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

Details Copolymer-homopolymer blends: global energy minimisation and global energy bounds Copolymer-homopolymer blends: global energy minimisation and global energy bounds

2007-04-24

arxiv.org/abs/0704.3222v5

Physics

Mathematical Physics

31 pages, 6 Postscript figures; to be published in Calc. Var. Partial Differential Equations. Version history: Changes in v2 w

Scientific paper

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.

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