Single Droplet Pattern in the Cylindrical Phase of Diblock Copolymer Morphology |
| |
Authors: | X Ren J Wei |
| |
Institution: | (1) Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA;(2) Department of Mathematics, Chinese University of Hong Kong, Hong Kong, People’s Republic of China |
| |
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 |
本文献已被 SpringerLink 等数据库收录! |
|