Résumé
Small-angle scattering is a powerful and popular technique for the characterization of the average structure of dense nanoparticle assemblies and aggregates. It is usually limited to not too big assemblies due to the limited q-range, and low enough concentrations to avoid interactions. A straightforward and quantitative analysis of the generally available scattered intensity – even for large assemblies, at high concentrations – at intermediate-q is detailed. It is based on the similarity in local structure between infinitely large homogeneous assemblies of hard spheres or moderately sticky hard spheres with any finite-sized nanoparticle assembly dominated by hard sphere interactions. The method provides information on the local volume fraction of particles. The approach is then extended to polydispersities up to 40%, using numerical simulations of hard spheres and mildly sticky hard spheres. As a result, a simple relationship between the observed structure factor minimum – termed the correlation hole – and the local volume fraction on the scale of neighboring particles, which is also linked to the coordination number, is given. This relationship shall be useful as a simple and efficient tool for the structural analysis of arbitrary aggregated colloidal systems. Finally, recent examples of filler structure in model and industrial polymer nanocomposites will be reviewed.