Competing morphologies and escaping to infinite size in geometrically frustrated assemblies

In geometrically frustrated assemblies (GFAs) interactions between self-assembling elements favor local packing that is incompatible with uniform global order in the assembly. This classification applies to a broad range of soft matter assemblies, including self-twisting protein bundles and spherical crystals (e.g. particle coated droplets and protein shells). There is a growing understanding that the ability of soft matter GFA to tolerate and build up gradients of imperfect order leads to anomalous behaviors. Most notably, GFA thermodynamics have the ability to "sense" domain sizes on length scales much larger than size individual sub-units or their interactions, opening up the unique possibility of self-limiting equilibria intermediate to dispersed and bulk assembly regimes. In this talk, I describe size-sensitive assembly predicted by two prototypical models of GFAs: frustrated chiral filament bundles and intrinsically-curved 2D crystals. Any given mechanism of assembly frustration (e.g. via chirality, curvature, etc.) poses the basic challenge to understand what are the fundamental limits on breadth of the self-limiting phase, and in turn, the range of self-limiting sizes possible. Underlying these limits is the potential for GFA to escape frustration (in full or in part) via any one of a number competing and structurally distinct morphological responses, including the formation of topological defects in the "bulk" assembly, the reshaping of the free boundary of the assembly (isotropic vs. anisotropic domains), and the elastic "flattening" of shape incompatibility. Each of these mechanisms relaxes the cost of frustration, but exhibit vastly different dependencies on the size, shape, thermodynamic properties of the assembly. I describe our current understanding of the competition between these distinct morphological responses and its implications for the broader phase diagrams of GFAs.