Pathways to Complexity with Imperfect Nanoparticles
Abstract
The central objective of this project is to find technologically-friendly pathways to high-performance materials with high complexity. A quarter of a century ago, Nobel Laureate, M. Gell-Mann, introduced a conceptual measure of effective complexity, EC, to describe structural sophistication of matter, but the general synthetic pathways to high-EC structures and actual mathematical methods for EC calculations remain unknown. This project will address these knowledge gaps by elaborating the theory and practice of high-EC materials made by self-assembly of inorganic nanoparticles (NPs). Perhaps counterintuitively, but in accord with Gell-Mann’s theory, materials with high EC will be formed when a degree of disorder is introduced by controlled increase of NP polydispersity. We will show theoretically, computationally, and experimentally that assembly of highly complex structures from polydispersed NPs can be realized when: (1) NP shape and some symmetry elements are conserved in the entire ensemble and (2) assembly processes involve competing frustrations necessitating that NP assemblies acquire complex geometries to accommodate them. Two theoretical methods will be utilized to find the synthetic paths to high-CE materials. (1) Description of NP assemblies in non-Euclidian curved space will guide the selection of preferential geometries and polydispersity. (2) Statistical thermodynamics of frustrated assemblies will inform our choice of critical states associated with high-EC assemblies. The complexity of nanoassemblies will be enumerated using Graph Theory by describing them as nodes representing NPs and edges representing supramolecular connections between them. A Python software package for EC calculations based on structural connectivity index (SCI) will be written and made freely available to the scientific community. These theoretical studies will be practically implemented for chiral CdTe tetrahedrons and MoS2 nanoplatelets. The EC will be calculated for different degrees of polydispersity leading to the analytical expression for the Goldilocks curve, which will serve as an engineering tool for creating high EC-materials.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 07, 2021
- Source ID
- HQ00342010033
Entities
People
- Nicholas A. Kotov
Organizations
- Office of the Secretary of Defense
- University of Michigan
- Washington Headquarters Services