Dynamical and equilibrium calculations of self-limited assembly through geometric frustration

The self-assembly of subunits into large structures with well-defined finite sizes is ubiquitous in biology. Understanding how to engineer self-assembling structures that exhibit such self-limiting assembly would have important applications in developing functional materials. Recent theoretical arguments have proposed a broad mechanism for self-limiting, geometrically frustrated assembly, in which the preferred local packing of subunits is frustrated by an incompatibility with the preferred global order of the assembly process.

In this talk, we use a recently developed dynamical MC algorithm and free energy calculations to study the assembly of subunits that undergo frustrated assembly. We consider triangular elastic subunits that assemble into a 2D sheet with local hexagonal packing, which is frustrated by the fact that the preferred inter-subunit binding angle favors a negative Gaussian curvature. This incompatibility induces a strain which grows with the size of the assemblage, in some cases leading to a finite size equilibrium assembly with open boundaries. We characterize the relationship between subunit geometry, material properties, the assembly size, and its robustness to parameter variations.