Focusing frustration for self-limiting assembly of flexible, curved particles

We show that geometric frustration in a broad class of deformable and naturally curved, shell-like colloidal particles gives rise to self-limiting assembly of finite-sized stacks that far exceed particle dimensions. When interparticle adhesions favor conformal stacking, particle shape requires curvature focusing in the stack, leading to a superextensive accumulation of bending costs that ultimately limit the ground-state stack size to a finite value. Using a combination of continuum theory and particle-based simulation, we demonstrate that the self-limiting size is controlled by the ratio of the intraparticle stiffness to interparticle adhesion, ultimately achieving assembly sizes that are tuned from a few, up to several tens of, particles. The range of self-limiting assembly is delimited by the two structural modes of "frustration escape" which evade the thermodynamic costs of curvature focusing. Crucially, each of these modes can be suppressed through suitable choice of adhesive range and patchiness of adhesion, providing feasible strategies to program finite assembly size via the interplay between shape frustration, binding, and deformability of colloidal building blocks.