Stationary disk assemblies in a ternary system with long range interaction
Stationary disk assemblies in a ternary system with long range interaction
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DOI：
10.1142/s0219199718500463
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发表时间：
2019-08
影响因子：
1.6
通讯作者：
Xiaofeng Ren;Chong Wang
中科院分区：
文献类型：
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作者：
Xiaofeng Ren;Chong Wang
三元体系（例如三嵌段共聚物）的自由能是两部分的总和：界面能由分隔三种成分的微域的界面尺寸决定，以及用于防止无限微域生长的长程相互作用能。在二维中，确定系统允许稳定的固定盘组件的参数范围。这种组件由由 I 型成分或 II 型成分制成的扰动盘组成。所有 I 型盘具有大致相同的半径，并且所有 II 型盘也具有大致相同的半径。磁盘的位置是通过函数的最小化来确定的。根据参数的不同，两种类型的磁盘可以以有组织的方式混合，也可以以随机的方式混合。它们也可以完全分离。第一种情况提供了聚合物科学家推测的三嵌段共聚物形态相存在的数学证明。最后一种情况表明三元系统能够产生两层结构。主要结构处于微观水平，圆盘形成近乎完美的晶格。二级结构在宏观水平上形成两个大区域，一个充满I型盘，另一个充满II型盘。宏观的圆形界面将这两个区域分开。
The free energy of a ternary system, such as a triblock copolymer, is a sum of two parts: an interface energy determined by the size of the interfaces separating the micro-domains of the three constituents, and a long range interaction energy that serves to prevent unlimited micro-domain growth. In two dimensions a parameter range is identified where the system admits stable stationary disk assemblies. Such an assembly consists of perturbed disks made from either type-I constituent or type-II constituent. All the type-I disks have approximately the same radius and all the type-II disks also have approximately the same radius. The locations of the disks are determined by minimization of a function. Depending on the parameters, the disks of the two types can be mixed in an organized way, or mixed in a random way. They can also be fully separated. The first scenario offers a mathematical proof of the existence of a morphological phase for triblock copolymers conjectured by polymer scientists. The last scenario shows that the ternary system is capable of producing two levels of structure. The primary structure is at the microscopic level where disks form near-perfect lattices. The secondary structure is at the macroscopic level forming two large regions, one filled with type-I disks and the other filled with type-II disks. A macroscopic, circular interface separates the two regions.