On the Ternary Ohta–Kawasaki Free Energy and Its One-dimensional Global Minimizers
On the Ternary Ohta–Kawasaki Free Energy and Its One-dimensional Global Minimizers
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DOI：
10.1007/s00332-022-09814-9
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发表时间：
2021-11
影响因子：
3
通讯作者：
Zirui Xu;Q. Du
中科院分区：
文献类型：
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作者：
Zirui Xu;Q. Du
我们研究了三元Ohta-Kawasaki自由能，它已被用来模拟三嵌段共聚物系统。证明了其一维全局极小元具有循环模式。然而，一些物理实验和计算机模拟发现，三嵌段共聚物形成非环状层状图案。在这项工作中，通过比较的自由能的循环模式和一些非循环的候选人，我们表明，该猜想不成立的一些参数的选择。我们的研究结果表明，即使在一维，全球最小可能采取非常不同的模式，在不同的参数制度。为了统一现有的选择的长程系数矩阵，我们提出了一个重新制定的长程长期使用广义的电荷解释，从而提出了矩阵上的条件，以使全球极小重现物理相关的嵌段共聚物的纳米结构。
We study the ternary Ohta–Kawasaki free energy that has been used to model triblock copolymer systems. Its one-dimensional global minimizers are conjectured to have cyclic patterns. However, some physical experiments and computer simulations found triblock copolymers forming noncyclic lamellar patterns. In this work, by comparing the free energies of the cyclic pattern and some noncyclic candidates, we show that the conjecture does not hold for some choices of parameters. Our results suggest that even in one dimension, the global minimizers may take on very different patterns in different parameter regimes. To unify the existing choices of the long-range coefficient matrix, we present a reformulation of the long-range term using a generalized charge interpretation and thereby propose conditions on the matrix in order for the global minimizers to reproduce physically relevant nanostructures of block copolymers.