Spherical Solutions to a Nonlocal Free Boundary Problem from Diblock Copolymer Morphology
Spherical Solutions to a Nonlocal Free Boundary Problem from Diblock Copolymer Morphology
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DOI：
10.1137/070690286
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发表时间：
2008-01
期刊：
影响因子：
--
通讯作者：
Xiaofeng Ren;Juncheng Wei
中科院分区：
文献类型：
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作者：
Xiaofeng Ren;Juncheng Wei
两嵌段共聚物的Ohta-Kawasaki密度泛函理论的极限是一个非局部自由边界问题。对于块体组成和非局域相互作用的某些值，在三维域中存在多个球的平衡模式。在多球图案稳定的地方找到了参数的子范围。这种稳定的模式模拟了两嵌段共聚物形态中的球形相。球体大致是圆形的。它们满足一个包含它们的平均曲率的方程和一个非局部依赖于整个图案的量。球体的位置通过区域的格林函数来确定。
The $\Gamma$-limit of the Ohta–Kawasaki density functional theory of diblock copolymers is a nonlocal free boundary problem. For some values of block composition and the nonlocal interaction, an equilibrium pattern of many spheres exists in a three-dimensional domain. A subrange of the parameters is found where the multiple sphere pattern is stable. This stable pattern models the spherical phase in the diblock copolymer morphology. The spheres are approximately round. They satisfy an equation that involves their mean curvature and a quantity that depends nonlocally on the whole pattern. The locations of the spheres are determined via a Green's function of the domain.