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  where analogous results are proved for the sharp interface limit of the functional considered.
Cite this article
Emanuele Nunzio Spadaro, Uniform energy and density distribution: diblock copolymers’ functional. Interfaces Free Bound. 11 (2009), no. 3, pp. 447–474DOI 10.4171/IFB/218