Polymers have many unique properties compared to small molecules, mainly because of their long chain and high molecular weight. High molecular weight reduces the translational entropy of polymers, making macroscopic phase separation more possible to occur between different polymers. In order to suppress macroscopic phase separation, covalent bonds are used to link different polymers to form block copolymers. Block copolymers can only undergo phase separation within the length scale of their chain size, forming periodically ordered structures, that is, self-assembly. Block copolymer self-assembly has attracted a great deal of theoretical and experimental research interest over the past few decades. Self-consistent field theory (SCFT) has become one of the most successful methods for studying the self-assembly of block copolymers. In particular, a variety of numerical schemes have been developed to solve SCFT equations, including spectral method, real-space method, and pseudospectral method. In addition, SCFT has several advantages: (1) it can accurately calculate the free energy of various ordered structures; (2) it provides a lot of useful information for dissecting the self-assembly mechanisms, including the density distribution (even for each segment), interaction energy, entropic contribution to the free energy, etc.; (3) it is applicable to various block copolymer systems, including different chain topologies, different blending systems, and even semi-rigid and charged systems. In the past two decades, the team of Yang has carried out a series of studies on the self-assembly of block copolymers using SCFT. They theoretically predicted a lot of novel self-assembled structures, and clarified the formation mechanism of these ordered structures. Many theoretical results have been confirmed by experiments. At the same time, high-efficiency methods for solving SCFT equations have been developed. These theoretical achievements not only deepen the understanding of block copolymer self-assembly, but also promote related experimental research. This chapter briefly summarizes the theoretical progress of Yang’s team in the field of block copolymer self-assembly, focusing on SCFT studies of the flexible Gaussian chain model.

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Self-consistent Field Theory Study on the Self-assembly of Block Copolymers

  • Xintong You,
  • Weihua Li

摘要

Polymers have many unique properties compared to small molecules, mainly because of their long chain and high molecular weight. High molecular weight reduces the translational entropy of polymers, making macroscopic phase separation more possible to occur between different polymers. In order to suppress macroscopic phase separation, covalent bonds are used to link different polymers to form block copolymers. Block copolymers can only undergo phase separation within the length scale of their chain size, forming periodically ordered structures, that is, self-assembly. Block copolymer self-assembly has attracted a great deal of theoretical and experimental research interest over the past few decades. Self-consistent field theory (SCFT) has become one of the most successful methods for studying the self-assembly of block copolymers. In particular, a variety of numerical schemes have been developed to solve SCFT equations, including spectral method, real-space method, and pseudospectral method. In addition, SCFT has several advantages: (1) it can accurately calculate the free energy of various ordered structures; (2) it provides a lot of useful information for dissecting the self-assembly mechanisms, including the density distribution (even for each segment), interaction energy, entropic contribution to the free energy, etc.; (3) it is applicable to various block copolymer systems, including different chain topologies, different blending systems, and even semi-rigid and charged systems. In the past two decades, the team of Yang has carried out a series of studies on the self-assembly of block copolymers using SCFT. They theoretically predicted a lot of novel self-assembled structures, and clarified the formation mechanism of these ordered structures. Many theoretical results have been confirmed by experiments. At the same time, high-efficiency methods for solving SCFT equations have been developed. These theoretical achievements not only deepen the understanding of block copolymer self-assembly, but also promote related experimental research. This chapter briefly summarizes the theoretical progress of Yang’s team in the field of block copolymer self-assembly, focusing on SCFT studies of the flexible Gaussian chain model.