Self-limiting states of polar misfits: Frustrated assembly of warped-jigsaw particles

TL;DR

This paper investigates how shape misfit polarity in warped-jigsaw particles influences the formation of self-limiting, mesoscopic ribbon domains, revealing the role of shape symmetry and thermodynamics in frustrated assembly behaviors.

Contribution

It demonstrates that shape-misfit polarity leads to distinct self-limiting morphologies and provides a framework for designing frustrated particles with controlled assembly properties.

Findings

Polarity in shape-misfit results in two distinct ribbon morphologies.

Thermodynamic stability depends on binding anisotropy and misfit orientation.

Shape symmetry influences the emergent mesoscale structures.

Abstract

We study the ground state thermodynamics of a model class of geometrically frustrated assemblies, known as {\it warped-jigsaw} particles. While it is known that frustration in soft matter assemblies has the ability to propagate up to mesoscopic, multi-particle size scales, notably through the selection of self-limiting domain, little is understood about how the symmetry of shape-misfit at the particle scale influences emergent morphologies at the mesoscale. Here we show that polarity in the shape-misfit of warped-jigsaw puzzles manifests at a larger scale in the morphology and thermodynamics of the ground-state assembly of self-limiting domains. We use a combination of continuum theory and discrete particle simulations to show that the polar misfit gives rise to two mesoscopically distinct polar, self-limiting ribbon domains. Thermodynamic selection between the two ribbon morphologies is controlled by a combination of the binding anisotropy along distinct neighbor directions and the orientation of polar shape-misfit. These predictions are valuable as design features for ongoing efforts to program self-limiting assemblies through the synthesis of intentionally frustrated particles, and further suggests a generic classification of frustrated assembly behavior in terms of the relative symmetries of shape-misfit and the underlying long-range inter-particle order it frustrates.