Construction and Properties of Sierpiński Triangular Fractals on Surfaces

Abstract

Fractal structures are of fundamental importance in science, engineering, mathematics, and aesthetics. Construction of molecular fractals on surfaces can help to understand the formation mechanism of fractals and a series of achievements have been acquired in the preparation of molecular fractals. This review focuses on Sierpiński triangles (STs), representatives of various prototypical fractals, on surfaces. They are investigated by Monte Carlo simulations and ultra-high vacuum scanning tunneling microscopy. STs are bonded through halogen bonds, hydrogen bonds, metal-organic coordination bonds and covalent bonds. The coexistence of and competition between fractals and crystals are realized for a hydrogen-bonded system. Electronic properties of two types of STs are summarized.

Keywords: Sierpiński triangle; fractals; scanning tunnelling microscopy; surface science; surface self-assembly.