Fractal scaling of soot packing density across five size decades

We experimentally map the scaling laws for packing density (θ_f, solid component volume fraction) of soot aggregates across five orders of magnitude of size (R_g/a, normalized radius of gyration by monomer radius). The θ_f − R_g/a scaling relationship evolves through three successive regimes with distinct power-law exponents of −1.20 ± 0.01, −0.58 ± 0.06, and −1.31 ± 0.14. The first cross-over agrees with the classical aerosol-to-gel transition theory. This agreement, however, breaks down at the second cross-over point, where a late-stage cluster-cluster aggregation of aerosol gels takes over.