Engineering Fractal Photonic Metamaterials by Stochastic Self-Assembly of Nanoparticles

The scale-invariant features of fractal-structured materials offer significant opportunities for the manipulation of short- and long-range lightmatter interactions in a 3D space, with recent photonics applications including biomolecular sensing and visible-blind photodetectors. The development of synthesis methods for the large-scale fabrication of fractal metamaterials with tuneable hierarchy bears significant potential and is the focus of many research fields. Among various fabrication routes, Brownian's motion-driven coagulation of nanomaterials, below their sintering temperature, leads to fractal-like structures presenting self-similar properties at different length scales. Herein, an in-depth investigation of the properties of fractal metamaterials obtained via the scalable self-assembly of hot aerosols of TiO2, Bi2O3, and Au-Bi2O3 nanoparticles, chosen as representative photonic materials, is reported. The fractal properties of these aerosol-synthesized nanoparticle powders and thin films are systematically investigated via small-angle X-ray scattering (SAXS), image analysis, and theoretical modeling. It is demonstrated that in the diffusion-limited aggregation (DLA) regime the fractal dimensions are preserved and in the range of 1.751.83 during the formation of the nanoparticle agglomerates, independently of the material. These findings provide a flexible platform for the engineering of macroscale 3D nanomaterials with hierarchical properties with potential applications ranging from energy harvesting to photocatalysis and sensing.