Selfconsistent field theory simulations of block copolymer assembly on a sphere

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Self-consistent field theory simulations of block
copolymer assembly on a sphere

• TL Chantawansri, AW Bosse, A Hexemer, HD
  Ceniceros, CJ García-Cervera, EJ Kramer, and GH
  Fredrickson
• UC Santa Barbara
• APS Meeting March 7,2007

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Field Theoretic Simulations
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2D Model

• Thin but finite film
• Composition only varies parallel to the film
  surface
• ? Colatitude ? 0,p
• F Longitude ? 0,2p)

A B
Thin Block Copolymer Film
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Basic Schematic
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Cylindrical Phase
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2D SCFT Model Cylindrical Phase ?N25.0, f 0.8
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SSL Model Cylindrical Phase ?N25.0, f 0.8

• Analytic Strong Segregation Limit Calculation
• Absence of 11 and 13 domain due to topological
  constraints on interfacial and stretching free
  energies.
• Higher symmetry solutions (12 and 14 domains)
  have lower free energy unit cell configurations.
• Low symmetry solutions (11, 13, 15 domains) are
  characterized by high-energy unit cells.

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Lamellar phase
Spiral
Hedgehog
Quasibaseball
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2D SCFT Model Lamellar Phase ?N12.5, f 0.5
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2D SCFT Model Lamellar Phase ?N12.5, f 0.5
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Analogy with Smectic-A Liquid Crystals

• Small sphere radius (Elastic LC theory below the
  short-length-scale cutoff/ does not apply)
• Larger sphere radius
• Competition between the bending and compression
  degrees of freedom
• Hedgehog morphology
• Minimum compression when the circumference is an
  integer multiple of lamellar spacing, while
  compression can be quite large for intermediate
  values
• Spiral morphology
• Introduces area of curvature (bend) to relieve
  compression for intermediate values of radius to
  lower overall free energy

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Assumptions/Experimental Validity

• Uniform and thin film in the radial direction
• Difficult to experimentally realize, in the form
  of colloids/ nanoparticles coated with a thin
  layer of block copolymer
• Neutralize inner and outer surface of layer so
  that the film is compositionally homogeneous in
  the radial direction
• Invest in a full 3D SCFT model

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3D Model- Currently Implementing/Optimizing

• A self-assembly model for a free AB diblock
  copolymer thin film on the surface of a sphere
• Surface can prefer either the A or B component
• A self-assembly model for grafted polymers on the
  surface of the sphere
• AB homopolymer blend
• AB diblock copolymers

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Acknowledgements

• Kirill Katsov, Richard Elliot, David R. Nelson,
  Vincenzo Vitelli, Erin M. Lennon, Won Bo Lee.
• Funding NSF IGERT grant DGE02-21715
• MRL Central Facilities MRSEC Program NSF
  DMR05-20415