Using density functional theory and master equation modeling, we have studied the kinetics of small unsaturated aliphatic molecules reacting with polycyclic aromatic hydrocarbon (PAH) molecules having a diradical character. We have found that these reactions follow the mechanism of carbon addition and hydrogen migration (CAHM) on both spin-triplet and open-shell singlet potential energy surfaces at a rate that is about ten times those of the hydrogen-abstraction-carbon-addition (HACA) reactions at 1500 K in the fuel-rich postflame region. The results also show that the most active reaction sites are in the center of the zigzag edges of the PAHs. Furthermore, the reaction products are more likely to form straight rather than branched aliphatic side chains in the case of reacting with diacetylene. The computed rate constants are also found to be independent of pressure at conditions of interest in soot formation, and the activation barriers of the CAHM reactions are linearly correlated with the diradical characters.