Self-assembled pattern formation of block copolymers on the surface of the sphere using self-consistent field theory |
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Authors: | J F Li J Fan H D Zhang F Qiu P Tang Y L Yang |
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Institution: | (1) The Key Laboratory of Molecular Engineering of Polymers, Ministry of Education of China, 200433 Shanghai, PRC;(2) Department of Macromolecular Science, Fudan University, 200433 Shanghai, PRC |
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Abstract: | The spherical surface is spatially discretized with triangular lattices to numerically calculate the Laplace-Beltrami operator
contained in the self-consistent field theory (SCFT) equations using a finite volume method. Based on this method we have
developed a spherical alternating-direction implicit (ADI) scheme for the first time to help extend real-space implementation
of SCFT in 2D flat space to the surface of the sphere. By using this method, we simulate the equilibrium microphase separation
morphology of block copolymers including AB diblocks, ABC linear triblocks and ABC star triblock copolymers occurred on the
spherical surface. In general, two classes of microphase separation morphologies such as striped patterns for compositionally
symmetric block copolymers and spotted patterns for asymmetric compositions have been found. In contrast to microphase separation
morphology in 2D flat space, the geometrical characteristics of a sphere has a large influence on the self-assembled morphology.
For striped patterns, several of spiral-form and ring-form patterns are found by changing the ratio of the radius of a sphere
to the averaging width of the stripes. The specific pattern such as the striped and spotted pattern with intrinsic dislocations
or defects stems from formed periodic patterns due to microphase separation of block copolymers arranged on the curved surface. |
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Keywords: | 83 80 Uv Block copolymers 36 20 -r Macromolecules and polymer molecules 68 08 De Structure: measurements and simulations |
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