C4H3 Structure and Temperature Control Early Carbon-Ring Formation in Soot Chemistry

Soot begins to form long before visible carbon particles appear. During high-temperature combustion, hydrocarbon fuels break down into small unsaturated molecules and radicals that can react to form the first carbon rings. These rings can then grow into polycyclic aromatic hydrocarbons and eventually soot particles. Understanding how these first rings form helps explain how soot develops. These early reactions can follow several competing pathways, and even small differences in molecular structure can change which products are formed. Among the species present in combustion environments are two structural forms of the C₄H₃ radical, n-C₄H₃ and i-C₄H₃, together with acetylene (C₂H₂). Reactions between C₄ species and acetylene have been associated with the formation of six-carbon structures, but the chemistry is more complicated than simply producing a benzene-type ring. Addition can generate several intermediates, followed by molecular rotations, hydrogen movements and ring closure. Five-, six- and even four-membered carbon rings may compete with one another. Which pathway is favored depends on the stability of the final product, the energy barriers, and the way the molecules are arranged during the reaction.

The two C₄H₃ radicals also have different structures. Although n-C₄H₃ and i-C₄H₃ contain the same atoms, their arrangement changes which carbon sites are easiest to reach. In i-C₄H₃, acetylene can react at more than one position, which can lead to different reaction pathways and different cyclic products. In a recent research paper published in Journal of Fuel Chemistry and Technology, Hongbin Yang, Chunchang Zhang and Li Yao from Shanghai Maritime University, working with Wenwen Xia from Dalian Maritime University, examined these competing pathways using density functional theory combined with transition state theory. They calculated the potential-energy profiles, transition states and temperature-dependent reaction rates for acetylene reacting with both C₄H₃ isomers. Their goal was to determine how radical structure, reaction site, ring-closure barrier and temperature interact to control the formation of early cyclic soot precursors.

For n-C₄H₃, acetylene initially attacks the radical center at the C1 carbon. The calculated barrier for this initial addition is only 2.99 kcal/mol, which allows the reaction to proceed readily into a sequence of structural rearrangements. The newly created structure does not immediately close into a ring. Instead, rotation around the new carbon–carbon bond and subsequent C–H torsion reorganize the molecule into a geometry from which several cyclization pathways become accessible. The calculations describe ring formation as a stepwise radical addition and rearrangement process rather than direct formation of a six-membered aromatic structure.

Once the authors formed the appropriate intermediate, three ring sizes compete. The five-membered pathway requires a ring-closure barrier of about 4.2 kcal/mol, closely followed by the six-membered pathway at about 4.38 kcal/mol. Forming the four-membered structure is far less favorable kinetically because its barrier rises to approximately 33.4 kcal/mol. Rate calculations consequently place fulvenyl formation through the five-membered pathway first, phenyl formation through the six-membered pathway second and the four-membered route last. An important point is that the six-membered structure can be more thermodynamically stable without being produced fastest. The product distribution is controlled by the kinetic path required to reach each structure, and the slightly smaller barrier for five-membered ring closure gives fulvenyl an advantage.

The chemistry of i-C₄H₃ depends strongly on where acetylene attaches. Addition can occur at either the C2 or C4 position, but the C4 site reacts considerably faster. The calculations attribute this preference to lower steric hindrance around C4, which allows acetylene to approach in a more favorable orientation and reduces the activation barrier. As a result, reaction is preferentially directed toward the more accessible C4 site.

Reaction through the C4 site can again produce four-, five- and six-membered structures, but its selectivity changes substantially with temperature. Below about 1800 K, five-membered ring formation is faster than the four-membered pathway. Above this temperature, the ordering reverses and the four-membered pathway becomes faster because its rate responds more strongly to increasing temperature. The six-membered route remains much slower because its transition state experiences considerable steric resistance associated with twisting of the conjugated carbon framework. Its predicted rate remains far below those of the competing pathways, although this disadvantage becomes smaller as temperature rises.

The C2 pathway follows a different molecular sequence. After acetylene addition and several conformational changes, the structure undergoes concerted ring closure to form a five-membered intermediate. Subsequent hydrogen migration toward fulvenyl formation requires a much larger energy barrier, making this step strongly temperature dependent. The difference between the C2 and C4 pathways shows that the reaction site can change both the mechanism and which products are favored.

Temperature also changes the balance among these reactions more generally. For n-C₄H₃, the addition rate increases sharply with temperature. Differences between competing cyclization channels likewise become smaller at elevated temperatures because activation-barrier differences exert less control over reaction rates. The calculations covered a broad temperature range, allowing the authors to describe how pathway competition changes under different combustion conditions.

The new study shows that the first carbon rings formed during soot formation depend on more than the stability of the final products. The structure of the reacting molecules, how easily a reaction pathway can proceed, and the temperature all influence which ring structures are more likely to form. Five-membered ring chemistry is especially important because the calculations support a possible early soot-growth pathway in which fulvenyl-type structures can compete effectively with the more familiar six-membered aromatic route. This helps explain why different carbon-ring structures can form during the early stages of soot formation. The calculations agree with earlier combustion studies that detected both C₄H₃ isomers and five-membered fulvene species. This agreement supports the proposed reaction pathways and can help improve models of how soot precursors form.