Frustrated Self-Assembly of Non-Euclidean Crystals of Nanoparticles

Abstract

Self-organized complex structures in nature, e.g. viral capsids, hierarchical biopolymers, and bacterial flagella, offer efficiency, adaptability, robustness, and multi-functionality. Can we program the self-assembly of three-dimensional (3D) complex structures with simple building blocks, and reach similar or higher level of sophistication in engineered materials? Here we present an analytic theory of tetrahedral nanoparticles (NPs) self-assembling in 3D space, where unavoidable geometrical frustration combined with competing attractive and repulsive inter-particle interactions lead to controllable, high-yield, and enantiopure self-assembly of helicoidal ribbons. This theory, based on crystal structures in non-Euclidean space, predicts morphologies that exhibit qualitative agreement with experimental observations. We expect that this theory will offer a general framework for the self-assembly of simple polyhedral building blocks into complex morphologies with new material capabilities such as tunable optical activity, essential for multiple emerging technologies.

Revised and updated main text and supplementary material. 20 pages, 6 figures

References in corpus (7)

• Elastic theory of unconstrained non-Euclidean plates
• Perspective: Geometrically-Frustrated Assemblies
• Shape Selection in Chiral Self-Assembly
• Director Deformations, Geometric Frustration, and Modulated Phases in Liquid Crystals
• Hard Discs on the Hyperbolic Plane
• Cumulative geometric frustration in physical assemblies
• Liquid crystal director fields in three-dimensional non-Euclidean geometries

Cited by in corpus (7)

• Chiral Assemblies of Pinwheel Superlattices on Substrates
• Cumulative geometric frustration in physical assemblies
• Focussing frustration for self-limiting assembly of flexible, curved particles
• Building blocks of non-Euclidean ribbons: Size-controlled self-assembly via discrete, frustrated particles
• Stress accumulation versus shape flattening in frustrated, warped-jigsaw particle assemblies
• Geometrically frustrated self-assembly of hyperbolic crystals from icosahedral nanoparticles
• Isometric Incompatibility in Growing Elastic Sheets