Journal of Nonlinear Science

, Volume 17, Issue 5, pp 471–503

Single Droplet Pattern in the Cylindrical Phase of Diblock Copolymer Morphology

Article

Abstract

The Ohta–Kawasaki density functional theory of diblock copolymers gives rise to a nonlocal free boundary problem. Under a proper condition between the block composition fraction and the nonlocal interaction parameter, a pattern of a single droplet is proved to exist in a general planar domain. A smaller parameter range is identified where the droplet solution is stable. The droplet is a set that is close to a round disc. The boundary of the droplet satisfies an equation that involves the curvature of the boundary and a quantity that depends nonlocally on the whole pattern. The location of the droplet is determined by the regular part of a Green’s function of the domain. This droplet pattern describes one cylinder in space in the cylindrical phase of diblock copolymer morphology.

Keywords

Cylindrical phase Diblock copolymer morphology Single droplet pattern 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUtah State UniversityLoganUSA
  2. 2.Department of MathematicsChinese University of Hong KongHong KongPeople’s Republic of China

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