Self-Assembly of Chiral Nanostructures with High Complexity

In materials engineering, structural disorder is often viewed as detrimental, while perfect order is linked to superior performance. Yet, attaining perfect order demands exponentially increasing energy, raising sustainability concerns. Biological materials—though rarely perfectly ordered—frequently surpass synthetic analogues in performance and multifunctionality. Studies of nacre-like nanocomposites [1,2] show that living systems purposefully combine disorder with repeatable motifs to achieve unique property combinations. However, the coexistence of order, disorder, and hierarchy in such systems defies classical analytical methods designed for crystals or glasses; what cannot be quantified cannot be rationally designed.

Nanofiber-based biomimetic composites present an exceptional opportunity to elucidate how order and disorder interplay in material performance. Self-assembling nanofibrous composites are also energy- and resource-efficient alternatives for load-bearing, charge-transporting, and optically active materials. We demonstrate that chirality is essential for obtaining materials with high complexity. Additionally, we show that quantitative assessment of complexity in hierarchically organized self-assembled materials can be achieved through graph theory (GT) [3,4].

GT represents materials as networks of nodes and edges, quantifying order and disorder across scales. GT descriptors derived from microscopy images capture short-, medium-, and long-range regularities while accounting for polydispersity. Examples include nanocomposites of cellulose nanocrystals, metal nanowires, gold nanodendrites, and aramid nanofibers, illustrating the universality of this approach. Topometric relationships—linking GT descriptors with physical properties—have been demonstrated for nanowire coatings, nanofibrous conductors [5], and chiroptical nanodendrites.