## Abstract

A free energy functional of nonlocal type is considered that was originally introduced to describe the micro-phase separation of diblock copolymer. A mathematical framework is given to the issues of the scaling law for stationary states and the governing equation of morphology. The scaling law is equivalent to finding a nice rescaling in order to have a well-defined limiting interfacial problem which is free from the interfacial thickness and the total chain length of copolymer, and the associated stationary problem becomes a morphology equation that governs the configuration of final patterns. Although the steady patterns become finer and finer in our scaling limit due to the mesoscopic nature, a possible rigorous approach is presented to stability and morphological selection problems for them.

Original language | English |
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Pages (from-to) | 31-39 |

Number of pages | 9 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 84 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1995 Jun 15 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics