Molecular k-Uniform tiling

Tessellation of the Euclidean plane into regular polygons – tiles – is a mathematical concept for the description of intricate geometries associated with complex structures potentially displaying unique properties. The synthetic protocols to prepare structures showing complex geometries are therefore desirable.

The multimethod approach provided by the complex UHV system of CEITEC Nano enabled the synthesis and identification of 2- and 3-uniform tilings.

Employing a combination of experimental methods (LEEM, STM, XPS), Lukáš Kormoš with his colleagues revealed that a directed chemical transformation of a 4,4’-biphenyl-dicarboxylic acid on a silver substrate results in a mixture of intact, partially, and fully chemically transformed molecules. At certain composition of the system, the molecules self-assemble into structures that can be associated with k-uniform tilings.

Nature Device and Materials Engineering Community post:
https://devicematerialscommunity.nature.com/users/384385-jan-cechal/posts/65313-kepler-would-love-it

L. Kormoš, P. Procházka, A. O. Makoveev, J. Čechal: Complex k-Uniform Tilings by a Simple Bitopic Precursor Self-Assembled on Ag(001) Surface. Nat. Commun. 11 (2020), 1856.

link: https://rdcu.be/b3FqK