θ溶剂中树枝形均聚物的自洽场理论计算

1. 复旦大学高分子科学系 聚合物分子工程国家重点实验室 上海 200433
• 投稿日期:2018-08-27 发布日期:2018-10-08
• 通讯作者: 杨颖梓 E-mail:yang_yingzi@fudan.edu.cn
• 基金资助:

项目受国家自然科学基金（Nos.21320102005，21774026）和中国人民共和国科学技术部（Nos.2016YFA0203301）资助.

Self-Consistent Field Theory of Dendritic Homopolymers in θ Solvent

Fu Chao, Yang Yingzi, Qiu Feng

1. Department of Macromolecular Science, State Key Laboratory of Molecular Engineering of Polymers, Fudan University, Shanghai 200433
• Received:2018-08-27 Published:2018-10-08
• Contact: 10.6023/A18080351 E-mail:yang_yingzi@fudan.edu.cn
• Supported by:

Project supported by the National Natural Science Foundation of China (Nos. 21320102005, 21774026) and Ministry of Science and Technology of the People's Republic of China (2016YFA0203301).

The dendrimers are a unique class of branched macromolecules with defined architectures synthesized by iterative reaction steps. Because of their highly branched structures, the dendrimers have a wide potential application in many fields, including sensing, drug delivery, catalysis, etc. In order to understand the thermal equilibrium behavior of the dendritic homopolymers in solution, we derived the self-consistent field theory (SCFT) for the dilute dendrimer solutions. The center segment is anchored on the origin of the space, and the shape of the dendrimer is assumed to be spherically symmetric. The pre-averaged interaction parameter u is employed to represent the volume exclusion interaction between the segments. We only focus on the dendrimer immersed in the θ solvent, where the volume exclusion interaction between the segments is negligible (u=0). The number density of the segments, φ(r), is calculated via systematically changing the topological parameters of the molecule, including the functionality f0 of the central segment, the functionality f of the branching points, the degree of polymerization of the spacers P, and the total generation number G. With all parameter combinations, φ(r) was found always maximized at the center and monotonically decreasing along the radial direction. Thus, the dendrimers in θ solvent obeys the "dense-core" model instead of the "dense-shell" model. Increasing f0, f and G results in the increase of φ(r) with any radius r. However, increasing P causes the decrease of φ(r) near the center region and the increase of φ(r) with larger r. The size of the dendrimer, analyzed by calculating the radius of gyration R, increases with f0, f, G and P. R calculated by our SCFT agrees well with the results obtained by the Rouse dynamics. With large f0, f and G, both SCFT and the Rouse dynamics predict the scaling law <R2>≈GPa2.