Isoreticular moiré metal-organic frameworks with quasiperiodicity.

The discovery of quasicrystals, characterized by unique, non-repeating atomic arrangements and forbidden rotational symmetries, has significantly expanded our understanding of structural order in materials. However, precise control over quasiperiodic length scales remains challenging due to the inherent constraints of atomic arrangements and chemical compositions. In this study, we utilized metal-organic frameworks (MOFs) as a designable platform to generate moiré patterns including dodecagonal quasiperiodic symmetry through the projection of twisted bilayer structures. Through rational ligand design based on isoreticular principles, the characteristic length scales of the resulting patterns can be systematically modulated, as demonstrated by high-resolution transmission electron microscopy (HR-TEM) and mathematical analysis. While the observed patterns exhibit characteristics reminiscent of quasicrystals, they result from the incidental stacking of twisted layers rather than intrinsic quasicrystalline order. This work provides a conceptual framework for incorporating quasiperiodicity into reticular chemistry and expands the structural design space for functional moiré materials.