We investigate equilibrium microstructures exhibited by diblock copolymers in confined 3D geometries. We perform Self-Consistent Field Theory (SCFT) simulations using a finite-element based computational framework (Ackerman et al. 2017), that provides the flexibility to compute equilibrium structures under arbitrary geometries. We consider a sequence of 3D geometries (tetrahedron to sphere) that have the same volume but exhibit varying curvature. This allows us to study the interplay between edge and curvature effects of the 3D geometries on the equilibrium microstructures. We observe that beyond a length scale, the equilibrium structure changes from an interconnected network to a multi-layered concentric shell as the curvature of the 3D geometry is reduced. However, below this length scale the equilibrium structure remains a multi-layered concentric shell independent of curvature. We additionally explore variations in the equilibrium microstructures at a few discrete volume fractions. This study provides insight into possible frustrated phases that can arise in AB diblock systems while varying the shape of confinement geometry.

中文翻译：

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3D约束下双嵌段共聚物的平衡微观结构

我们研究了二嵌段共聚物在受限 3D 几何结构中表现出的平衡微结构。我们使用基于有限元的计算框架 (Ackerman et al. 2017) 执行自洽场论 (SCFT) 模拟，该框架提供了计算任意几何形状下的平衡结构的灵活性。我们考虑具有相同体积但表现出不同曲率的一系列 3D 几何体（四面体到球体）。这使我们能够研究 3D 几何形状对平衡微结构的边缘和曲率影响之间的相互作用。我们观察到，超出长度尺度，随着 3D 几何体的曲率减小，平衡结构从互连网络变为多层同心壳。然而，在这个长度尺度之下，平衡结构仍然是一个与曲率无关的多层同心壳。我们还探索了几个离散体积分数下平衡微观结构的变化。这项研究提供了对 AB 双嵌段系统中可能出现的受挫阶段的洞察，同时改变了限制几何形状。