GRADUATE SEMINAR 1

Abstract

In materials engineering, structural disorder is typically viewed as a detriment, while perfect order is often equated with high performance. However, achieving high degrees of order requires significant energy input, raising sustainability concerns for future technologies. In contrast, biological materials rarely exhibit perfect order, yet they frequently surpass synthetic counterparts in performance and multifunctionality [1]. Studies of biomimetic nanocomposites suggest that living organisms incorporate disorder as a deliberate design parameter to achieve otherwise incompatible combinations of properties, such as strength, toughness, ion selectivity, and optical activity [1,2]. However, the large degree of disorder in Nature-designed materials makes it difficult to describe their structure and even more difficult to design and adapt. At the same time materials with disorder as designer parameters are more suitable for adaptive and additive manufacture while requiring less energy for their production.

This problem can be addressed using graph theory (GT) and topometric materials design [3]. Graphs—comprising nodes and edges—provide a mathematical framework to represent both ordered and disordered components in hierarchically structured materials. We show that GT descriptors, derived from electron microscopy images, can accurately quantify short-, medium-, and long-range structural motifs, including irregularities [4]. This methodology is demonstrated using fibrous nanocomposites composed of aramid nanofibers, cellulose nanocrystals, metal nanowires, and gold nanodendrites. Structure–property relationships were established through combined graph-theoretical and metric parameters. The generality and practical utility of this approach are further validated in the design of transparent electrodes [5], membranes and battery cathodes, demonstrating the potential of GT-based methods to guide the engineering of materials that integrate both order and disorder. The fundamental importance of GT methods for better understanding of interactions at nanoscale can be demonstrated by the identification of multi-body interactions during self-assembly of nanoparticles in dispersions [6] that can be generalized across multiple types of nanoparticles.

References:

[1] M. Yang, N. A. Kotov Quantitative biomimetics of high-performance materials, Nature Reviews Materials, 2025 10(5) 382-395.
[2] X. Mao, N. Kotov, Complexity, disorder, and functionality of nanoscale materials, MRS Bulletin, 2024, 49, 352.
[3] Jiang, W.; Emergence of Complexity in Hierarchically Organized Chiral Particles; Science, 2020, 368, 6491, 642.
[4] D.A.Vecchio, et al Spanning Network Gels from Nanoparticles and Graph Theoretical Analysis of Their Structure and Properties, Advanced Materials, 2022, 34, 23, 2201313.
[6] W. Wu, et al Layer-by-Layer Assembled Nanowire Networks Enable Graph-Theoretical Design of Multifunctional Coatings, MATTER, 2025, 8, 1, 101870.
[6] J. Hallstrom et al, Decoding Collective Dynamics and Complexity in Nanoparticle Assemblies via Graph Theory, Science, 2026, 392 (6799), eaeb5134.