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Uniform energy and density distribution: diblock copolymers' functional


Spadaro, E N (2009). Uniform energy and density distribution: diblock copolymers' functional. Interfaces and Free Boundaries, 11(3):447-474.

Abstract

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.

Abstract

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2009
Deposited On:08 Mar 2010 16:28
Last Modified:05 Apr 2016 13:55
Publisher:European Mathematical Society
ISSN:1463-9963
Publisher DOI:https://doi.org/10.4171/IFB/218
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2546607

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