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

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.

References in corpus (6)

• Reversible self-assembly of patchy particles into monodisperse icosahedral clusters
• The role of collective motion in examples of coarsening and self-assembly
• Designed Interaction Potentials via Inverse Methods for Self-Assembly
• Classical dimers with aligning interactions on the square lattice
• Theory and simulation of two-dimensional nematic and tetratic phases
• Entropically-stabilised growth of a two-dimensional random tiling