Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
J Chem Phys. 2022 Sep 21;157(11):114112. doi: 10.1063/5.0106131.
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 ∈ {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.
我们描述了一种用于衍生胶体系统表面功能化模式的方法，该方法可以在平面界面上将自组装诱导为任何所需的周期性对称。结果是一个字母序列，s ∈ {A,T,C,G}，或一个基因，它描述了胶体物体的周长并编程其自组装。这代表了一个有限的基因组，可以进行详尽的枚举。这些基因源于对称性，对称性可以用二维抛物线奇点来拓扑表示；由于这些奇点是可以从第一性原理推导出来的表面，这代表了胶体功能的从头开始的途径。这些基因是人类可读的，可以方便地设计胶体单元。我们采用生物学（遗传）类比来演示这一点，并说明它们与 Maurits Cornelis (M.C.) Escher 的设计的联系。
