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In this study, we investigated the self-ordering process in Langmuir films ofpolydisperse iron oxide nanoparticles on a water surface, employing in-situX-ray scattering, surface pressure-area isotherm analysis, and Brewster anglemicroscopy. X-ray reflectometry confirmed the formation of a monolayer, whilegrazing incidence small-angle X-ray scattering revealed short-range lateralcorrelations with a characteristic length equal to the mean particle size.Remarkably, our findings indicated that at zero surface pressure, the particlesorganized into submicrometer clusters, merging upon compression to form ahomogeneous layer. These layers were subsequently transferred to a solidsubstrate using the Langmuir-Schaefer technique and further characterized viascanning electron microscopy and polarized neutron reflectometry. Notably, ourmeasurements unveiled a second characteristic length in the lateralcorrelations, orders of magnitude longer than the mean particle diameter, withpolydisperse particles forming circular clusters densely packed in a hexagonallattice. Furthermore, our evidence suggested that the lattice constant of thismesocrystal 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, wherelarger particles were positioned closer to the center of the cluster. Finally,polarized neutron reflectometry measurements provided valuable insights intothe magnetization profile across the layer.

Mesoscale self-organization of polydisperse magnetic nanoparticles at the water surface