(421e) Programming Self-Assembly of Colloidal Films Using Escher’s Genetic Code

Numerous modern applications of two-dimensional (2D) colloidal materials rely on the precise organization of colloids at a planar interface. Colloids are facile building blocks whose shape, size, and surface functionality can be easily designed in-silico to self-assemble into a wide range of desirable patterns; however, it remains a challenge to experimentally realize many such designs, as does understanding the connection between optimal sets of these features and the final structure. To close this knowledge gap, we developed a method for deriving surface functionalization patterns from isohedral tilings that induce self-assembly into any chosen 2D symmetry group at a planar interface. The result is a sequence of letters, s ∈ {A, T, C, G}, or a gene, that describes the colloid’s anisotropic shape and chemical patterning. This topological genome is finite and can be exhaustively enumerated. Moreover, these genes are human readable and can be used intuitively to design colloids. This technique bears a striking similarity to methods Maurits Cornelis (M. C.) Escher used to design his artwork which illustrates the how flexible this approach can be. We further show how to optimize features of a gene to design patchy particles which are both simple to realize and self-assemble into a film with chosen porosity determined a priori. This provides a derivable route to colloid functionality that enables film porosity and symmetry to be simultaneously programmed explicitly.