Journal of Nonlinear Science

, Volume 17, Issue 5, pp 471–503

Single Droplet Pattern in the Cylindrical Phase of Diblock Copolymer Morphology


DOI: 10.1007/s00332-007-9005-7

Cite this article as:
Ren, X. & Wei, J. J Nonlinear Sci (2007) 17: 471. doi:10.1007/s00332-007-9005-7


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.


Cylindrical phaseDiblock copolymer morphologySingle droplet pattern

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