Stability of Dodecagonal Quasicrystalline Tiling in ABC Star Terpolymers*

In this work, the thermodynamic stability of cylindrical dodecagonal quasicrystalline (DDQC) phase in ABC star-shaped triblock terpolymers for both neat and blending systems is investigated. A systematic comparison of our theoretical results to those of experiments by Matsushita's group is performed using the self-consistent field theory (SCFT). Based on our previous work, SCFT coupled with the Stampfli self-similarity construction is adopted to accurately calculate the free energy of the periodic DDQC approximants and then a cluster model is used to predict the stability of aperiodic DDQC phase. We find that ideal tiling DDQC in these ABC star terpolymers is also metastable. Furthermore we show that the DDQC morphology observed experimentally is a kind of random tiling pattern as the mesoscopic coexistence of the (3,3,4,3,4) Archimedean tiling pattern and the 8/3 approximant. Accordingly, we conclude that the formation of random tiling DDQC structure may be possible in self-assembling block copolymer melts.