Dodecagonal Quasicrystal Phase in Block Copolymers: Stable or Metastable?

In the last decade, quasicrystal (QC) phases as a special kind of ordered aperiodic structures have been observed in various soft matter systems including self-assembling block copolymer(BCP) melts. However, the thermodynamic stability of QC is a long-standing problem in the community of condensed matter physics. In this presentation, the relative stability of cylindrical dodecagonal quasicrystal (DDQC) phase formed by ABCB tetrablock terpolymers is studied using the self-consistent field theory (SCFT). To circumvent the aperiodicity, the free energy of DDQC is determined by SCFT coupled with the Stampfli self-similarity construction, and it is compared with a series of competitive periodic DDQC approximants. Additionally, the cluster model originally from hard DDQCs is introduced to quantitatively analyze the relative stabilities between DDQC and its approximants, revealing a general conclusion of metastable DDQC in BCP melt systems as well as a robust mechanism of packing frustration closely related to the mismatch of lattice constants.