Formation pathways of polycyclic aromatic hydrocarbons (PAHs) in butane or butadiene flames

The reaction pathways from phenyl radicals to phenanthrene (A3) and pyrene (A4) via C2H3 and C4H4 additions were investigated using the G3(MP2, CC) method. Rate constants of elementary reactions were calculated. The influence of additions, H-abstraction ways and reactive sites on the reaction rates were considered. These polycyclic aromatic hydrocarbon (PAH) formation pathways were used to improve the combustion chemistry model for C4 fuels, and the results from the improved model and the original model were compared with experimental data. H atoms are important for PAH formation owing to their influential roles in the production of aromatic radicals and stable aromatic structures. C2H3 and C4H4 addition reactions can occur at low temperature, and need less energy than C2H2 addition. The PAH formation pathways determined from G3 calculations, which were used to improve the model, were effective in promoting PAH formations in this model. Comparison of PAH formation in butane and butadiene flames showed both the C2H3 and C4H4 addition pathways included in this work can improve the formation of PAHs in butadiene and butane flames. C4H4 addition pathways in a butane flame were better for PAH formation than C2H3 addition.


Introduction
Polycyclic aromatic hydrocarbons (PAHs), which mainly come from the incomplete combustion of fuel, are extremely harmful to humans and the environment. So far, the most commonlyused addition for PAH growth is C 2 H 2 , and the most popular PAH formation mechanism is H-abstraction-C 2 H 2 -addition (HACA). [1][2][3][4][5] However, the HACA mechanism underestimates the concentrations of PAHs and soot compared with the experimental results. [6][7][8][9] This underestimation may be explained by two main reasons. Firstly, there are many non-acetylene organic compounds (e.g. CH 3 , C 3 H 3 , C 3 H 4 , C 3 H 6 , C 4 H 2 , C 4 H 4 , C 4 H 6 and C 5 H 8 ) that also contribute to PAH growth in various ame congurations. [8][9][10][11][12][13] Secondly, many PAH formation reactions in the HACA mechanism are reversible. 14 Hence, more additions in PAH formation should be considered to perfect the PAH formation mechanism.
Many non-acetylene additions have been proved experimentally to be important for PAHs formation. C 4 H 4 addition can effectively lead to PAHs formation. 15 C 2 H 3 addition is critical for the formation of PAHs and soot. 16 The hydrogen abstraction/vinyl radical addition (HAVA) mechanism may be the best complement to the HACA mechanism, and the phenyl addition/cyclization (PAC) mechanism can promote the growth of molecular mass and ring number of PAHs without the limit of reactive sites. 10,17 Hence, the additions of C 2 H 3 , C 4 H 4 and C 6 H 5 contribute greatly to PAHs formation, and more research on PAHs formation from C 2 H 3 , C 4 H 4 and C 6 H 5 additions is needed.
Butane and butadiene, two light hydrocarbons, are both benecial to the environment and can relieve energy shortage. In this research, PAHs formation routes via C 2 H 3 , C 4 H 4 and C 6 H 5 additions within all reaction rates of elementary reactions in the modied Arrhenius equation were studied and coupled to a chemical kinetic model for butadiene and butanol. The effects of additions, reaction types and reaction sites were considered during PAHs formation.

Methods
All molecular structures involved in the reactions under study were optimized by using the hybrid B3LYP functional with the 6-311++G(d,p) basis set. [18][19][20] Vibrational frequency was calculated at the same level to identify the optimized structures as local minimum or rst-point saddle points and to provide their zeropoint vibrational energy (ZPE). Intrinsic reaction coordinate calculations were implemented to ensure that the transition states connect to relevant reactants and products correctly. The nal single-point energies of all species were determined using the G3(MP2, CC) method, 21,22 which is expected to generate relative energies of various species within the accuracy of 1-2 kcal mol À1 (ref. 23) and is extensively used to study PAHs growth mechanisms. 21,[24][25][26][27][28] The intermediate species and transition structures found in this study were all closed shell singlets or open shell doubles. Molecular properties of chemical species (CS) and transition states (TS) are shown in ESI. † The G3(MP2, CC) energies are calculated as follows: is the basis set correction; DE(SO) is the spin-orbit   correction, included for atomic species only. For molecules, higher level correction (HLC) is DE(HLC) ¼ ÀAn b À B(n a À n b ) with A ¼ 9.279 mHartrees and B ¼ 4.471 mHartrees, and for atoms, is DE(HLC) ¼ ÀCn b À D(n a À n b ) with C ¼ 9.345 mHartrees and D ¼ 2.021 mHartrees, where n a and n b are the numbers of a and b valence electrons, respectively. All calculations were performed on Gaussian 09. 29 Based on the calculated potential energy surface (PES) and molecular characteristics, Rice-Ramsperger-Kassel-Marcus (RRKM) and transitional state theory (TST) were used to determine reaction rates by ChemRate program. 30 Noticeably, none of the rate constants were arbitrarily changed or intuitively estimated to match the computed and the experimental results. The calculated PAHs formation pathways were used to update Hansen's mechanism 31 which consists of 216 species connected via 1028 reactions. Then the updated mechanism was used to simulate the premixed 1,3-butadiene or butane ame and to discuss the roles of our pathways in PAHs formation under 1,3butadiene or butane ame.

PAHs formation pathways
Four PAHs formation pathways were studied ( Fig. 1-4): (i) formation of phenanthrene via once addition of phenyl radical (C 6 H 5 ) and twice additions of C 2 H 3 onto phenyl radical; (ii) formation of phenanthrene via once addition of C 4 H 4 onto naphthyl radical; (iii) formation of pyrene via once addition of C 2 H 3 onto phenanthryl radical; (iv) formation of pyrene via once addition of C 4 H 4 onto 1-ethynylnaphthyl radical. Comparisons  between H abstraction reactions of biphenyl via H atom, O atom or OH radical at same reactive site were studied. The effects of reactive sites to hydrogen abstraction, carbon addition, ring closure, and hydrogen atom loss reactions were investigated. The barrier heights and reaction energies for all steps are collected in Table S1. † Meanwhile, to understand the thermodynamics of the studied reactions better, the enthalpies and Gibbs free energies are illustrated in Tables S2 and S3. † The molecular geometries, vibrational frequencies, moments of inertia, and rotational constants of the chemical species (CS) and transition states (TS) involved in all routes are shown in Table S5. † 3.1.1 Phenanthrene formation pathway via C 2 H 3 additions. As shown in Fig. 1, phenanthrene was formed through Habstractions, C-additions and ring formation reactions, and the barrier heights and reaction energies were determined in Table  1. The initial association of two C 6 H 5 additions results in the formation of CS2, biphenyl. This thermodynamically and kinetically favorable process is highly exothermic (119.7 kcal mol À1 ) with a barrier of 14.3 kcal mol À1 , leading to a quick increase of ring number. In Fig. 6, C 2 H 2 , and especially C 6 H 5 and C 2 H 3 addition reactions are all exothermic. Besides, C 2 H 3 addition reaction occurs more easily than C 2 H 2 or C 6 H 5 addition reaction.
H-abstractions may produce singlet PAH intermediates such as CS31 and CS7, or radicals such as CS3 and CS5. 32 Most of the former H-abstractions are exothermic, and most of the later Habstractions are endothermic, providing precondition for the possible carbon additions or cyclization reactions. To explore the easier formation of larger PAHs molecules, we calculated and compared ve radical site formation processes via H, O, OH, C 2 H 3 and C 6 H 5 respectively to provide a prime radical formation process. The barriers and reaction heats were shown in Table 1 and all H-abstraction reactions with assistance of H, O, OH, C 2 H 3 and C 6 H 5 in this pathway together with Habstraction reaction R29 from literature 32 were compared in Fig. 5. Comparison of R2, Ra, Rb, Rc and Rd showed the barriers of the H-abstraction reactions via O and OH radicals were much higher than those via H, C 2 H 3 and C 6 H 5 radicals. This means that, depending on the concentrations of H, C 2 H 3 and C 6 H 5 radicals in combustion environments, H, C 2 H 3 and C 6 H 5 radicals can much more easily initiate H-abstractions than O and OH radicals. However, the concentration H radicals in combustion environments is generally higher than those of C 2 H 3 and C 6 H 5 radicals. [8][9][10] Thus, H radical is much easier to initiate H-abstractions than O, OH, C 2 H 3 and C 6 H 5 radicals.   (Fig. 7). The addition of C 4 H 4 leads to CS9 with a barrier of 3.4 kcal mol À1 , which is lower than that of C 2 H 2 addition, RI. Aer that, the reaction CS9 / CS10 is internal hydrogen abstraction via migration of a hydrogen atom from the aromatic ring to the second carbon of the C4 fragment, producing a butadiene chain with a barrier of 39.1 kcal mol À1 . Then to prepare for the cyclization, CS10 undergoes cis-trans isomerization, forming CS11 with a barrier of 38.6 kcal mol À1 . Due to its structural characteristics, the CS11 adduct can be cyclized, producing the phenanthrene precursor CS12, which yields phenanthrene aer hydrogen atom elimination. The barrier of the cyclization step CS11 / CS12 is only 0.4 kcal mol À1 , which can be ignored easily. Also, the reaction is highly exothermic by 65.1 kcal mol À1 . The hydrogen atom elimination step CS12 / CS7 + H overcomes a barrier of 40.5 kcal mol À1 , and is the rate determining step of this pathway.
3.1.3 Pyrene formation pathway via C 2 H 3 additions. The reaction process from phenanthrene to pyrene via C 2 H 3 addition and the energy of this process were shown in Fig. 3 and Table 2. The C 2 H 3 addition reaction is followed by activation of     phenanthrene via H-abstraction, forming a radical structure, CS13. Aer that, the C 2 H 3 addition onto CS13 is highly exothermic with a barrier of only 5.4 kcal mol À1 . Then CS14 undergoes H-abstraction and cyclization, producing CS16, with barriers of 31.0 and 5.3 kcal mol À1 , respectively. At last, CS16 emits a H atom to produce CS17, pyrene. This reaction is a ratedetermining step of this pathway, overcoming a barrier of 38.2 kcal mol À1 . Fig. 8 compares two C 2 H 3 additions onto CS3 and CS13 separately. Little difference is found in the barrier heights or reaction energy between these two addition steps. This may be because the reactive sites on CS3 and CS13 are similar between "armchair" and "free edge" as shown by red lines in Fig. 8. Fig. 9 shows two hydrogen atom loss reactions that produce phenanthrene and pyrene, respectively. Compared with Habstractions via the assistance of H atom, these two H atom loss reactions without the assistance of H atom need to overcome higher barriers and are both endothermic. Thus, the assistance of H atom is benecial for H loss.
Furthermore, both reaction CS15 / CS16 and reaction CS5 / CS6 are ring formation processes that occur at the edge of vinyl group and the carbon of aromatic ring between "armchair" and "free edge" (Fig. 1, 3 and 10). These two reactions are both exothermic with low barriers.
3.1.4 Pyrene formation pathways via C 4 H 4 addition onto CS18. Fig. 11 provides the energy diagram for pyrene formation pathway initiated from the C 4 H 4 addition onto CS18. The energies of the intermediate species and the transition states are relative to the total energy of CS18 and C 4 H 4 . The C 4 H 4 addition onto the radical site of CS18 to form CS19 requires a barrier of 0.4 kcal mol À1 , which is 3.0 kcal mol À1 lower than the C 4 H 4 addition step above, CS8 + C 4 H 4 / CS9. This may be because of the existence of the acetylene group in CS18. Aer that, the reaction CS19 / CS20 is internal hydrogen abstraction via migration of a hydrogen atom, producing a butadiene chain with a barrier of 39.0 kcal mol À1 . The energetics of this reaction is rather similar to that observed for another internal hydrogen migration step CS9 / CS10. The barrier heights range within 39.0-39.1 kcal mol À1 , and reaction exothermicities are about 11.6-14.3 kcal mol À1 . Aer that, cyclization occurs at the end of the butadiene group and the radical site of aromatic ring, CS20 / CS21, which requires an activation energy of 7.9 kcal mol À1 , forming a six-membered ring. Later, another cyclization process takes place at the vinyl radical group and the newly-formed ring, forming the forth ring structure, CS23, with a barrier of 7.1 kcal mol À1 . Finally, adduct CS23 eliminates an "extra" hydrogen atom to produce CS17, pyrene. Fig. 12 provides the energy diagram for pyrene formation pathway initiated from the C 4 H 4 addition onto CS24. The energies of the intermediate species and the transition states are relative to the total energy of CS18 and C 4 H 4 . The C 4 H 4 addition onto the radical site of CS24 to produce CS25 requires a barrier of 4.2 kcal mol À1 , which is higher than C 4 H 4 addition steps via TS7 and TS17. This may be because the reactive site for C 4 H 4 addition is near the shared carbons of two aromatic rings. The exothermicity of this addition reaction is 48.2 kcal mol À1 , which differs by only 0.1 and 2.8 kcal mol À1 with the other two C 4 H 4 addition steps via TS7 and TS17, respectively, but is signicantly lower than the reaction energies for C 6 H 5 and C 2 H 3 addition reactions, R1, R3 and R13. Combined with Fig. 6 and 8, in the addition reactions, the same added species may contribute equally to similar reaction kinetics, just like C 2 H 3 and C 4 H 4 . Aer the addition of C 4 H 4 , the internal hydrogen migration from C4 group to acetylene group adjusts the structure of CS25 to adduct CS26, which yields CS27 within three aromatic rings through cyclization via TS25. At this point, another internal hydrogen migration via TS26 has a large thermodynamic driving force for the subsequent formation of PAHs, CS29. At last, pyrene is formed through the elimination of an "extra" hydrogen atom from adduct CS29. In this pathway, the structure of TS25, which is the transition state for CS26 / CS27, was not found. Thus, the highest barrier of this pathway is 41.8 kcal mol À1 so far, and the rate-deciding step is the dehydrogenation, CS29 / CS17 + H.

Elementary reaction rate constants
The high-pressure limit rate constants of the elementary reactions involved above are listed in Table 3 ranging from 300 to 2500 K. Fig. 13 and 14 demonstrate the rate constants for C 2 H 2 , C 4 H 4 and C 6 H 5 additions, and for C 2 H 3 and C 4 H 4 additions along temperature respectively. Fig. 15 shows the aromatic structures for C 2 H 3 and C 4 H 4 additions. Results imply that reactions R48 and R53 almost share the same rate constants at different temperatures, which is because the reactive sites of CS38 and CS43 are both armchair sites. Moreover, for C 4 H 4 additions, the rate constant added onto CS1 is the fastest, followed by CS48, and that of CS53 is the last. All reactive sites on CS1, CS48 and CS53 are free edges with no adjacent groups, and the molecular mass of CS1 is the lightest, followed by CS48, and that of CS53 is the heaviest. Thus, we believe C 4 H 4 can be more easily added onto aromatic structures with light mass.

Kinetic modeling
The mechanism investigated here was improved from Hansen's mechanism 31 by the quantum chemical calculations reported before 32 and in this work. The improvements of the new mechanism are shown in Fig. 16. All computations for laminar ames were performed with the code PREMIX from CHEMKIN II. 34 Thermodynamic and transport data for the species involved in the mechanism were taken from Hansen's mechanism 31 or evaluated by applying group additives rules. The improved mechanism was veried in premixed butane and butadiene ames separately. Species concentrations determined from these ames were compared with the experimental results and the simulation results from Hansen's mechanism. Thereby, the inuence of new PAHs formation routes on predicting PAHs formation was analyzed.
3.3.1 Species concentration in premixed 1,3-butadiene ame. With the improved chemical mechanism, we simulated the variation in concentrations of the main intermediates and PAHs in the premixed 1,3-butadiene ame. All modelling parameters were cited from experiments, 35 and all results were shown in Fig. 17 compared with experiments 35 and simulation of Hansen's mechanism. 31 The mole concentrations of C 2 H 2 , C 2 H 3 , C 4 H 4 , A 1 and A 1 C 2 H 3 decrease at low temperature (Fig. 17). Among them, the consumption of C 2 H 3 , C 4 H 4 , A 1 and A 1 C 2 H 3 may be because of the newly-added PAHs formation routes, and the C 2 H 2 concentration decreases probably because of the transition of C 2 H 2 into C 2 H 3 and C 4 H 4 for chemical equilibrium. Specically, the added PAHs formation routes do contribute to PAHs formation, especially at low temperature.
The mole concentrations of A 1 CH 3 and A 2 increase, but those of A 1 C 2 H and A 2 C 2 H decrease compared with the results of Hansen's mechanism. A 2 forms from HACA routes, conjugation of A 1 CH 2 radical and C 3 H 3 radical, or conjugation of two cyclopentadienyl radical in Hansen's mechanism (Fig. 16). A 2 formation routes via C 2 H 3 and C 4 H 4 additions are newly-added in this study. Hence, the increase of the A 2 mole concentration compared to the results of Hansen's mechanism is mainly due to the new added routes. As a consequence of chemical equilibrium, the mole concentration of A 1 CH 3 also increases. Since A 1 C 2 H and A 2 C 2 H are both reactants in the new added PAHs formation routes, their mole concentrations decrease compared with the results of Hansen's mechanism.
3.3.2 Species concentration in premixed butane ame. The variations in the concentrations of main intermediates and PAHs in the premixed butane ame were simulated according to experiments, 36 Hansen's mechanism 31 and the improved mechanism in this study. All results were shown in Fig. 18.
The C 2 H 3 mole concentration from the improved mechanism agrees well with the data from Hansen's mechanism (Fig. 18). Namely, the newly-added PAHs formation routes via C 2 H 3 addition were not brought into full play in butane ame. Fig. 16 PAHs formation process in the improved mechanism (black lines: from Hansen's mechanism; red lines: from quantum chemical calculations reported before 32 and in this study).
additions in butane ame. This is mainly because of the geometries of 1,3-butadiene and butane.

Conclusions
Detailed A 3 and A 4 formation routes via C 2 H 3 and C 4 H 4 addition reactions onto aromatic radicals were investigated with the G3(MP2, CC) method. The inuences of reaction sites, reaction types and additions to PAHs formation rates were discussed. The PAHs formation routes gained in this study and reported before were used to improve an existing mechanism. This improved mechanism was veried and compared to experimental results and the modelling results of the original mechanism. The contributions of C 2 H 3 and C 4 H 4 addition routes to PAHs formation in both butadiene and butane ame were studied. (1) Compared with C 2 H 2 addition, C 2 H 3 and C 4 H 4 addition reactions occurred more easily at the radicals of aromatics; C 2 H 3 , C 4 H 4 and C 6 H 5 additions were more irreversible, and the formed PAH geometries were more irreversible. All these addition reactions easily occurred in ame, and were veried to produce PAHs at low temperature in both butadiene and butane ame.
(2) H atoms are important for PAHs formation. On one hand, almost all H-abstractions with the assistance of H atoms need barriers about 30 kcal mol À1 , and disproportionations need to overcome high barriers and are highly endothermic. That is, H atoms decreased the energies for radical production, and made the reactions more irreversible. On the other hand, H loss with the assistance of O atom and OH radical needs to overcome much higher barriers than that with the assistance of H atom. In other words, H atoms more easily induce H loss than O atoms and OH radicals.
(3) The C 2 H 3 and C 4 H 4 addition routes are both benecial to PAHs formation in 1,3-butadiene ame, and the C 4 H 4 addition route benets PAHs formation in butane ame. This is mainly because C 4 H 4 can be effectively formed from continuous dehydrogenations of 1,3-butadiene and butane. C 2 H 3 can be formed easily from the breakage of C-C in 1,3-butadiene structure, but difficultly from the corresponding reactions of butane molecules.

Conflicts of interest
There are no conicts to declare.