Self-consistent field theory for diblock copolymers grafted to a sphere
Vorselaars, B., Kim, J. U., Chantawansri, T. L., Fredrickson, G. H. and Matsen, M. W. (2011) Self-consistent field theory for diblock copolymers grafted to a sphere. Soft Matter, 7 (11). pp. 5128-5137. ISSN 1744-683X
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To link to this article DOI: 10.1039/c0sm01242d
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 pseudospectral 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.