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 using simple building blocks, and reach similar or higher level of sophistication in engineered materials? Here we present an analytic theory for the self-assembly of polyhedral nanoparticles (NPs) based on their crystal structures in non-Euclidean space. We show that the unavoidable geometrical frustration of these particle shapes, combined with competing attractive and repulsive interparticle interactions, lead to controllable self-assembly of structures of complex order. Applying this theory to tetrahedral NPs, we find high-yield and enantiopure self-assembly of helicoidal ribbons, exhibiting 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 rich complex morphologies with new material capabilities such as tunable optical activity, essential for multiple emerging technologies.
Highlights
Self-organized complex structures in nature, e.g., viral capsids, hierarchical biopolymers, and bacterial flagella, offer efficiency, adaptability, robustness, and multi-functionality
Recent experiments revealed that under attractive interactions from van der Waals forces, hydrogen bonds, and coordination bonds, these NPs can form a number of assemblies with interesting structural order, high complexity, and hierarchy at the nanoscale, from helices to curved platelets, capsids, and hedgehogs[2,3,4,5,6,7,8,9,10,11]. How these simple polyhedral building blocks led to the observed complex structures remains an open fundamental question
We show that non-Euclidean crystals provide us with sets of “reference metrics” g42 of the stress-free packing of these polyhedral NPs, characterizing their thermodynamic ground states, and offer a starting point to construct an energy functional of the assembled structures, the minimization of which guides us in the search for self-assembly morphologies
Summary
Self-organized complex structures in nature, e.g., viral capsids, hierarchical biopolymers, and bacterial flagella, offer efficiency, adaptability, robustness, and multi-functionality. As mentioned in the section “Model energy of frustrated nanoparticle self-assembly ”, Ebind + Esurface depends on how the slice M is cut from the non-Euclidean crystal, and is not affected by the morphology.
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