Li Jianfeng, Zhang Hongdong, Qiu Feng
The State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, 200433, Shanghai, China,
Eur Phys J E Soft Matter. 2014 Mar;37(3):18. doi: 10.1140/epje/i2014-14018-1. Epub 2014 Mar 26.
In this work, we propose a theoretical framework based on the self-consistent field theory (SCFT) for the study of self-assembling block copolymers on a general curved surface. Relevant numerical algorithms are also developed. To demonstrate the power of the approach, we calculate the self-assembled patterns of diblock copolymers on three distinct curved surfaces with different genus. We specially study the geometrical effects of curved surfaces on the conformation of polymer chains as well as on the pattern formation of block copolymers. By carefully examining the diffusion equation of the propagator on curved surfaces, it is predicted that Gaussian chains are completely unaware of the extrinsic curvature but that they will respond to the intrinsic curvature of the surface. This theoretical assertion is consistent with our SCFT simulations of block copolymers on general curved surfaces.
在这项工作中，我们提出了一个基于自洽场理论（SCFT）的理论框架，用于研究一般曲面上的自组装嵌段共聚物。还开发了相关的数值算法。为了证明该方法的有效性，我们计算了双嵌段共聚物在三种具有不同亏格的不同曲面上的自组装图案。我们特别研究了曲面的几何效应，包括对聚合物链构象以及嵌段共聚物图案形成的影响。通过仔细研究传播子在曲面上的扩散方程，预测高斯链完全不受外在曲率的影响，但会对曲面的内在曲率做出响应。这一理论论断与我们对一般曲面上嵌段共聚物的SCFT模拟结果一致。
