The inception process of PAH radicals in Fig. is investigated using a nanoreactor scheme, where a sphere boundary potential with periodic changes in radius is imposed on the PAH radicals to accelerate the collision and reaction process. Seven PAH species are considered (Fig. ). For each type of PAH, the atom number in the maximum cluster is calculated and normalized by PAH size for comparison. Figure shows the normalized max cluster size of PAH-b andf in the first 40 ps. In Fig. , the reactor radius (r) shows a variation with the time-dependent rectangular waveform. The period of each cycle is 4 ps. It starts with a relaxing stage of r=24.8 Å within the first 2 ps, followed by two compression stages with r=15.6 Å and r=13.0 Å for 1 ps each. Later, a new relaxing and compression cycle continues until simulations end. A reversible inception process is observed in the nanoreactor. During the compression stage, the reactor is compressed into a small volume (1/7 of the volume in the relaxing stage). PAH radicals collide with each other to form PAH clusters via physical interactions or chemical bonds. The reactor expands out with cluster decomposition in the next relaxation stage. The evolutions of cluster size are different for PAH-b and PAH-f. Cluster sizes in PAH-b fluctuate with the variation of reactor radius and remain a small value after 10 cycles (e.g., 40 ps). In contrast, the cluster for PAH-f gradually grows to a size of 44, although a decomposition stage is also observed in each relaxing stage. The clustering behaviors of PAH-b are somehow unexpected, as PAH-b is reported to form a crosslinked dimer. However, within the simulation time in the nanoreactor, it cannot further grow into large clusters. The evolution of cluster numbers (Ncluster) and normalized maximum cluster size (Scluster) is listed in Fig. . To inhibit fluctuations induced by the compression and relaxing process, only the maximum of Ncluster and the minimum of Scluster in each relaxing stage are plotted, which represent the actual clustering state. For small radicals (<200 Da), such as PAH-a and PAH-b, the number of clusters decreases to ~40 at 100 ps, while the maximum cluster size remains lower than 5. As the physical interaction is proportional to molecule size, it is expected that the inception of these radicals is only induced by a chemical bond. The fraction of reactive collisions (Freac) for these PAH radicals has been systematically examined by Martin et al. , which indicates the possibility of forming covalent bonds between two PAH radical monomers in a collision. PAH-a has a high fraction of reactive collisions (e.g., 0.023) among these PAH radicals. However, chemical bonding does not generate a large number of clusters within the simulation time. For medium-sized radicals (200-400 Da), such as PAH-c and -d, cluster sizes continue to grow at a flame temperature (1500 K). These radicals are much smaller than the minimum requirement for physical inception (e.g., 667 Da ), indicating the feasibility of physically stabilized soot inception. For large radicals (>400 Da), such as PAH-e, -f, and -g, the growth rates of cluster size are faster than those for medium-sized PAH radicals due to the strong physical interaction. The fraction of reactive collisions has a relation of PAH-g (Freac=0.024) > PAH-f (Freac=0.013) > PAH-e (Freac=0.008) but shows the same clustering trends (see Fig. ), suggesting that physical interactions play a more important role than chemical bonds for large radicals. Chemical nucleation is also observed in these radicals, but their rates are much lower than those of physical nucleation, which agrees with the calculations by Menon et al. . In addition, we also note that the chemical nucleation in the large cluster is slightly different from that in the dimer. Since the radicals in the dimer are always in a parallel stacked structure, Martin et al . reported that σ-radical dimers have weaker physical enhancement than π-radicals because the C-C bond prefers to be collinear with the aromatic planes. However, there are multiple stacks in a large cluster, which enable chemical nucleation between σ-radicals in the same plane. For example, chemical cross-links between different stacks of σ-radicals are observed in PAH-e clusters. In Fig. , we summarize the physical enhancement of the nucleation mechanism of dimers and large clusters. In a dimer, PAH radicals are stacked in parallel due to physical interactions, which can accelerate the cross-linking between π-radicals but does not affect σ-radicals. In a large cluster, there are multiple stacks, and σ-radicals can form cross-links with adjacent stacks.