Effective density and packing of compacted soot aggregates

The mass concentration of soot aggregates is often estimated from mobility size distributions using a mobility-based effective density, ρeff. This ρeff changes with aggregate morphology. In particular, the ρeff of a soot core increases when it becomes compacted by the surface tension of condensing coatings, such as combustion-related vapours, secondary aerosols, and cloud water. The extent of this compaction is a function of coating volume, up to an asymptotic limit of complete compaction. While complete compaction has previously been shown to correspond to a universal, scale-invariant packing factor for sufficiently large aggregates, it has not previously been explicitly quantified. Here, we critically reanalyze multiple datasets compiled from the literature on the ρeff of completely compact soot. We show that, regardless of the coating material, soot aggregates generally become completely compacted following a 5-fold increase in volume. The final aggregate shape is more simply described by ρeff than by mobility diameter or shape factor. Below 140 nm diameter (about 20 aggregate monomers), the compacted ρeff obeys a power law; above 140 nm, it reaches a constant value of 651 ± 8 kg m–3. This ρeff is 3 times larger than that of freshly-produced soot at 140 nm. We provide a parameterization of the compacted ρeff for the estimation of soot mass concentration after coating, or, conversely, for use as a benchmark to estimate the extent of aggregate restructuring. Our parameterization can be easily adapted to other nanoparticle aggregates whose material density is known.