Towards programmable assembly via geometric frustration

Geometric frustration is most often associated with the disruption of long-range order and proliferation of defects in the bulk state of a self-organizing system.  Soft and self-assembled materials, on the other hand, are able to tolerate some measure of local misfit due to frustration, allowing imperfect order to extend over at least some finite range. This talk focuses on theoretical frameworks for exploiting geometrically-frustrated assemblies (GFAs) to realize size-controlled, self-limiting assembly.  In GFAs self-assembling elements (e.g. particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly.  While concepts of GFA have been used to describe a broad range of soft matter structures, from self-twisting protein filament bundles, chiral membranes, to spherical shells, current challenges focus on exploiting the scale-dependent thermodynamics of GFA to design and realize new classes of intentionally ill-fitting assemblies that target equilibrium architectures with well-defined dimensions on length scales that extend far beyond the size of the building blocks.  In this talk, I describe some of the emerging principles and ongoing efforts to engineer the intra-assembly stress propagation and thermodynamic self-limitation in assemblies through the shape, interaction and flexibility of those building blocks.  A generic feature of soft GFA systems, are mechanisms of frustration escape, structural modes that limit the maximum range of self-limitation, which in turn define key design features frustrated building blocks that extend the range of accessible self-limiting size well beyond the few-particle size.