Construction of Sierpiński Triangles up to the Fifth Order

Self-similar fractal structures are of fundamental importance in science, mathematics, and aesthetics. A series of molecular defect-free Sierpiński triangle fractals have been constructed on surfaces recently. However, the highest order of the fractals is only 4 because of the limitation of kinetic growth. Here complete fifth-order Sierpiński triangles with a lateral length of 0.05 μm were successfully prepared in ultrahigh vacuum by a combination of templating and coassembly methods. Fe atoms, 4,4″-dicyano-1,1′:3′,1″-terphenyl, and 1,3-bis(4-pyridyl)benzene molecules were used to build fractals on the reconstructed Au(100)-(hex) surface. The new strategy may be applied to construct various Sierpiński triangles of higher orders.

 

Construction of Sierpiński Triangles up to the Fifth Order

Chao Li, et al.

J. Am. Chem. Soc., Article ASAP
DOI: 10.1021/jacs.7b05720

Source: pubs.acs.org