Derivable genetic programming for two-dimensional colloidal materials

We describe a method for deriving surface functionalization patterns for colloidal systems that can induce self-assembly into any chosen periodic symmetry at a planar interface. The result is a sequence of letters, s is an element of{A,T,C,G}, or a gene, that describes the perimeter of the colloidal object and programs its self-assembly. This represents a genome that is finite and can be exhaustively enumerated. These genes derive from symmetry, which may be topologically represented by two-dimensional parabolic orbifolds; since these orbifolds are surfaces that may be derived from first principles, this represents an ab initio route to colloid functionality. The genes are human readable and can be employed to easily design colloidal units. We employ a biological (genetic) analogy to demonstrate this and illustrate their connection to the designs of Maurits Cornelis (M. C.) Escher. Published by AIP Publishing.

Automated summary

This paper describes a method for deriving surface functionalization patterns for colloidal systems, enabling them to self-assemble into chosen periodic symmetries. The genes for symmetry are derived from 2D parabolic orbifolds based on first principles, providing a new approach for designing colloidal units.