A rigorous derivation of mean-field models describing 2D micro phase separation
A rigorous derivation of mean-field models describing 2D micro phase separation
复制标题
描述二维微相分离的平均场模型的严格推导
DOI：
10.1007/s00526-020-1706-x
复制
发表时间：
2020
影响因子：
2.1
通讯作者：
Oshita Yoshihito
中科院分区：
文献类型：
--
作者：
Niethammer Barbara;Oshita Yoshihito
本文研究了自由边界问题，该问题描述了两嵌段共聚物熔体在一个组分具有小体积分数的体系中的微相分离，使得微相分离产生一个组分的小圆盘系综。我们在本文中考虑二维情况，而在Niethammer和Oshita（Calc Var PDE 39：273-305，2010）中已经考虑了三维情况。本文从圆盘的自由边界问题出发，严格导出了时间尺度为的非均匀平均场方程，其中，圆盘的平均半径为。在这个时间尺度上，演化是由盘半径的粗化和稳定化主导的，而盘的迁移只在更大的时间尺度上才变得相关。
We study the free boundary problem describing the micro phase separation of diblock copolymer melts in the regime that one component has small volume fractionsuch that the micro phase separation results in an ensemble of small disks of one component. We consider the two dimensional case in this paper, whereas the three dimensional case was already considered in Niethammer and Oshita (Calc Var PDE 39:273–305, 2010). Starting from the free boundary problem restricted to disks we rigorously derive the heterogeneous mean-field equations on a time scale of the order of, whereis the mean radius of disks. On this time scale, the evolution is dominated by coarsening and stabilization of the radii of the disks, whereas migration of disks becomes only relevant on a larger time scale.