Interfaces and Free Boundaries

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Volume 11, Issue 3, 2009, pp. 447–474
DOI: 10.4171/IFB/218

Uniform energy and density distribution: diblock copolymers’ functional

Emanuele Nunzio Spadaro[1]

(1) Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057, ZÜRICH, SWITZERLAND

We study a nonlocal variational problem arising in diblock copolymers models, whose energy is given by the Cahn–Hilliard functional plus a long-range interaction term. We prove that minimizers develop uniform energy and density distributions, thus justifying partially the highly regular microphase separation observed in diblock copolymers’ melts. We also give a new proof of the scaling law for the minimum energy. This work extends the techniques introduced in [1] where analogous results are proved for the sharp interface limit of the functional considered.

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Nunzio Spadaro Emanuele: Uniform energy and density distribution: diblock copolymers’ functional. Interfaces Free Bound. 11 (2009), 447-474. doi: 10.4171/IFB/218