Key Laboratory of Molecular Engineering of Polymers of Ministry of Education, Department of Macromolecular Science, Fudan University, Shanghai, China.
J Chem Phys. 2011 Apr 7;134(13):134903. doi: 10.1063/1.3575180.
Microphase separation of mixed A∕B polymer brushes grafted onto a nanosphere with its radius comparable to the size of polymers is investigated by numerical implementation of the self-consistent field theory. The idea is to embed the sphere within a larger cubic computational cell and use a "masking" technique to treat the spherical boundary. The partial differential equations for the chain propagator on the sphere can thus be readily solved with an efficient and high-order accurate pseudospectral method involving fast Fourier transform on a cubic cell. This numerical technique can circumvent the "pole problem" due to the use of a spherical coordinate system in conventional finite difference or finite element grid. We systematically investigate the effect of the total grafting density, composition, chain length asymmetry between two grafted homopolymers as well as spherical radius, i.e., substrate curvature on the formation of island structure with specific arrangement in a regular lattice. A series of island structures with different island numbers representing specific structure symmetry ranging from 2 to 12 except for 11 are found, in contrast to conventional hexagonal arrangement for polymer brushes on a planar substrate. Among these parameters, the spherical radius plays a significant role in determining the type of island structures, i.e., the morphology formed on the sphere.
通过数值实现自洽场理论，研究了与聚合物尺寸相当的纳米球上接枝的混合 A∕B 聚合物刷的微相分离。该方法是将球体嵌入更大的立方计算单元中，并使用“屏蔽”技术来处理球体边界。因此，可以使用涉及立方单元上快速傅里叶变换的高效和高精度伪谱方法，轻松解决球体上链传播子的偏微分方程。这种数值技术可以避免由于在传统有限差分或有限元网格中使用球坐标系而产生的“极点问题”。我们系统地研究了总接枝密度、组成、两种接枝均聚物之间的链长不对称性以及球形半径（即基底曲率）对在规则晶格中具有特定排列的岛状结构形成的影响。除了 11 之外，我们发现了一系列具有不同岛数的岛状结构，代表了从 2 到 12 的特定结构对称性，而不是在平面基底上聚合物刷的常规六边形排列。在这些参数中，球形半径在确定岛状结构的类型方面起着重要作用，即球体上形成的形态。
