Self-Assembly of Biomimetic Nanostructures with High Complexity

In materials engineering, the belief that perfect order equals high performance is challenged by the high energy cost and sustainability concerns of achieving it. Studies on nacre-like biomimetic nanocomposites suggest that living organisms strategically integrate disorder with repeatable organizational motifs to achieve difficult-to-attain property combinations. However, the simultaneous presence of order, disorder, and the typical hierarchical organization of biological materials makes them intractable to conventional structural analysis developed for crystals or glasses.

Biomimetic nanocomposites, particularly those based on cellulose and other nanofibers, present an ideal opportunity to understand the interplay between order and disorder. They are also an attractive, resource- and energy-conscious alternative for load-bearing, charge-transporting, ion-selective, and optically-active materials. We propose an integrated approach to account for (1) structural stochasticity (disorder), (2) repeatable structural patterns (order), and (3) hierarchical organization in complex high-performance nanocomposites using Graph Theory (GT) and topometric materials design. Graphs, composed of nodes and edges, enable the quantification of order and disorder across multiple structural scales. GT descriptors, extracted from electron microscopy images, reveal regularities while accounting for statistical variation. Examples involving fibrous nanocomposites (cellulose nanocrystals, metal nanowires, gold nanodendrites, and aramid nanofibers) demonstrate the universality of this approach.

Topometric relationships—where physical properties are derived from both GT descriptors and metric parameters—have been shown for nanowire coatings, battery cathodes, and chiroptical nanodendrites. GT methods can be applied to both synthetic and evolution-optimized biomaterials, enabling the quantitative replication and ultimate outperformance of biological blueprints. Crucially, the deliberate and controllable integration of disorder in materials design offers a pathway to scalability, addressing critical bottlenecks in modern nanocomposites