Chirality-Complexity Relations and Graph Theory of Nanostructures

15^th March 2023, 13:00 Gossage Lecture Theatre, Chemistry
Prof. Nicholas Kotov
Chemical Engineering, University of Michigan

Abstract

Since Leonardo Da Vinci discoveries in science and
engineering were inspired by evolution-optimized geometry of
molecules, tissues, and organisms found in biology using
non-biological preparatory techniques. Chiral nanostructures – a large
and rapidly evolving class of metal, semiconductor, and ceramic
materials is one of these materials. Besides fascinating optical,
catalytic, and biological properties, the studies of chiral
nanostructures revealed something more. Unlike other geometric
properties, mirror asymmetry is invariant to scales. Thus, the
synthesis and self-assembly of chiral nanostructures showed how basic
geometric properties of Nature’s smallest building blocks can produce
highly complex and adaptable structures at macroscale.

Analysis of the hierarchically organized micro- and macrostructures
obtained by self-assembly of the chiral nanoparticles (NPs)
demonstrated the mechanism of emergence of effective complexity in
such systems and how such diversity of the building blocks contributes
to it. These findings became possible by applying graph theory (GT)
for calculation of the quantitative measures of their complexity by
describing the constituent NPs as nodes and the interfaces between
them as edges of graphs. Taking an example of hierarchically organized
particles with twisted spikes from polydisperse Au-cystein
nanoplatelets [1], we found that (a) formation of complex structures
does not require monodispersity; (b) complexity index (CI) of the
synthetic particles can be higher than biological prototypes; and (c)
complexity emerges from competing chirality-dependent assembly
restrictions. The GT description of chiral hedgehogs can also be
expanded to other nanoscale structures creating analogs of chemical
formulas for particle systems [2]. Among other outcomes of the
analysis of the chirality-complexity relations, GT-based description
of nanostructures leads to quantitative description of biomimetic
materials combining order and disorder that is essential to their
functionality. Expansion of GT principles from particles to composites
enabled transition from inexact approach of their good-luck-based
engineering to function-driven design encompassing multiple
properties. While this work is still in progress, the methods of
GT-based biomimetic materials engineering can be demonstrated by the
multiparameter optimization of complex networks of aramid nanofibers
for batteries for robotics [3] and biomedical implants [4].

References
[1] W. Jiang, et al, Emergence of Complexity in Hierarchically
Organized Chiral Particles, Science, 2020, 368, 6491, 642.
[2] S. Zhou, et al, Chiral assemblies of pinwheel superlattices on
substrates, Nature, 2022, 612, 259.
[3] Wang, M.; Vecchio, D.; et al Biomorphic Structural Batteries for
Robotics. Sci. Robot. 2020, 5 (45), eaba1912.
[4] H. Zhang, et al Graph Theoretical Design of Biomimetic Aramid
Nanofiber Nanocomposites as Insulation Coatings for Implantable
Bioelectronics, MRS Bulletin, 2021, 46, 7, 576.

Abstract with images:
http://kurlin.org/MIFplusplus/15March2023-Nicholas-Kotov.pdf

Additional Materials

• http://kurlin.org/MIFplusplus/15March2023-Nicholas-Kotov.pdf