  In this study, we investigated the self-ordering process in Langmuir films of
polydisperse iron oxide nanoparticles on a water surface, employing in-situ
X-ray scattering, surface pressure-area isotherm analysis, and Brewster angle
microscopy. X-ray reflectometry confirmed the formation of a monolayer, while
grazing incidence small-angle X-ray scattering revealed short-range lateral
correlations with a characteristic length equal to the mean particle size.
Remarkably, our findings indicated that at zero surface pressure, the particles
organized into submicrometer clusters, merging upon compression to form a
homogeneous layer. These layers were subsequently transferred to a solid
substrate using the Langmuir-Schaefer technique and further characterized via
scanning electron microscopy and polarized neutron reflectometry. Notably, our
measurements unveiled a second characteristic length in the lateral
correlations, orders of magnitude longer than the mean particle diameter, with
polydisperse particles forming circular clusters densely packed in a hexagonal
lattice. Furthermore, our evidence suggested that the lattice constant of this
mesocrystal depended on the characteristics of the particle size distribution,
specifically the mean particle size and the width of the size distribution.
Additionally, we observed internal size separation within these clusters, where
larger particles were positioned closer to the center of the cluster. Finally,
polarized neutron reflectometry measurements provided valuable insights into
the magnetization profile across the layer.
