Scaling Laws in Microphase Separation of Diblock Copolymers
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In this note, we study a nonlocal variational problem modeling microphase separation of diblock copolymers (, , ). We apply certain new tools developed in  to determine the principal part of the asymptotic expansion of the minimum free energy. That is, we prove a scaling law for the minimum energy and confirm that it is attained by a simple periodic lamellar structure. A previous result of Ohnishi et al.  was for one space dimension. Here, we obtain a similar result for the full three-dimensional problem.
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