Copolymer–homopolymer blends: global energy minimisation and global energy bounds

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Abstract

We study a variational model for a diblock copolymer–homopolymer blend. The energy functional is a sharp-interface limit of a generalisation of the Ohta–Kawasaki energy. In one dimension, on the real line and on the torus, we prove existence of minimisers of this functional and we describe in complete detail the structure and energy of stationary points. Furthermore we characterise the conditions under which the minimisers may be non-unique. In higher dimensions we construct lower and upper bounds on the energy of minimisers, and explicitly compute the energy of spherically symmetric configurations.

Mathematics Subject Classification (2000)

49N99 82D60 

Notes

Open Access

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Copyright information

© The Author(s) 2008

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenThe Netherlands

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