Crystallization in block copolymer melts with a dominant phase [arXiv]

Bourne, D. and Peletier, M.A. (2013) Crystallization in block copolymer melts with a dominant phase [arXiv]. (Unpublished)

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<p>In this paper we derive a new model for diblock copolymer melts with a dominant phase that is simple enough to be amenable not only to numerics but also to analysis, yet sophisticated enough to reproduce the hexagonally packed cylinder patterns observed in experiments.</p> <p>Starting from a sharp-interface continuum model, a nonlocal energy functional involving a Wasserstein cost, we derive the new model using Gamma-convergence in a limit where the volume fraction of one phase tends to zero. The limit energy is defined on atomic measures; in three dimensions the atoms represent small spherical blobs of the minority phase, in two dimensions they represent thin cylinders of the minority phase.</p> <p>We then study minimisers of the limit energy. Numerical minimisation is performed in two dimensions by recasting the problem as a computational geometry problem involving power diagrams. The numerical results suggest that the small particles of the minority phase tend to arrange themselves on a triangular lattice as the number of particles goes to infinity. This is proved in the companion paper [BPT] and agrees with patterns observed in experiments. This is a rare example of a nonlocal energy-driven pattern formation problem in two dimensions where it can be proved that the optimal pattern is periodic, and the first time it has been proved that minimisers of a diblock copolymer energy are periodic.</p>

Item Type:Articles
Glasgow Author(s) Enlighten ID:Bourne, Dr David
Authors: Bourne, D., and Peletier, M.A.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
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