(145a) Embracing Disorder: Quantitative Biomimetics of Fibrous Nanocomposites through Graph Theory

Biomimetic nanocomposites derived from cellulose and other nanofibers offer resource- conscious alternatives to many current load-bearing, charge-transporting, ion-selective, and
optically-active materials. These composites feature a superposition of order and disorder, making them inherently difficult to design and optimize, albeit easy to make, adapt, and scale. A similar interplay between non-random structure and stochastic variation is observed in high-performance biomaterials that exhibit exceptional mechanical, transport, and optical properties. In both natural and synthetic systems, such combinations of hard-to-achieve properties are realized through the intertwining of structural motifs across multiple length scales. However, the high degree of stochasticity in these materials renders traditional structural analysis tools—developed for crystals, quasicrystals, and glasses—ineffective.

Recent studies show that this challenge, relevant across disciplines, can be addressed using graph theory (GT) and topometric materials design. Graphs—comprising nodes and
edges—are uniquely suited to capture both ordered and disordered features in hierarchically organized systems. We demonstrate that GT descriptors extracted from electron microscopy images can quantitatively identify structural motifs with short-, medium-, and long-range regularities. Using examples of fibrous nanocomposites based on cellulose nanocrystals, metal nanowires, gold nanodendrites, and aramid nanofibers, we illustrate the versatility and generality of this approach. Furthermore, we develop topometric relationships—where physical properties are linked to both topological and metric features—for nanowire coatings, nanofibrous battery cathodes, and chiroptical nanodendrites. GT methodologies offer a pathway for replicating and surpassing biological architectures, enabling scalable biomimetics and removing critical bottlenecks in modern materials design.

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