(525e) Self-Assembly Templates for Two-Dimensional Colloidal Crystals Derived from Symmetry

We investigate self-assembling rings that can template the organization of an arbitrary colloid into any desired periodic symmetry in two Euclidean dimensions. By viewing this as a tiling problem, we illustrate how the shape and chemical patterning of these rings may be derived from symmetry, rather than through iterative inverse-design methods. Moreover, we illustrate how these features are explicitly reflected by their orbifold symbol, which provides a natural language to express them. We performed molecular dynamics simulations to observe the self-assembly of these rings and found 5 different characteristics which could be easily rationalized on the basis of their orbifold symbol. These include systems which (1) undergo chiral phase separation, (2) are addressably complex, (3) exhibit self-limiting growth into clusters, (4) may form a nematic phase, and (5) those from symmetry groups which allow one to select rings which exhibit different self-assembly behaviors. We discuss how the curvature of a ring’s edges plays an integral role in achieving correct self-assembly, and we illustrate how to derive these ring shapes. This provides a method for patterning colloidal systems at interfaces without explicitly programming this information onto the colloid itself.