Single Droplet Pattern in the Cylindrical Phase of Diblock Copolymer Morphology

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 which 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. Key words. Cylindrical phase, diblock copolymer morphology, single droplet pattern. 2000 AMS subject classification. 35R35, 82B24, 82D60. Abbreviated title. Single droplet pattern.

• Type: Journal
• Year: 2007
• Where: JNS
• Authors: X. Ren, J. Wei
• Keywords: Droplet, Droplet Pattern, JNS 2007, Single Droplet