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Symmetry-derived Structure Directing Agents for Two-dimensional Crystals of Arbitrary Colloids



Nathan Mahynski, Vincent K. Shen


We derive properties of self-assembling rings which can template the organization of an arbitrary colloid into any periodic symmetry in two Euclidean dimensions. By viewing this as a tiling problem, we illustrate how the shape and chemical patterning of these rings are derivable, and are explicitly reflected by the symmetry group's orbifold symbol. We performed molecular dynamics simulations to observe their self-assembly and found 5 different characteristics which could be easily rationalized on the basis of this symbol. These include systems which undergo chiral phase separation, are addressably complex, exhibit self-limiting growth into clusters, form ordered "rods" in only one-dimension akin to a smectic phase, and those from symmetry groups which are pluripotent and allow one to select rings which exhibit different behaviors. We discuss how the curvature of the ring's edges plays an integral role in achieving correct self-assembly, and illustrate how to obtain these shapes. This provides a method for patterning colloidal systems at interfaces without explicitly programming this information onto the colloid itself.
Soft Matter


colloids, self assembly, films, functional materials, materials


Mahynski, N. and Shen, V. (2021), Symmetry-derived Structure Directing Agents for Two-dimensional Crystals of Arbitrary Colloids, Soft Matter, [online],, (Accessed June 18, 2024)


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Created August 12, 2021, Updated November 29, 2022