fig. 11. In most alkane models, the rate constants of these two types of hydrogen abstraction


22

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reactions were taken from Westbrook et al.55 in 1984 on the study of C3H8, for example in the nheptane model of Chaos et al.56 Peukert et al.57 calculated the rate constants of hydrogen abstraction reactions of n-C4H10 using a high-level quantum method (CCSD(T)/cc-pV∞Z//M062X/cc-pVTZ) and validated the results against experiments. The rate constants were adopted in the combustion model of n-tetradecane by Zeng et al.58, as shown in Fig. 11. The hydrogen abstraction rate constants on p and s sites of n-C18H38 in this work were compared with literature data. For a direct comparison, we have computed the rate constants of hydrogen abstraction reaction of n-C4H10 using the same method as n-C18H38. It is worth noting that, the rate constants for primary and secondary hydrogen abstractions in the n-heptane model of Seidel et al.59 are 6 and 5 times as big as that in the model of Chaos et al.56, respectively. This is because they multiplied the source rate constants from Westbrook et al.55 by reaction path degeneracies, which however, had already been included in the source rate constants. Figure 11 shows that k(n-C4H10 +H) by Peukert et al.57 are slightly higher than our results at 500–2000 K, which is mainly due to the differences in energy barriers, where the CCSD(T)/ccpV∞Z energy barriers are lower than the M06-2X/6-311++G(d,p) ones by 0.8 and 0.7 kcal/mol for the primary and secondary hydrogen abstractions of n-C4H10, respectively. If the CCSD(T)/ccpV∞Z method were used for energy calculations, the computed rate constants of C4H10 + H would be highly consistent with those in Peukert et al.57 Comparing the rate constants of n-C4H10 and nC18H38, the hydrogen abstraction on the p site of n-C4H10 is about twice as fast as that of n-C18H38. This deviation comes from the difference in entropy changes since the energy barriers are nearly the same (about 10.9 kcal/mol), while the entropy decrease between the transition state and


23


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reactants in the primary hydrogen abstraction reaction of n-C18H38 is smaller than that for n-C4H10. Similarly, the secondary hydrogen abstraction reactions of n-C4H10 are also faster than those of nC18H38 by up to three times in spite of the minor difference in energy barriers.

(a)

(b)

Figure 11. The H-atom abstraction reaction rate constants at several representative sites of n-alkanes

Table 1. Energy barriers of the hydrogen abstractions of n-C4H10 and n-C18H38

reactant

reaction site

energy barrier

method


source

24

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(kcal/mol) n-C4H10

p site

10.07

CCSD(T)/cc-pV∞Z

Peukert et al. 57

n-C4H10

p site

10.88

M06-2X/6-311++G(d,p)

This work

n-C18H38

p site

10.85

M06-2X/6-311++G(d,p)

This work

n-C4H10

s site

7.21

CCSD(T)/cc-pV∞Z

Peukert et al. 57

n-C4H10

s site

7.91

M06-2X/6-311++G(d,p)

This work

n-C18H38

s site (RA14)

7.82

M06-2X/6-311++G(d,p)

This work

n-C18H38

s site (RA7)

7.72

M06-2X/6-311++G(d,p)

This work

 CONCLUSIONS For obtaining accurate rate constants of hydrogen abstraction reactions of large methyl esters, and for a better understanding of the difference of the hydrogen abstraction reactions between long-chain alkanes and esters, we performed a theoretical investigation on the hydrogen abstraction reactions of methyl palmitate and octadecane by hydrogen atoms. Firstly, the generalized energy-based fragmentation (GEBF) method was used to calculate energy barriers of C15H31COOCH3 + H. The good agreement between the energy barriers calculated with the GEBF[CCSD(T)-F12a/cc-pVTZ] method and those in previous studies has justified the applicability and accuracy of the GEBF[CCSD(T)-F12a/cc-pVTZ] method in energy barrier calculations. The M06-2X/6-311++G(d,p) has also been proven to be accurate enough for computing energy barriers of C15H31COOCH3 + H as the absolute deviations from the GEBF


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results are less than 0.7 kcal/mol. The rate constants of the C15H31COOCH3 + H and n-C18H38 + H systems in the temperature range of 500 K to 2000 K were calculated by applying the transition state theory based on the M06-2X/6-311++G(d,p) quantum chemical results. In order to take the hindered rotations into consideration more efficiently, we proposed a simplified one-dimensional hindered rotors treatment method. It allows most of the internal rotation potential energy surfaces of the transition states to be replaced by those of the corresponding ones in the reactants, except for the three internal rotations on each side of the reaction sites for n-C18H38 + H and C15H31COOCH3 + H and the two additional rotations around b3 and b4 near the ester group for the latter. The rate constants obtained using this simplified treatment are within an uncertainty factor of 2 of those with all rotors taken into consideration. As a simple estimation, the use of M06-2X/6-311++G(d,p) and the simplified treatment of hindered rotors would introduce an uncertainty factor of 2.5~4 for the rate constants at 500-2000 K. The results show that for the C15H31COOCH3 + H system, the fastest hydrogen abstraction reactions are RE6 and RE13, not the α hydrogen abstraction RE1 as suggested before. The rate constants of most secondary hydrogen abstraction reactions differ among one another by less than a factor of 3 except for RE4, whose rate constants are about an order of magnitude lower despite of their similar barrier heights, due to the higher sensible enthalpy and lower entropy of the transition state of RE4. Hydrogen abstractions from the two methyl groups were found to have lower rate constants with RE16 being the slowest, due to the higher barrier heights. In the n-C18H38 + H system, the secondary hydrogen abstraction reaction rate constants differ among one another by no more than a factor 4. It is also more difficult to abstract


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hydrogen atoms from the primary C-H bonds of n-C18H38, especially at low temperatures. Based on the calculated results in this work, in the combustion kinetic models of long-chain methyl esters, the rate constants of the hydrogen abstraction reactions on the methoxyl sites in most models should be lowered to 1/4–1/2 of those of the primary hydrogen abstraction reactions. And the rate constants of α hydrogen abstraction reactions should also be reduced to 1/3–1/2 of those of the secondary hydrogen abstraction reactions for large methyl esters. More attention should be given to the hydrogen abstraction reaction that happens on the fourth carbon away from the ester group. For the combustion models of long-chain alkanes, the rate constants of hydrogen abstraction reactions are slightly slower than those of the small alkanes.

 ASSOCIATED CONTENT Supporting Information. Geometries by M06-2X/6-311++G(d,p) for all species; the potential energy scans of internal rotations for all species; the Arrhenius parameters of the computed highpressure limit rate constants. This material is available free of charge via the Internet at http://pubs.acs.org.

 ACKNOWLEDGMENT This work was supported by the National Science Foundation of China (91841301), and the Foundation of State Key Laboratory of Coal Combustion (FSKLCCA1701).


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Heptane Flame. Combust. Flame 2015, 162, 2045-2058.


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TOC Graphic


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Kinetics of Hydrogen Abstraction Reactions of Methyl Palmitate and

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