Citation: Fu Chao, Yang Yingzi, Qiu Feng. Self-Consistent Field Theory of Dendritic Homopolymers in θ Solvent[J]. Acta Chimica Sinica, ;2019, 77(1): 95-102. doi: 10.6023/A18080351 shu

Self-Consistent Field Theory of Dendritic Homopolymers in θ Solvent

Department of Macromolecular Science, State Key Laboratory of Molecular Engineering of Polymers, Fudan University, Shanghai 200433

Corresponding author: Yang Yingzi, yang_yingzi@fudan.edu.cn
Received Date: 27 August 2018
Available Online: 8 January 2018
Fund Project: the National Natural Science Foundation of China 21320102005Ministry of Science and Technology of the People's Republic of China 2016YFA0203301the National Natural Science Foundation of China 21774026Project 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)

Figures(9)

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.
- dendrimer,
- self-consistent field theory,
- segment density profile,
- scaling law
1. [1]
  Xia, K.; Sheng, R.; Zhu, Y.; Li, H.; Luo, T.; Xu, Y.; Cao, A. Acta Chim. Sinica 2010, 68, 1130 (in Chinese).
2. [2]
  Li, J.; Zeng, Y.; Zhang, X.; Yu, T.; Chen, J.; Li, Y. Acta Chim. Sinica 2014, 72, 1157 (in Chinese).
3. [3]
  Qin, T.; Zeng, Y.; Chen, J.; Yu, T.; Li, Y. Acta Chim. Sinica. 2017, 75, 99 (in Chinese).
4. [4]
  Adachi, N.; Sugiyama, H.; Arai, M.; Ogawa, H. Molecules 2014, 19, 4135; doi: 10.3390/molecules19044135
5. [5]
  Shaw, P. E.; Cavaye, H.; Chen, S. S. Y.; James, M.; Gentle, I. R.; Burn, P. L. Phys. Chem. Chem. Phys. 2013, 15, 9845. doi: 10.1039/c3cp51372f
6. [6]
  Rahman, M. A.; Noh, H. B.; Shim, Y. B. Anal. Chem. 2008, 80, 8020 doi: 10.1021/ac801033s
7. [7]
  Peng, X. H.; Pan, Q. M.; Rempel, G. L. Chem. Soc. Rev. 2008, 37, 1619. doi: 10.1039/b716441f
8. [8]
  Yoon, H. C.; Hong, M. Y.; Kim, H. S. Anal. Chem. 2000, 72, 4420. doi: 10.1021/ac0003044
9. [9]
  Bielinska, A. U.; Yen, A.; Wu, H. L.; Zahos, K. M.; Sun, R.; Weiner, N. D.; Baker, J. R.; Roessler, B. J. Biomaterials 2000, 21, 877. doi: 10.1016/S0142-9612(99)00229-X
10. [10]
  Vincent, L.; Varet, J.; Pille, J.-Y.; Bompais, H.; Opolon, P.; Maksimenko, A.; Malvy, C.; Mirshahi, M.; Lu, H.; Vannier, J.-P.; Soria, C.; Li, H. Int. J. Cancer 2003, 105, 419. doi: 10.1002/(ISSN)1097-0215
11. [11]
  Jain, S.; Kaur, A.; Puri, R.; Utreja, P.; Jain, A.; Bhide, M.; Ratnam, R.; Singh, V.; Patil, A. S.; Jayaraman, N.; Kaushik, G.; Yadav, S.; Khanduja, K. L. Eur. J. Med. Chem. 2010, 45, 4997. doi: 10.1016/j.ejmech.2010.08.006
12. [12]
  Kesharwani, P.; Jain, K.; Jain, K. N. Prog. Polym. Sci. 2014, 39, 268. doi: 10.1016/j.progpolymsci.2013.07.005
13. [13]
  Astruc, D.; Boisselier, E.; Ornelas, C. Chem. Rev. 2010, 110, 1857. doi: 10.1021/cr900327d
14. [14]
  Buhleier, G. E.; Wehner, W.; Vögtle, F. Chemischer Informationsdienst 1978, 2, 155.
15. [15]
  Cloninger, M. J. Curr. Opin. Chem. Biol. 2002, 6, 742. doi: 10.1016/S1367-5931(02)00400-3
16. [16]
  de Gennes, P. G.; Hervet, H. Journal de Physique-Lettres 1983, 44, L351. doi: 10.1051/jphyslet:01983004409035100
17. [17]
  Lescanec, R. L.; Muthukumar, M. Macromolecules 1990, 23, 2280. doi: 10.1021/ma00210a026
18. [18]
  Mansfield, M. L.; Klushin, L. I.; Klushint, L. I. Macromolecules 1993, 26, 4262. doi: 10.1021/ma00068a029
19. [19]
  Biswas, P.; Cherayilk, B. J.; Klushint, L. I. J. Chem. Phys. 1993, 26, 4262.
20. [20]
  Chen, Z. Y.; Cui, S.-M. Macromolecules 1996, 29, 7943. doi: 10.1021/ma9514636
21. [21]
  Carl, M. J. Chem. Soc. 1996, 92, 4151.
22. [22]
  Carbone, P.; Müller-Plathe, F. Soft Matter 2009, 5, 2638.
23. [23]
  Jurjiu, A.; Dockhorn, N.; Mironova, O.; Sommer, J.-U. Soft Matter 2014, 10, 4935. doi: 10.1039/c4sm00711e
24. [24]
  Freire, J. J.; Rubio, A. M. Polymer 2008, 49, 2762. doi: 10.1016/j.polymer.2008.04.024
25. [25]
  Boris, D.; Rubinstein, M. Macromolecules 1996, 29, 7251. doi: 10.1021/ma960397k
26. [26]
  Götze, I. O.; Likos, C. N. Macromolecules 2003, 36, 8189. doi: 10.1021/ma030137k
27. [27]
  Lyulin, A. V.; Davies, G. R.; Adolf, D. B. Macromolecules 2000, 33, 6899. doi: 10.1021/ma0003811
28. [28]
  Sheng, Y. J.; Jiang, S. Y.; Tsao, H. K. Macromolecules 2002, 35, 7865. doi: 10.1021/ma025561k
29. [29]
  Kumar, A.; Biswas, P. J. Chem. Phys. 2011, 134, 214901.
30. [30]
  Kumar, A.; Biswas, P. Macromolecules 2010, 43, 7378. doi: 10.1021/ma101142z
31. [31]
  Cui, W.; Su, C. F.; Merlitz, H.; Wu, C. X.; Sommer, J. U. Macromolecules 2014, 47, 3645. doi: 10.1021/ma500129h
32. [32]
  Bosko, J. T.; Prakash, J. R. Macromolecules2011, 44, 660. doi: 10.1021/ma102094f
33. [33]
  Rubio, A. M.; McBride, C.; Freire, J. J. Macromolecules 2014, 47, 5379. doi: 10.1021/ma501127f
34. [34]
  Mandal, T.; Dasgupta, C.; Maiti, P. K. J. Chem. Phys.2014, 141, 144901. doi: 10.1063/1.4897160
35. [35]
  Lu, Y.; An, L.; Wang, Z. G. Macromolecules 2013, 46, 5731. doi: 10.1021/ma400872s
36. [36]
  Jana, C.; Jayamurugan, G.; Ganapathy, R.; Maiti, P. K.; Jayaraman, N.; Sood, A. K. J. Chem. Phys. 2006, 124, 204719. doi: 10.1063/1.2194538
37. [37]
  Porcar, L.; Hong, K.; Butler, P. D.; Herwig, K. W.; Smith, G. S.; Liu, Y.; Chen, W. R. J. Phys. Chem. B 2010, 114, 1751. doi: 10.1021/jp9064455
38. [38]
  Prosa, T. J.; Bauer, B. J.; Amis, E. J. Macromolecules 2001, 34, 4897. doi: 10.1021/ma0002186
39. [39]
  Pötschke, D.; Ballauf, M.; Lindner, P.; Fischer, M.; Vögtle, F. J. Appl. Crystallogr. 2000, 33, 605. doi: 10.1107/S0021889899013795
40. [40]
  Rosenfeldt, S.; Dingenouts, N.; Ballauf, M.; Werner, N.; Vögtle, F.; Lindner, P. Macromolecules2002, 35, 8098. doi: 10.1021/ma020585c
41. [41]
  Prosa, T. J.; Bauer, B. J.; Amis, E. J.; Tomalia, D. A.; Scherrenberg, R. J. Polym. Sci. Part B Polym. Phys. 1997, 35, 2913. doi: 10.1002/(ISSN)1099-0488
42. [42]
  Rathgeber, S.; Monkenbusch, M.; Kreitschmann, M.; Urban, V.; Brulet, A. J. Chem. Phys. 2002, 117, 4047.
43. [43]
  Caminade, A. M.; Laurent, R.; Majoral, J. P. Adv. Drug Deliver. Rev. 2005, 57, 2130. doi: 10.1016/j.addr.2005.09.011
44. [44]
  Tanaka, H.; Koizumi, S.; Hashimoto, T.; Iyoh, H.; Satoh, M.; Naka, K.; Chujo, Y. Macromolecules 2007, 40, 4327. doi: 10.1021/ma062930u
45. [45]
  Klos, J. S.; Sommer, J. U. Macromolecules 2013, 46, 3107. doi: 10.1021/ma4001989
46. [46]
  Shi, M.; Yang, Y. Z.; Qiu, F. Acta Chim. Sinica 2018, 76, 715 (in Chinese).
47. [47]
  Mallamace, F.; Canetta, E.; Lombardo, D.; Mazzaglia, A.; Romeo, A.; Scolaro, L. M.; Maino, G. Physica A 2002, 304, 235. doi: 10.1016/S0378-4371(01)00548-9
48. [48]
  Yang, Y. Z.; Qiu, F.; Zhang, H. D.; Yang, Y. L. Macromolecules 2017, 50, 4007. doi: 10.1021/acs.macromol.7b00040
49. [49]
  Yang, Y. L.; Qiu, F.; Tang, P.; Zhang, H. D. Sci. China Chem. 2006, 36, 1 (in Chinese).
1. [1]
  Keweiyang Zhang , Zihan Fan , Liyuan Xiao , Haitao Long , Jing Jing . Unveiling Crystal Field Theory: Preparation, Characterization, and Performance Assessment of Nickel Macrocyclic Complexes. University Chemistry, 2024, 39(5): 163-171. doi: 10.3866/PKU.DXHX202310084
2. [2]
  Zongfei YANG , Xiaosen ZHAO , Jing LI , Wenchang ZHUANG . Research advances in heteropolyoxoniobates. Chinese Journal of Inorganic Chemistry, 2024, 40(3): 465-480. doi: 10.11862/CJIC.20230306
3. [3]
  Cunling Ye , Xitong Zhao , Hongfang Wang , Zhike Wang . A Formula for the Calculation of Complex Concentrations Arising from Side Reactions and Its Applications. University Chemistry, 2024, 39(4): 382-386. doi: 10.3866/PKU.DXHX202310043
4. [4]
  Hong Zheng , Xin Peng , Chunwang Yi . The Tale of Caprolactam Cyclic Oligomers: The Ever-changing Life of “Princess Cyclo”. University Chemistry, 2024, 39(9): 40-47. doi: 10.12461/PKU.DXHX202403058
5. [5]
  Yan LIU , Jiaxin GUO , Song YANG , Shixian XU , Yanyan YANG , Zhongliang YU , Xiaogang HAO . Exclusionary recovery of phosphate anions with low concentration from wastewater using a CoNi-layered double hydroxide/graphene electronically controlled separation film. Chinese Journal of Inorganic Chemistry, 2024, 40(9): 1775-1783. doi: 10.11862/CJIC.20240043
6. [6]
  Shuhui Li , Jing Wang , Haitao Tang , Yingming Pan . A Taste Journey with Sauerkraut. University Chemistry, 2024, 39(9): 59-63. doi: 10.12461/PKU.DXHX202404061
7. [7]
  Pingwei Wu . Application of Diamond Software in Simplex Teaching. University Chemistry, 2024, 39(3): 118-121. doi: 10.3866/PKU.DXHX202311043
8. [8]
  Wendian XIE , Yuehua LONG , Jianyang XIE , Liqun XING , Shixiong SHE , Yan YANG , Zhihao HUANG . Preparation and ion separation performance of oligoether chains enriched covalent organic framework membrane. Chinese Journal of Inorganic Chemistry, 2024, 40(8): 1528-1536. doi: 10.11862/CJIC.20240050
9. [9]
  Ruilin Han , Xiaoqi Yan . Comparison of Multiple Function Methods for Fitting Surface Tension and Concentration Curves. University Chemistry, 2024, 39(7): 381-385. doi: 10.3866/PKU.DXHX202311023
10. [10]
  Shengyan Yang , Xiangzhen Meng , Xin Wang , Yang Zhang . Construction and Exploration of an Online-Offline Blended “Eight-Link” Teaching Method for Physical Chemistry Experiments Based on OBE Concept. University Chemistry, 2024, 39(11): 28-37. doi: 10.3866/PKU.DXHX202402019
11. [11]
  Hua Hou , Baoshan Wang . Course Ideology and Politics Education in Theoretical and Computational Chemistry. University Chemistry, 2024, 39(2): 307-313. doi: 10.3866/PKU.DXHX202309045
12. [12]
  Jia Yao , Xiaogang Peng . Theory of Macroscopic Molecular Systems: Theoretical Framework of the Physical Chemistry Course in the Chemistry “101 Plan”. University Chemistry, 2024, 39(10): 27-37. doi: 10.12461/PKU.DXHX202408117
13. [13]
  Qingqing SHEN , Xiangbowen DU , Kaicheng QIAN , Zhikang JIN , Zheng FANG , Tong WEI , Renhong LI . Self-supporting Cu/α-FeOOH/foam nickel composite catalyst for efficient hydrogen production by coupling methanol oxidation and water electrolysis. Chinese Journal of Inorganic Chemistry, 2024, 40(10): 1953-1964. doi: 10.11862/CJIC.20240028
14. [14]
  Zhihuan XU , Qing KANG , Yuzhen LONG , Qian YUAN , Cidong LIU , Xin LI , Genghuai TANG , Yuqing LIAO . Effect of graphene oxide concentration on the electrochemical properties of reduced graphene oxide/ZnS. Chinese Journal of Inorganic Chemistry, 2024, 40(7): 1329-1336. doi: 10.11862/CJIC.20230447
15. [15]
  Shunliu Deng , Haifeng Su , Yaxian Zhu , Yuzhi Wang , Yuhua Weng , Zhaobin Chen , Shunü Peng , Yinyun Lü , Xinyi Hong , Yiru Wang , Xiaozhen Huang , Zhimin Lin , Lansun Zheng . Course Ideological and Political Design for Self-Building Experiments of Scientific Instruments: Taking the Construction, Debugging, and Application of Teaching Mass Spectrometer as an Example. University Chemistry, 2024, 39(2): 127-132. doi: 10.3866/PKU.DXHX202308002
16. [16]
  Xiaomei Ning , Liang Zhan , Xiaosong Zhou , Jin Luo , Xunfu Zhou , Cuifen Luo . Preparation and Electro-Oxidation Performance of PtBi Supported on Carbon Cloth: A Recommended Comprehensive Chemical Experiment. University Chemistry, 2024, 39(11): 217-224. doi: 10.3866/PKU.DXHX202401085
17. [17]
  Xuyang Wang , Jiapei Zhang , Lirui Zhao , Xiaowen Xu , Guizheng Zou , Bin Zhang . Theoretical Study on the Structure and Stability of Copper-Ammonia Coordination Ions. University Chemistry, 2024, 39(3): 384-389. doi: 10.3866/PKU.DXHX202309065
18. [18]
  Qiang Xu , Rong Zhang , Liyan Zhang , Jinxuan Liu , Shuo Wu , Rongwen Lv . Exploration and Practice of Ideological and Political Education Construction in the Course of Practical Instrument Analysis Theory. University Chemistry, 2024, 39(6): 132-136. doi: 10.3866/PKU.DXHX202311018
19. [19]
  Yaling Chen . Basic Theory and Competitive Exam Analysis of Dynamic Isotope Effect. University Chemistry, 2024, 39(8): 403-410. doi: 10.3866/PKU.DXHX202311093
20. [20]
  Chengqian Mao , Yanghan Chen , Haotong Bai , Junru Huang , Junpeng Zhuang . Photodimerization of Styrylpyridinium Salt and Its Application in Silk Screen Printing. University Chemistry, 2024, 39(5): 354-362. doi: 10.3866/PKU.DXHX202312014

Get Citation

PDF

XML

Metrics

PDF Downloads(12)
Abstract views(1014)
HTML views(169)

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142