Soft Mechanisms of Escape in Geometrically Frustrated Assembly

Geometrically frustrated assembly (GFA) has garnered interest as a mechanism for achieving self-limitation in systems of assembling particles. In a previous work [1], we developed a minimal lattice model of frustrated assembly —focusing on the case of fixed frustration — where the super-extensive accumulation of strain persists to infinite size. Here, dispersion, self-limitation and defect proliferation provide the only means of alleviating frustration. However, in most physical examples of GFA, the source of frustration is not perfectly rigid and can be elastically deformed— or flattened —thus providing an additional method of strain attenuation. In this talk, we extend our model to include such an additional soft mode of frustration escape. Then — using a combination of numerical and theoretical techniques — we study its affect on the phase behavior of frustrated assembly, with a particular focus on how flattening alters the self-limited domain size. In the end, we conclude with a discussion of how this extended model maps onto the broader class of orientationally frustrated assembly and allows us to address basic questions about whether or not different mechanisms of soft frustration escape can lead to fundamentally different phase behaviors.

[1] Hackney et. al. PRX 2023.