Scalable Quasiperiodicity of Two-Dimensional Moiré Metal-Organic Frameworks

The discovery of quasicrystals, characterized by unique, non-repeating atomic arrangements and forbidden rotational symmetries, has significantly expanded our understanding of crystalline materials. However, controlling quasiperiodic length scales remains challenging because the quasiperiodic arrangements are often influenced by chemical compositions. In this study, we utilized metal-organic frameworks (MOFs) as a highly designable platform to achieve scalable quasiperiodicity. Using isoreticular design principles, we demonstrated the formation of dodecagonal quasiperiodic patterns in two-dimensional Moiré MOFs with various ditopic organic ligands. By precisely controlling ligand lengths, we achieved angstrom-level modulation of quasiperiodic length scales, as evidenced by high-resolution transmission electron microscope (HR-TEM) and mathematical validation. This work bridges the gap between quasiperiodicity and MOFs, highlighting the potential of MOFs for the systematic and scalable exploration of quasiperiodic patterns.