Pushing the Limits of Size Control for Geometrically Frustrated Assembly of Ribbons and Rings*

Robust control of equilibrium assembly sizes allows templating, scaffolding and functional materials at scales much larger than the dimensions of the building blocks. Geometrically frustrated assembly achieves this size control, where assembly stress can accumulate over lengths determined by both the geometry of molecular misfit and assembly elasticity. The limits of this size control depend on modes of assembly softness.
We describe a system of negatively curved 2d assemblies that form rings and ribbons limited by geometric frustration. We connect a continuum theory description to a new particle model, and show how this realization preferentially flattens by unbending rather than untwisting. The consequence of differing soft modes on stress accumulation is that additional molecular geometry appears in the continuum description, where previous work showed equivalent frustration independent of the programmed extrinsic geometry. We expect these effects will generally apply to molecular design of geometrically frustrated assembly.