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.
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