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 revealed 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 suggests that the lattice constant of this mesocrystal depends on the characteristics of the particle size distribution, specifically the mean particle size and the width of the size distribution. In addition, 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.
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