Particle Design Rules for Size Control of Frustrated Assembly : Role of Interaction Range

Recent developments in the precise tuning of soft particle geometry and interactions provide new opportunities to design functional nanostructures with equilibrium size control by geometric frustration. A current theoretical challenge is to understand the role of discrete particles, and how limitations apparent in discrete particle design connect to limits in the achievable size control as consequences of various modes of frustration escape, such as defect formation and morphology transitions.

In this talk, we connect continuum modeling of frustrated crystalline membrane rings and ribbons to discrete particle geometry and interactions. The first mechanism of size control escape is the transition to an un-frustrated tube morphology, and the particle geometry is connected to distinct flattening costs for untwisting versus unbending. We show an additional enhancement of flattening with shorter-range interactions, and a distinct mechanism to limit size control by a transition to yielded structures.