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Issue 11, 2011
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Self-consistent field theory for diblock copolymers grafted to a sphere

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Abstract

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.

Graphical abstract: Self-consistent field theory for diblock copolymers grafted to a sphere

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Article information


Submitted
02 Nov 2010
Accepted
12 Jan 2011
First published
17 Feb 2011

Soft Matter, 2011,7, 5128-5137
Article type
Paper

Self-consistent field theory for diblock copolymers grafted to a sphere

B. Vorselaars, J. U. Kim, T. L. Chantawansri, G. H. Fredrickson and M. W. Matsen, Soft Matter, 2011, 7, 5128
DOI: 10.1039/C0SM01242D

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