Uniform energy and density distribution: diblock copolymers’ functional

Uniform energy and density distribution: diblock copolymers’ functional

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 s...

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Veröffentlicht in:Interfaces and free boundaries 2009-01, Vol.11 (3), p.447-474
1. Verfasser: Nunzio Spadaro, Emanuele
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Calculus of variations and optimal control
Mechanics of particles and systems
optimization
Partial differential equations
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description 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.
doi_str_mv 10.4171/IFB/218
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subjects Calculus of variations and optimal control
Mechanics of particles and systems
optimization
Partial differential equations
title Uniform energy and density distribution: diblock copolymers’ functional
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