Packing density of rigid aggregates is independent of scale

Large planetary seedlings, comets, microscale pharmaceuticals, and nanoscale soot particles are made from rigid, aggregated subunits that are compacted under low compression into larger structures spanning over 10 orders of magnitude in dimensional space. Here, we demonstrate that the packing density (θf) of compacted rigid aggregates is independent of spatial scale for systems under weak compaction. The θf of rigid aggregated structures across six orders of magnitude were measured using nanoscale spherical soot aerosol composed of aggregates with ∼ 17-nm monomeric subunits and aggregates made from uniform monomeric 6-mm spherical subunits at the macroscale. We find θf = 0.36 ± 0.02 at both dimensions. These values are remarkably similar to θf observed for comet nuclei and measured values of other rigid aggregated systems across a wide variety of spatial and formative conditions. We present a packing model that incorporates the aggregate morphology and show that θf is independent of both monomer and aggregate size. These observations suggest that the θf of rigid aggregates subject to weak compaction forces is independent of spatial dimension across varied formative conditions.