Layer-by-layer assembled nanowire networks enable graph-theoretical design of multifunctional coatings

Complex multifunctional coatings combining order and disorder are central for information, biomedical, transportation, and energy technologies. Their scalable fabrication is possible using nanostructured composites made by layer-by-layer assembly (LBL). Here, we show that structural descriptions encompassing their nonrandom disorder and related property-focused design are possible using graph theory (GT). Two-dimensional images of LBL films of silver and gold nanowires (NWs) were used to calculate GT representations. We found that random stick computational models often used to describe NW, nanofiber, and nanotube materials give inaccurate predictions of their structure. Concurrently, image-informed GT models accurately predict the structure and properties of the LBL films, including the unexpected nonlinearity of charge transport vs. LBL cycles. The conductivity anisotropy in LBL composites, not readily detectable with microscopy, was accurately predicted using GT models. Spray-assisted LBL offers the direct translation of GT predictions to additive, scalable coatings for drones and potentially other technologies.