Calculus of Variations and Partial Differential Equations

, Volume 33, Issue 1, pp 75–111

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

Authors

  • Yves van Gennip
    • Department of Mathematics and Computer ScienceTechnische Universiteit Eindhoven
    • Department of Mathematics and Computer ScienceTechnische Universiteit Eindhoven
Open AccessArticle

DOI: 10.1007/s00526-007-0147-0

Cite this article as:
van Gennip, Y. & Peletier, M.A. Calc. Var. (2008) 33: 75. doi:10.1007/s00526-007-0147-0

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)

49N9982D60
Download to read the full article text

Copyright information

© The Author(s) 2008