Self-consistent field theory for diblock copolymers grafted to a sphere
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- Self-consistent field theory for diblock copolymers grafted to a sphere
- Vorselaars, Bart; Kim, Jaeup U.; Chantawansri, Tanya L.; Fredrickson, Glenn H.; Matsen, Mark W.
- Angular coordinates; Crank-Nicolson methods; Diblock copolymer; Diblocks; Diffusion equations; Dynamical parameters; Equilibrium morphology; Finite surface; Radial direction; Real-space; Self-consistent field; Self-consistent-field theory; Spherical surface; Structured polymers
- Issue Date
- ROYAL SOC CHEMISTRY
- SOFT MATTER, v.7, no.11, pp.5128 - 5137
- An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudo-spectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank-Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.
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