Acta Chim. Sinica ›› 2018, Vol. 76 ›› Issue (9): 715-722.

Article

柔性树枝形大分子溶液的自洽场理论计算

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:2018-05-09 发布日期:2018-06-22
• 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 Studies of Flexible Dendrimer in Good Solvent

Shi Meng, Yang Yingzi, Qiu Feng

1. State Key Laboratory of Molecular Engineering of Polymers, Fudan University, Shanghai 200433
• Received:2018-05-09 Published:2018-06-22
• Contact: 10.6023/A18050192 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 (No. 2016YFA0203301).

Dendrimers are a class of novel polymer materials, which have received a lot of attention in past decades. The property of a dendrimer material strongly depends on the conformational details of the molecules, including the monomer density distribution, the functional end-group distribution, and the molecular size. In this paper, we consider a dendrimer composed of flexible and long spacers, immersed in the athermal or good solvent. A self-consistent field theory (SCFT) with a pre-averaged excluded volume potential is employed to calculate the density profiles of the segments and the radius of gyration R of the dendrimers. The stretched conformation of the spacers, and the scaling laws between the dendrimer size and its topologic parameters are analyzed. Our main results are:(1) The segment density of the dendrimers obeys the "dense-core" model, and decreases smoothly along the radial direction. (2) Due to the folding-back conformation, the local density of the end-segments is proportional to the local segment density. The density profile of the end-segments does not have a lifted peak at the outer layer of the spherical molecule. (3) The conformation of the spacers with lower generation numbers is strongly stretched in the central region where the segments are crowded. The first-generation spacers are mostly stretched. However, the spacers with higher generation numbers are much weakly stretched in the outer region. (4) Our self-consistent field theory calculations give the scaling law of the dendrimer size R~(GP)1/5N2/5, where G is the generation number of the dendrimer, P is the spacer segment number, and N is the total segment number. This agrees with the Flory mean field calculation for dendrimer based on full segment number. But it disagrees with the pioneer theories based on a linear side chains and the results from Monte Carlo simulations, which gave R~(GP)2/5N1/5. This disagreement is attributed to the limited bond length in simulations and the unlimited stretchable spacers in SCFT. (5) If G is fixed, the scaling law is simplified to R~P3/5 in good solvent, which agrees with the pioneer theories.