Determination of the local density of polydisperse nanoparticle assemblies

Quantitative characterization of the average structure of dense nanoparticle assemblies and aggregates is a common problem in nanoscience. Small-angle scattering is a suitable technique, but it is usually limited to not too big assemblies due to the limited experimental range, low concentrations to avoid interactions, and monodispersity to keep calculations tractable. In the present paper, a straightforward analysis of the generally available scattered intensity - even for large assemblies, at high concentrations - is detailed, providing information on the local volume fraction of polydisperse particles with hard sphere interactions. It is based on the identical local structure of infinite homogeneous nanoparticle assemblies and their subsets forming finite-sized clusters. This approach is extended to polydispersity, using Monte-Carlo simulations of hard and moderately sticky hard spheres. As a result, a simple relationship between the observed structure factor minimum - termed the correlation hole - and the average local volume fraction κ on the scale of neighboring particles is proposed and validated through independent aggregate simulations. This relationship shall be useful as an efficient tool for the structural analysis of arbitrarily aggregated colloidal systems.