Exploring the pyrolysis chemistry of prototype aromatic ester phenyl formate: Reaction pathways, thermodynamics and kinetics

Combustion and Flame 211 (2020) 337–346

Contents lists available at ScienceDirect

Combustion and Flame journal homepage: www.elsevier.com/locate/combustflame

Exploring the pyrolysis chemistry of prototype aromatic ester phenyl formate: Reaction pathways, thermodynamics and kinetics Hongbo Ning a, Junjun Wu b, Liuhao Ma b, Wei Ren b,c,∗ a

Key Laboratory of Advanced Technologies of Materials, Ministry of Education, and Institute of Material Dynamics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China b Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, New Territories, Hong Kong SAR, China c Shenzhen Research Institute, The Chinese University of Hong Kong, New Territories, Hong Kong SAR, China

a r t i c l e

i n f o

Article history: Received 30 May 2019 Revised 19 August 2019 Accepted 1 October 2019

Keywords: Phenyl formate Pyrolysis Ab initio calculation Reaction kinetics

a b s t r a c t We performed systematic ab initio calculations for the pyrolysis of phenyl formate (PF), the simplest aromatic ester, to establish the potential energy surfaces (PESs), thermodynamics and reaction kinetics. Reaction pathways considered in this work include direct bond fission and intramolecular H-shift, as well as subsequent radical decomposition and ipso-addition by H, O and OH radicals. The energies of reactants, transition states and products were determined at the ROCBS-QB3//M062X/cc-pVTZ level of theory. The standard enthalpy of formation of each species was determined using the atomization method, showing a good agreement with the literature results. For the PF unimolecular decomposition, the intramolecular H-shift reactions to produce phenol + CO and 2,4-cyclohexadienone + CO are the dominant decomposition pathways. Among the decomposition reactions of PF radicals, the isomerization and β -scission channels to form phenoxy + CO and C6 H4 OH + CO are the dominant pathways. Additionally, for the ipso-addition reactions, PF + H/O → HCOO + C6 H6 /C6 H5 O and PF + OH → HCOOH + C6 H5 O are the major pathways. Multiwell and multi-channel phenomenological rate constants were determined using the Rice–Ramsperger– Kassel–Marcus/master equation (RRKM/ME) method at 50 0−20 0 0 K and the pressure range of 0.01 atm to the high-pressure limit. It is of interest to observe that the corresponding intermediates for PF radical decompositions with lower energy barriers are merged at higher temperatures and lower pressures. The rate constants of ipso-addition reactions are almost pressure-independence especially at higher temperatures (> 10 0 0 K). © 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Biodiesel is a prevalent alternative that can be used as a neat fuel or in blends with fossil fuels. It is derived from the soybean oil (primary source in US) or rapeseed oil (major source in Europe) and consists of varying amounts of C16 −C18 saturated and unsaturated methyl esters [1]. The ultra low sulfur makes it even more attractive for reducing pollutant emissions. The biodiesel-hybrid diesel can also enhance the thermal efficiencies of traditional diesel fuels [2]. Moreover, the presence of oxygen atoms in biodiesel molecules reduces the soot formation in diesel engines [3]. Hence, it is particularly important to elucidate the chemical kinetics of biodiesels to appropriately identify their combustion and emission characteristics. Unfortunately, only a few studies on large biodiesels have been reported [1,4–10] due to

∗ Corresponding author at: Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, New Territories, Hong Kong SAR, China. E-mail address: [email protected] (W. Ren).

the large molecular size and the reaction complexity of the ester functional group. Most of the previous studies focused on smaller straight-chain methyl esters (i.e., methyl formate, MF; methyl acetate, MA; methyl propanoate, MP; methyl butanoate, MB) as surrogates to help understand the kinetic behavior of the practical biodiesels. Little attention has been devoted to understanding the chemical kinetics of aromatic esters which may help us fully understand the combustion chemistry of esters. Phenyl formate (PF) is the simplest aromatic ester that can be produced by esterification of phenol and formic acid. This molecule also contains two very interesting functional groups, phenyl and ester groups. It is of kinetic interest to investigate how PF behaves differently from the conventional aromatic hydrocarbons and alkyl esters, as well as to understand the interaction between these two functional groups. In addition, we find that PF could be a potential fuel or surrogate for the following three reasons: (1) PF has the similar reactivity as anisole (a significant biomass surrogate) shown in Fig. 1; (2) PF has a higher oxygenated content (26.2%) than anisole (14.8%); and (3) the reaction heat released by

https://doi.org/10.1016/j.combustflame.2019.10.002 0010-2180/© 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

338

H. Ning, J. Wu and L. Ma et al. / Combustion and Flame 211 (2020) 337–346 Table 1 The standard enthalpy of formation (kcal mol−1 ) of species in PF decomposition at 298.15 K.

Fig. 1. Bond dissociation energies of PF [11] and anisole [12].

PF (−778.4 kcal mol−1 ) and anisole (−870 kcal mol−1 ) has a slight difference of 10%. Note that the enthalpy of formation of PF is calculated to be −53.3 kcal mol−1 , compared to −19.4 kcal mol−1 for anisole. In our recent study [11], the H-abstraction reaction kinetics of PF by different radical species (H, O, OH and HO2 ) were theoretically investigated and validated by shock tube experiments. The bond dissociation energy (BDE) calculations revealed there was a significant difference in the C–O bond between PF and the alky esters. It was found that the H-abstraction from the formic acid site dominated the consumption of PF. By comparing the rate constants of PF with other alkyl esters and aromatics such as C6 H6 and C6 H5 CH3 , we observed the distinct kinetic behaviors of PF due to the existence of both aromatic ring and ester group in the molecule. To provide a more comprehensive understanding of PF chemistry, this study was devoted to extending the chemical kinetics of unimolecular decomposition. We aim to theoretically determine the PESs, thermodynamics, and reaction kinetics of (1) the C–O/C– H bond fission and intramolecular H-shift of PF unimolecular decomposition, (2) the PF radical and subsequent intermediate decompositions, and (3) the ipso-addition reactions of PF by H, O, and OH radicals. With the developed pyrolysis mechanism of PF, this study provides a consolidated foundation for the pyrolysis model development of PF and other aromatic esters. 2. Computational details Geometries of the critical points on PESs were determined at the M062X/cc-pVTZ level [13] using Gaussian 09 [14]. The equilibrium geometries and transition states (TSs) were confirmed with all real frequencies and a single imaginary frequency, respectively. Intrinsic reaction coordinate (IRC) analyses were only performed for the specific reactions with questionable TSs [15]. The scale factors of 0.985 and 0.971 were used to correct the frequency and zero-point energy (ZPE), respectively [13]. To be consistent with the previous theoretical work [11], the energy of each critical point was refined using the ROCBS-QB3 method, where the standard deviation of the relative energy for C/H/O system was ~ 1.2 kcal mol−1 [16]. The low-frequency torsional modes were treated with the 1D separable-hindered rotor approximation that uncoupled internal rotations were assumed and the harmonic contribution of specific normal modes was replaced by the solution of 1-D torsional calculations [17]. Hence, the relaxed PES scans were performed for the internal rotations of reactants, intermediates and products as a function of the dihedral angle at the M062X/6–31G(d,p) level. Note that the lengths of the breaking and forming bonds of TSs were frozen with the rest geometric parameters fully optimized. Such treatment not only reduces the computational cost significantly but also provides a good approximation compared to the hindered-rotor potentials obtained with relaxed scans done for equilibrium structures [6,17]. The global minimum from these PESs was screened out and taken as the lowest energy conformer and

Species

◦  f H298 .15

OH CO CO2 HCO HCOO HOCO-trans HCOOH-trans C6 H4 C6 H5 C6 H5 O C6 H6 C6 H5 OH C6 H6 O C6 H4 OH C6 H4 CO2 C5 H4 CO PFR1 PFR2 PF PFR1-IM1 PFR1-IM2 PFR2-IM1 PFR2-IM2 PFR2-IM3 PFR2-IM4

8.8 −26.5 −95.1 10.0 −31.6 −44.2 −91.4 112.3 82.4 13.5 19.5 −21.3 −2.0 40.4 −13.3 27.5 −7.2 8.9 −53.3 10.7 12.7 1.3 30.0 −14.0 −15.5

K

(this work)

◦  f H298 .15 K (literature)

9.0 [22] −26.4 [22] −94.0 [22] 10.0 [22] −30.2 [22] −44.0 [22] −90.5 [23] 110.1 [22] 80.6 [22] 14.3 [24] 19.9 [22] −21.9 [24] −4.4 ± 2.4 [25] − − − − − − − − − − − −

fitted to the truncated Fourier series which were further used as the input parameters for 1-D separable-hindered rotor approximation. Based on the calculated energies and molecular properties, the high-pressure limit and pressure-dependent rate constants for the multi-well and multi-channel reactions were calculated using RRKM/ME method in the MESS code [18]. Argon was used as the bath gas with the Lennard-Jones (L-J) collision parame˚ ɛ = 64.8 cm−1 ). The Lennard-Jones (L-J) paramters (σ = 3.542 A; ˚ ε = 515.19 cm−1 ) were calculated using eters for PF (σ = 5.70 A; the empirical formula proposed by Wang et al. [19]. For the collisional energy transfer coefficient, a single exponential down model Edown  = 30 0(T /30 0)0.85 cm−1 was used for a reasonable reproduction of experimental data across a wide of temperature and pressure [20]. In addition, the asymmetric Eckart approximation was used to account for the tunneling correction [21]. Finally, the PLOG format was adopted to describe the temperature- and pressure-dependent rate constants: k(T , P ) = A(P )T n (P )exp[−E (P )/RT ]. 3. Results and discussion Herein we firstly calculated the standard enthalpy of formation of key species relevant to PF pyrolysis using the atomization enthalpy method, as summarized in Table 1. The thermodynamic data reported by Ruscic et al. [22], Goldsmith et al. [23], Dorofeeva et al. [24], and Zhu et al. [25] are also listed in Table 1 for comparison. The mean unsigned deviation is 0.9 kcal mol−1 and the maximum deviation is 2.4 kcal mol−1 . Note that there is an uncertainty of ± 2.4 kcal mol−1 for 2,4-cyclohexadienone (C6 H6 O) in Zhu et al.’s work [25]. The current calculations using the ROCBSQB3 method are in good agreement with the thermodynamic data in the literature [22–25]. All the structural data including visual structures and Cartesian coordinates are also presented in the Supplementary Material. 3.1. Unimolecular decomposition of PF PF decomposes via the direct bond fissions of C−O and C−H, as well as the intramolecular H-shifts. Figure 2 depicts seven reaction

H. Ning, J. Wu and L. Ma et al. / Combustion and Flame 211 (2020) 337–346

339

Fig. 2. Reaction pathways including bond fissions and intramolecular H-shifts for PF unimolecular decomposition. The corresponding potential energy profile is determined at ROCBS-QB3//M06-2X/cc-pVTZ level (including the zero-point energy, kcal mol−1 ).

pathways (R1−R7) of PF decomposition considered in this work and the corresponding potential energy profiles. Among these channels, the following four reactions dominate:



K

= 77.8 kcal mol−1



K

= 6.1 kcal mol−1

298.15 PF = C6 H5 O + HCO Hrxn 298.15 = C6 H5 OH + CO Hrxn



298.15 = C6 H6 + CO2 Hrxn



298.15 = C6 H6 O + CO Hrxn

K

K



= −20.0 kcal mol−1 = 25.3 kcal mol−1







(R3) (R4) (R5) (R7)

298.15 K ) for R3, R4 and The positive reaction enthalpies (Hrxn R7 indicate the endothermic process of these reactions. Due to the lower enthalpy of formation for CO2 (−95.1 kcal mol−1 ), the formation of C6 H6 + CO2 (R5) is an exothermic reaction. In general, PF takes the 1,2-intramolecular H-shift from the formic

acid C to O to produce phenol (C6 H5 OH) + CO (R4) with a barrier height of 59.3 kcal mol−1 , or undergoes the 1,3-intramolecular H-shift from the formic acid C to the benzene C to generate C6 H6 (benzene) + CO2 (R5) with a barrier height of 78.4 kcal mol−1 . In particular, PF may go through the 1,4-intramolecular H-shift to form 2,4-cyclohexadienone (C6 H6 O) + CO (R7) with the lowest barrier height of 53.4 kcal mol−1 . The intermediates phenol and 2,4-cyclohexadienone may isomerize via the keto-enol tautomerization by 1,3-intramolecular H-shift. Zhu et al. [25] calculated the barrier height of 51.1 kcal mol−1 from 2,4-cyclohexadienone to phenol. Brezinsky et al. [26] experimentally studied the pyrolysis and oxidation of phenol and found CO, cyclopentadiene (C5 H6 ) and benzene were the major products. Xu et al. [27] theoretically studied the phenol unimolecular decomposition and found the major channel of isomerization and decomposition of phenol via 2,4-cyclohexadienone to produce C5 H6 + CO. Hence, the key intermediates phenol and 2,4-cyclohexadienone significantly affect the final product yields of PF pyrolysis.

340

H. Ning, J. Wu and L. Ma et al. / Combustion and Flame 211 (2020) 337–346

Fig. 3. Reaction pathways of PFR1 decomposition and the corresponding potential energy profile at ROCBS/QB3//M06-2X/cc-pVTZ level (including the zero-point energy, kcal mol−1 ).

Among the bond-fission reactions, there is no well-defined saddle point for the barrierless reaction phenoxy (C6 H5 O) + HCO (R3). The minimum energy potential (MEP) was obtained along the dissociation of C−O bond (0.1 A˚ interval) at the uM062X/cc-pVTZ level of theory. For each point on the MEP, the complex energy was multiplied by a scaling factor that accounts for the difference between the ROCBS-QB3 reaction enthalpy and the uM062X/cc-pVTZ reaction energy [28]. All the MEPs are provided in Fig. S1 of Supplementary Material. 3.2. PF radical decomposition PF radicals are produced by H-abstraction reactions by small radicals (such as H, O, OH, and HO2 ). The previous study indicates that the H-abstraction from the formic acid site to form PFR1 radical contributes mainly to the consumption of PF compared with that from the aromatic ring [11]. Hence, we only focused on the decomposition of PFR1 radical in this study. Figure 3 depicts the major reaction pathways of PFR1 decomposition including three β scission and three isomerization reactions. The H atom on the aromatic ring takes 1,4- and 1,6-intramolecular H-shift to form PFR2 (R12) and PFR4 (R13) with a barrier height of 28.6 and 125.4 kcal mol−1 , respectively. Note that the TS of 1,5-intramolecular H-shift to form PFR3 is not located at the uM062X/cc-pVTZ level. For the decomposition channels, the C−O bond β -scission to produce C6 H5 O + CO (R9) has the lowest barrier height of 11.8 kcal mol−1 . Compared to the carbonyl C atom added to the aromatic ring to form intermediate PFR1-IM1 (R11) and the formation of products C6 H5 + CO2 (R8), the formation of products C6 H4 + HOCO-trans with a barrier height of 97.8 kcal mol−1 (R10) is hardly competitive. Hence, the four dominant reaction channels R8, R9, R11 and R12 and subsequent reactions of the intermediates are included in rate constant calculations. Four decomposition channels were considered for intermediate PFR1-IM1 with the corresponding potential energy profiles presented in Fig. 4. All these pathways feature bottlenecks with energies higher than the entrance channels. Similar to the PFR1 radical, C−C and C−O bond fissions of PFR1-IM1 leading

to phenoxy + CO (R14) and intermediate PFR1-IM2 (R17) have competitive energy barriers of 20.8 and 19.1 kcal mol−1 , respectively. The other two channels to form phenyl + CO2 (R15) and eight-membered ring intermediate (R16) have a higher energy barrier of 35.2 and 41.0 kcal mol−1 , respectively. Furthermore, the intermediate PFR1-IM2 decomposes to phenoxy + CO (R18) with an energy barrier of −0.6 kcal mol−1 . As the energy barrier of R18 is negative, we performed the IRC analysis (see Fig. S2 in Supplementary Material) for this TS to confirm its connection with the desired reactant (PFR1-IM2) and products (phenoxy + CO). Hence, the products phenoxy + CO are preferred for PFR1-IM1 decomposition and reactions R14, R17 and R18 are included in the following RRKM/ME calculations. Figure 5 presents ten decomposition channels for intermediate PFR2 and the corresponding potential energy profiles. The β -scissions of C−H/C−C bonds in the aromatic ring to form triple bond product (R19) and ring-open intermediate (R20) have a high energy barrier of 78.2 and 76.8 kcal mol−1 , respectively. Note that the TS for the β -scission of C−O bond to form C6 H4 + HCOO (R28) is not located at the M062X/cc-pVTZ level. Additionally, as the relative energy of product C6 H4 + HCOO is 70.9 kcal mol−1 above PFR2, these decomposition pathways of PFR2 are almost negligible. The elimination reaction to form HCO (R21), the 1,4-H shift reaction and subsequent elimination to form CO (R22), and three 1,2-H shift reactions of the aromatic ring H (R24, R26 and R27) also have a high energy barrier of 95.6, 54.0, 59.9, 58.4 and 88.1 kcal mol−1 , respectively. In comparison, the formation reactions of intermediates PFR2-IM1 (R23) and PFR2-IM2 (R25) have the same lowest energy barrier of 22.7 kcal mol−1 . Hence, the subsequent decompositions of PFR2-IM1 and PFR2-IM2 are considered. Hence, the reaction channels R23, R25 and PFR2-IM1 = C5 H4 CO + CO are included in the following RRKM/ME calculations. Figure 6 presents the decomposition channels for intermediate PFR2-IM2 and the corresponding potential energy profiles. Among the four decomposition reactions, the β -scissions of C−O and C−H bonds to form the intermediate PFR2-IM3 (R32) and products C6 H4 CO2 + H (R33) have lower energy barriers of −2.6 and 16.6 kcal mol−1 , respectively. The IRC analysis also provided

H. Ning, J. Wu and L. Ma et al. / Combustion and Flame 211 (2020) 337–346

341

Fig. 4. Decomposition of PFR1-IM1 and the corresponding potential energy profile at the ROCBS/QB3//M06-2X/cc-pVTZ level (including the zero-point energy, kcal mol−1 ).

Fig. 5. Decomposition of PFR2 and the corresponding potential energy profile at the ROCBS/QB3//M06-2X/cc-pVTZ level (including the zero-point energy, kcal mol−1 ).

342

H. Ning, J. Wu and L. Ma et al. / Combustion and Flame 211 (2020) 337–346

Fig. 6. Decomposition of PFR2-IM2 and the potential energy profile at the ROCBS/QB3//M06-2X/cc-pVTZ level (including the zero-point energy, kcal mol−1 ).

in Fig. S3 of Supplementary Material confirms the TS of reaction R32 connects with the desired reactant (PFR2-IM2) and product (PFR2-IM3). The subsequent decomposition of PFR2-IM3 undergoes the 1,4-H shift to produce PFR2-IM4 with an energy barrier of 23.6 kcal mol−1 (R34), followed by β -scission of PFR2-IM4 to produce C6 H4 OH + CO with an energy barrier of 28.1 kcal mol−1 (R35). Hence, the reaction channels R32−R35 are included in the RRKM/ME calculations. 3.3. Ipso-addition reactions Figure 7 presents the ipso-addition reactions by H, O and OH radicals and the corresponding potential energy profiles. Taking H radical as an example, the H atom firstly adds to the double bond of the aromatic ring of PF and then takes the β -scission

to form benzene and HCOO radical. This process is the so-called ipso-addition reaction. Note that H atom may also attract the single bond of O atom to form phenol and HCO radicals, but with a much higher energy of 37.2 kcal mol−1 . The calculated PESs showed that the energy barrier of ipso-addition reaction was much lower (29.7 − 63.5 kcal mol−1 ) than the other reaction channels. In addition, it is interesting to see that the final products of ipso-addition reaction PF + OH are phenoxy + HCOOH rather than phenol + HCOO. Hence, these ipso-addition reaction channels are included in the RRKM/ME calculations. 3.4. Rate constant determination The obtained high-pressure limit (HPL) and pressure-dependent rate constants of the key reactions of PF decomposition are

H. Ning, J. Wu and L. Ma et al. / Combustion and Flame 211 (2020) 337–346

343

Fig. 7. The ipso-addition reactions of PF with H, O and OH radicals and the corresponding potential energy diagram at ROCBS-QB3//M06-2X/cc-pVTZ level (including the zero-point energy, kcal mol−1 ).

summarized in Table 2. To our knowledge, no direct rate constant measurements of PF decomposition have been reported yet except the recent study of H-abstraction reactions of PF [11]. The pressure-dependent rate constants of four main channels of PF unimolecular decomposition have a wide temperature range of 50 0−20 0 0 K at pressure 0.01 atm to HPL. Figure 8 depicts the branching ratio of PF unimolecular decomposition at HPL and 1 atm and 50 0−20 0 0 K. It is seen that reactions R4 and R7 dominate the PF consumption to form the products phenol + CO and 2,4-cyclohexadienone + CO over the entire temperature range. However, for the decomposition pathways of PF radicals, many lower energy wells merged as the corresponding chemically

significant eigenmodes (CSEs) lay in the quasi-continuum of internal energy relaxation eigenmodes (IEREs) by solving the master equation. The similar well-merged phenomenon was also reported in the previous study of ethyl formate decomposition [29]. Among the ipso-addition reactions of PF, Fig. 9 plots the rate constants of ipso-addition reaction PF + H = C6H6 + HCOO at different pressures. It is interesting to see that the rate constants are almost pressure-independent, except the case at lower temperatures. The intermediate PF-H-IM is merged at lower pressures and higher temperatures, making the ipso-addition reaction equivalent to a bimolecular reaction.

344

H. Ning, J. Wu and L. Ma et al. / Combustion and Flame 211 (2020) 337–346 Table 2 Rate constants (HPL and 0.01−100 atm) of PF pyrolysis at 50 0−20 0 0 K. Reactions

P(atm)/Ar

T (K)

Log(A) (s−1 )

n

E (cal mol−1 )

PF = C6 H5 OH + CO

0.01 0.1 1 10 100 H-P 0.01 0.1 1 10 100 H-P 0.01 0.1 1 10 100 H-P 0.01 0.1 1 10 100 H-P 1 1 1 H-P H-P H-P H-P H-P H-P H-P H-P H-P H-P H-P H-P H-P H-P 100 10 100 100 0.01 0.1 1 10 100 0.01 0.1 1 10 100 0.01 0.1 1 10 100 0.01 0.1 1 10 100

500−1700 500−1900 500−2000 500−2000 500−2000 500−2000 500−1700 500−1900 500−2000 500−2000 500−2000 500−2000 500−1700 500−1900 500−2000 500−2000 500−2000 500−2000 500−1700 500−1900 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−2000 500−800 500−900 500−1200 500−800 500−1000 500−1100 500−1300 500−1500 500−1800 500−800 500−900 500−1000 500−1100 500−1200 500−900 500−1000 500−1200 500−1400 500−1900 500−800 500−900 500−1000 500−1100 500−1200

51.40 41.97 30.65 19.30 12.55 9.64 70.66 58.82 43.14 25.92 14.18 8.14 43.99 35.93 26.08 16.30 10.63 8.28 71.67 59.68 44.20 27.49 16.24 10.55 11.07 10.24 10.24 5.61 9.49 10.08 11.27 8.97 9.99 13.26 13.41 12.46 14.50 13.08 10.53 12.88 15.25 30.13 15.09 15.11 27.83 61.76 50.35 41.59 34.93 25.39 74.65 69.14 61.29 51.10 39.59 68.01 62.06 61.07 55.33 47.18 72.20 69.93 65.97 58.50 47.21

−11.31 −8.34 −4.87 −1.45 0.57 1.44 −17.77 −13.87 −8.97 −3.74 −0.21 1.59 −9.32 −6.80 −3.79 −0.85 0.84 1.55 −17.77 −13.84 −9.02 −3.94 −0.56 1.13 0.64 0.73 0.57 2.00 0.83 1.08 0.90 0.82 0.62 0.17 0.18 0.15 0.86 0.08 0.99 −0.04 0.28 −5.31 −1.17 −0.95 −4.69 −15.42 −11.61 −8.68 −6.41 −3.35 −20.22 −18.14 −15.40 −12.03 −8.33 −17.46 −15.15 −14.44 −12.36 −9.67 −18.84 −17.71 −16.08 −13.43 −9.71

75,501.6 72,337.0 67,795.1 62,786.4 59,697.8 58,337.1 100,568.1 97,703.2 92,086.2 84,834.3 79,578.4 76,798.0 67,224.6 64,404.7 60,367.0 56,004.9 53,400.5 52,295.1 99,911.0 96,850.8 91,234.0 84,162.7 79,116.7 76,492.1 7552.9 6584.8 4733.9 24,826.7 27,946.4 37,025.3 12,782.1 20,890.0 21,912.0 19,977.7 21,735.8 24.30 86,699.6 −1875.4 16,563.4 23,835.6 31,037.8 17,735.2 10,479.3 12,216.1 15,461.4 45,256.2 42,531.5 40,825.2 40,505.9 39,473.8 41,040.8 40,951.3 39,779.9 37,306.2 33,798.6 44,204.9 45,264.7 48,553.7 49,994.2 50,112.3 44,589.2 45,602.0 46,202.5 45,339.9 42,476.1

PF = C6 H6 + CO2

PF = C6 H6 O + CO

PF = C6 H5 O + HCO

PF + H = C6H6 + HCOO PF + O = C6H5O + HCOO PF + OH = C6 H5 O + HCOOH PFR1 = PFR2 PFR1 = PFR1-IM1 PFR1 = C6 H5 + CO2 PFR1 = C6 H5 O + CO PFR2 = PFR2-IM1 PFR2 = PFR2-IM2 PFR1-IM1 = PFR1-IM2 PFR1-IM1 = C6 H5 O + CO PFR1-IM2 = C6 H5 O + CO PFR2-IM1 = C5 H4 CO + HCO PFR2-IM2 = PFR2-IM3 PFR2-IM2 = C6 H4 CO2 + H PFR2-IM3 = PFR2-IM4 PFR2-IM4 = C6 H4 OH + CO PFR1 = C6 H5 O + CO PFR2 = C6 H5 O + CO PFR1-IM1 = C6 H5 O + CO PFR2IM1 = C6 H5 O + CO

PFR2IM3 = PFR2IM4

PFR2IM3 = C6 H4 OH + CO

PFR2IM4 = C6 H4 OH + CO

In the absence of reliable experiments, we chose the ipsoaddition reaction of PF + H and anisole + H [12] for comparison to justify the theoretical calculation. Both reaction systems have the similar structures and bond dissociation energies (see Fig. 1). The rate constants obtained in this work are in good agreement with the literature results (within a factor of 2) shown in Fig. 10(a). In addition, Fig. 10(b) compares the rate constants of

beta-scission reaction PFR1 = C6 H5 + CO2 with that of anisole radical C6 H5 OCH2 = C6 H5 + CH2 O, showing a deviation by a factor of 2.5. Note that the rate constants of anisole radical beta-scission were calculated by the CBS-QB3 method combined with the transition state theory. Further details are provided in Supplementary Material. According to the above discussion, we believe that the rate constants obtained in this work are acceptable.

H. Ning, J. Wu and L. Ma et al. / Combustion and Flame 211 (2020) 337–346

345

Fig. 8. Branching ratio of PF unimolecular decomposition.

Fig. 9. Rate constants of ipso-addition reaction PF + H = C6 H6 + HCOO at different pressures determined in this work. The rate constants at 0.01–1 atm overlap and cannot be differentiated in the figure.

Finally, we developed a kinetic mechanism of PF pyrolysis based on the current study; and the complelete thermal data and reaction kinetics are provided in the Supplementary Material. The kinetic model mainly contains three sub-mechanisms: (1) the PF sub-mechanism inclduing unimolecular decompostion, PF radical isomerization and subsquent decompostion, ipso-addition investigated in this work and H-abstraction reactions obtained in [11]; (2) the sub-mechanism of the important internmidiates C6 H6 O and C6 H5 OH [25]; and (3) the core mechanism Aramco 2.0 including C6 H6 , C6 H5 , C6 H4 OH, C5 H6 and C5 H5 , etc. [30]. Note that except for the thermal data of PF sub-mechanism, the other thermal data are directly adopted from the Aramco 2.0 mechanism. In total, the detialed pyrolysis model incldues 503 species and 2743 reactions. This model could be directly used as the original model for analyzing the pyrolysis of PF in shock tube or plug flow reactor experiments, as well as the core kinetic mechanism of larger aromatic esters.

combined with the RRKM/ME theory. The PESs indicate the unimolecular decomposition of PF to produce phenol + CO (R4) and 2,4-cyclohexadienone + CO (R7) are the dominant decomposition pathways. The generated two key intermediates, phenol and 2,4cyclohexadienone, significantly affect the final product especially for CO. For the decomposition of PF radicals, many intermediates with low energy barriers are merged to produce C6 H5 O + CO and C6 H4 OH + CO. The ipso-addition reactions of PF by H/O radicals mainly produce C6 H6 + HCOO and C6 H5 O + HCOO, while the ipso-addition by OH generates C6 H5 O + HCOOH rather than C6 H5 OH + HCOO. The rate constants of ipso-addition reactions show relatively weak pressure dependence. Acknowledgments This work is supported by Research Grants Council of the Hong Kong SAR, China (14234116). We are also thankful to Shenzhen Supercomputing Center for providing computational facilities.

4. Conclusions In this work the PESs, thermodynamics and reaction of PF unimolecular decomposition, the subsequent radical position and ipso-addition reactions were systematically gated using the composite ROCBS-QB3//M062X/cc-pVTZ

Fig. 10. Comparison of rate constants for the representative reactions obtained in this work with the relevant theoretical results available in the literature: (a) rate constants of ipso-addition reactions for PF (this work, black line) and anisole (M. Nowakowska et al. [12], red line); (b) high-pressure limit rate constants of beta-scission reaction PF = C6 H5 + CO2 (this work, black line) and C6 H5 OCH2 = C6 H5 + CH2 O (Supplementary Material, red line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

kinetics decominvestimethod

Declaration of Competing Interest None.

346

H. Ning, J. Wu and L. Ma et al. / Combustion and Flame 211 (2020) 337–346

Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.combustflame.2019.10. 002. References [1] C.K. Westbrook, C.V. Naik, O. Herbinet, W.J. Pitz, M. Mehl, S.M. Sarathy, H.J. Curran, Detailed chemical kinetic reaction mechanisms for soy and rapeseed biodiesel fuels, Combust. Flame 158 (2011) 742–755. [2] W.K. Metcalfe, S. Dooley, H.J. Curran, J.M. Simmie, A.M. El-Nahas, M.V. Navarro, Experimental and modeling study of C5 H10 O2 ethyl and methyl esters, J. Phys. Chem. A 111 (2007) 4001–4014. [3] C.K. Westbrook, W.J. Pitz, P.R. Westmoreland, F.L. Dryer, M. Chaos, P. Osswald, K. Kohse-Ho¨inghaus, T.A. Cool, J. Wang, B. Yang, N. Hansen, T. Kasper, A detailed chemical kinetic reaction mechanism for oxidation of four small alkyl esters in laminar premixed flames, Proc. Combust. Inst. 32 (2009) 221–228. [4] P. Dagaut, S. Gaı¨l, M. Sahasrabudhe, Rapeseed oil methyl ester oxidation over extended ranges of pressure, temperature, and equivalence ratio: experimental and modeling kinetic study, Proc. Combust. Inst. 31 (2007) 2955–2961. [5] O. Herbinet, W.J. Pitz, C.K. Westbrook, Detailed chemical kinetic mechanism for the oxidation of biodiesel fuels blend surrogate, Combust. Flame 157 (2010) 893–908. [6] H. Tao, K.C. Lin, Kinetic barriers, rate constants and branching ratios for unimolecular reactions of methyl octanoate peroxy radicals: a computational study of a mid-sized biodiesel fuel surrogate, Combust. Flame 180 (2017) 148–157. [7] Y. Chi, X. You, L. Zhang, W. Li, Utilization of generalized energy-based fragmentation method on the study of hydrogen abstraction reactions of large methyl esters, Combust. Flame 190 (2018) 467–476. [8] L. Zhang, Q. Meng, Y. Chi, P. Zhang, Toward high-level theoretical studies of large biodiesel molecules: an oniom (QCISD(T)/CBS:DFT) study of the reactions between unsaturated methyl esters (Cn H2n–1 COOCH3 ) and hydrogen radical, J. Phys. Chem. A 122 (2018) 4882–4893. [9] Y. Chi, X. You, Kinetics of hydrogen abstraction reactions of methyl palmitate and octadecane by hydrogen atoms, J. Phys. Chem. A 123 (2019) 3058–3067. [10] J. Wu, H. Ning, X. Xu, W. Ren, Accurate entropy calculation for large flexible hydrocarbons using a multi-structural 2-dimensional torsion method, Phys. Chem. Chem. Phys. 21 (2019) 10 0 03–10 010. [11] H. Ning, D. Liu, J. Wu, L. Ma, W. Ren, A. Farooq, A theoretical and shock tube kinetic study of H-abstraction from phenyl formate, Phys. Chem. Chem. Phys. 20 (2018) 21280–21285. [12] M. Nowakowska, O. Herbinet, A. Dufour, P.-.A. Glaude, Detailed kinetic study of anisole pyrolysis and oxidation to understand TAR formation during biomass combustion and gasification, Combust. Flame 161 (2014) 1474–1488.

[13] Y. Zhao, D.G. Truhlar, The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals, Theor. Chem. Acc. 120 (2008) 215–241. [14] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb et al., Gaussian 09, Revision D.01, Gaussian Inc., Wallingford, CT, 2009. [15] K. Fukui, The path of chemical reactions-the IRC approach, Acc. Chem. Res. 14 (1981) 363–368. [16] G.P.F. Wood, L. Radom, G.A. Petersson, E.C. Barnes, M.J. Frisch, J.A. Montgomery Jr., A restricted-open-shell complete-basis-set model chemistry, J. Chem. Phys. 125 (2006) 094106–094120. [17] J. Pfaendtner, X. Yu, L. Broadbelt, The 1-D hindered rotor approximation, Theor. Chem. Acc. 118 (2007) 881–898. [18] Y. Georgievskii, S.J. Klippenstein, MESS code. http://tcg.cse.anl.gov/papr/codes/ mess.html (Accessed March 2018). [19] H. Wang, M. Frenklach, Transport properties of polycyclic aromatic hydrocarbons for flame modeling, Combust. Flame 96 (1994) 163–170. [20] S.J. Klippenstein, From theoretical reaction dynamics to chemical modeling of combustion, Proc. Combust. Inst. 36 (2017) 77–111. [21] C. Eckart, The penetration of a potential barrier by electrons, Phys. Rev. 35 (1930) 1303–1309. [22] Ruscic, B. Active thermochemical tables: version alpha 1.122 of the core (argonne) thermochemical network, 2016 https://atct.anl.gov (Accessed March 2018). [23] C.F. Goldsmith, G.R. Magoon, W.H. Green, Database of small molecule thermochemistry for combustion, J. Phys. Chem. A 116 (2012) 9033–9057. [24] O.V. Dorofeeva, O.N. Ryzhova, Enthalpy of formation and o−h bond dissociation enthalpy of phenol: inconsistency between theory and experiment, J. Phys. Chem. A 120 (2016) 2471–2479. [25] L. Zhu, J.W. Bozzelli, Kinetics and thermochemistry for the gas-phase keto-enol tautomerism of phenol ↔ 2,4-cyclohexadienone, J. Phys. Chem. A 107 (2003) 3696–3703. [26] K. Brezinsky, M. Pecullan, I. Glassman, Pyrolysis and oxidation of phenol, J. Phys. Chem. A 102 (1998) 8614–8619. [27] Z.F. Xu, M.C. Lin, Ab initio kinetics for the unimolecular reaction C6 H5 OH = Co + C5 H6 , J. Phys. Chem. A 110 (2006) 1672–1677. [28] G. da Silva, M.R. Hamdan, J.W. Bozzelli, Oxidation of the benzyl radical: mechanism, thermochemistry, and kinetics for the reactions of benzyl hydroperoxide, J. Chem. Theory Comput. 5 (2009) 3185–3194. [29] H. Ning, J. Wu, L. Ma, W. Ren, D.F. Davidson, R.K. Hanson, Combined ab initio, kinetic modeling, and shock tube study of the thermal decomposition of ethyl formate, J. Phys. Chem. A 121 (2017) 6568–6579. [30] C.-.W. Zhou, Y. Li, E. O’Connor, K.P. Somers, S. Thion, C. Keesee, O. Mathieu, E.L. Petersen, T.A. DeVerter, M.A. Oehlschlaeger, G. Kukkadapu, C.-.J. Sung, M. Alrefae, F. Khaled, A. Farooq, P. Dirrenberger, P.-.A. Glaude, F. Battin-Leclerc, J. Santner, Y. Ju, T. Held, F.M. Haas, F.L. Dryer, H.J. Curran, A comprehensive experimental and modeling study of isobutene oxidation, Combust. Flame 167 (2016) 353–379.