Emergent rhombus tilings from molecular interactions with $M$-fold rotational symmetry

TL;DR

This paper demonstrates that molecules with specific rotational symmetries can spontaneously self-assemble into rhombus tilings, revealing emergent network structures driven by geometric and symmetry considerations.

Contribution

It introduces a model showing how molecular rotational symmetry leads to emergent rhombus tilings and explores conditions for reconfiguration into triangular tilings.

Findings

Molecules with certain symmetries form rhombus tilings spontaneously.

Emergent networks can reconfigure into triangular tilings under specific conditions.

Geometrical arguments explain the formation of these network structures.

Abstract

We show that model molecules with particular rotational symmetries can self-assemble into network structures equivalent to rhombus tilings. This assembly happens in an emergent way, in the sense that molecules spontaneously select irregular 4-fold local coordination from a larger set of possible local binding geometries. The existence of such networks can be rationalized by simple geometrical arguments, but the same arguments do not guarantee networks' spontaneous self-assembly. This class of structures must in certain regimes of parameter space be able to reconfigure into networks equivalent to triangular tilings.