Solution landscapes of the diblock copolymer-homopolymer model under two-dimensional confinement

Zhen Xu, Yucen Han, Jianyuan Yin, Bing Yu, Yasumasa Nishiura, Lei Zhang

Research output: Contribution to journalArticlepeer-review


We investigate the solution landscapes of the confined diblock copolymer and homopolymer in two-dimensional domain by using the extended Ohta--Kawasaki model. The projected saddle dynamics method is developed to compute the saddle points with mass conservation and construct the solution landscape by coupling with downward/upward search algorithms. A variety of novel stationary solutions are identified and classified in the solution landscape, including Flower class, Mosaic class, Core-shell class, and Tai-chi class. The relationships between different stable states are shown by either transition pathways connected by index-1 saddle points or dynamical pathways connected by a high-index saddle point. The solution landscapes also demonstrate the symmetry-breaking phenomena, in which more solutions with high symmetry are found when the domain size increases.
Original languageEnglish
Article number014505
JournalPhysical Review E
Issue number1
Publication statusPublished - 29 Jul 2021


  • diblock copolymers
  • homopolymers
  • solution landscapes
  • solar cells


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