Relevance of Packing to Colloidal Self-Assembly

TL;DR

This paper critically examines the role of packing arguments in the self-assembly of colloidal crystals, revealing that packing is not the causal mechanism and that optimal shapes are imperfect versions of ideal packings.

Contribution

It demonstrates that packing is not the primary cause of colloidal crystal formation and identifies that the best particle shapes are imperfect packings, challenging previous assumptions.

Findings

Packing is not the causal mechanism in colloidal self-assembly.

Ideal packing shapes are not the optimal particle shapes at high pressure.

Imperfect shapes of ideal packings are more effective for self-assembly.

Abstract

Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they often, but not always, work. We examine when, if ever, packing is a causal mechanism in hard particle approximations of colloidal crystals. We investigate three crystal structures comprised of their ideal packing shapes. We show that, contrary to expectations, the ordering mechanism cannot be packing, even when the thermodynamically self-assembled structure is the same as that of the densest packing. We also show that the best particle shapes for hard particle colloidal crystals in the infinite pressure limit are imperfect versions of the ideal packing shape.