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Copolymers are the products obtained from the polymerization of multiple monomer species. So, in a polymer chain itself, there can be multiple repeating units that come from different monomers. The process of synthesizing a polymer from different monomer species is called copolymerization. When two monomers are involved, the polymer is known as a bipolymer. Polymers with three and four monomers are termed terpolymers and quaterpolymers, respectively. Figure 1 depicts the copolymerization of...
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Defect structures and ordering behaviours of diblock copolymers self-assembling on spherical substrates.

Liangshun Zhang1, Liquan Wang, Jiaping Lin

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Topological defects in block copolymers on spherical surfaces differ significantly. This study reveals defect structures and ordering dynamics for lamellar and cylindrical phases using Landau-Brazovskii theory and spectral methods.

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Area of Science:

  • Soft Matter Physics
  • Materials Science
  • Polymer Science

Background:

  • Ordered structures in block copolymers exhibit unique topological defects when confined to curved surfaces.
  • Understanding these defects is crucial for controlling material properties and self-assembly.

Purpose of the Study:

  • To investigate the defect structures and ordering behaviors of lamellar and cylindrical block copolymer phases confined on spherical substrates.
  • To elucidate the mechanisms governing defect formation and annihilation in these confined systems.

Main Methods:

  • Utilized the Landau-Brazovskii theory to model the system.
  • Employed a highly accurate spectral method with a spherical harmonic basis for numerical solutions.

Main Results:

  • For cylindrical phases, isolated disclinations and scars were observed, with scar dislocation number linearly dependent on sphere radius.
  • Defect fraction decayed exponentially, indicating ordering dynamics.
  • Scars formed from disclinations via mini-scars.
  • For lamellar phases, hedgehog, spiral, and quasi-baseball defect structures were identified.
  • Disclination annihilation was found to be the primary ordering mechanism.

Conclusions:

  • Confined block copolymer phases on spheres exhibit distinct defect structures and ordering mechanisms compared to flat surfaces.
  • The Landau-Brazovskii theory and spectral methods provide accurate insights into these complex phenomena.
  • Defect dynamics, including annihilation and formation, play a critical role in the self-assembly of block copolymers on curved substrates.