Frustrated Self-Assembly of Non-Euclidean Crystals of Nanoparticles

TL;DR

This paper develops an analytic theory for the self-assembly of tetrahedral nanoparticles into complex 3D structures, revealing how geometrical frustration and inter-particle interactions enable controllable, high-yield formation of helicoidal ribbons with potential technological applications.

Contribution

It introduces a novel theoretical framework based on non-Euclidean crystal structures to predict complex nanoparticle morphologies, advancing the understanding of programmable self-assembly.

Findings

Predicts formation of helicoidal ribbons with high yield

Shows qualitative agreement with experimental observations

Provides a general framework for designing complex nanostructures

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.