Citation: Shi Meng, Yang Yingzi, Qiu Feng. Self-Consistent Field Theory Studies of Flexible Dendrimer in Good Solvent[J]. Acta Chimica Sinica, ;2018, 76(9): 715-722. doi: 10.6023/A18050192 shu

Self-Consistent Field Theory Studies of Flexible Dendrimer in Good Solvent

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

Corresponding author: Yang Yingzi, yang_yingzi@fudan.edu.cn
Received Date: 9 May 2018
Available Online: 22 September 2018
Fund Project: the National Natural Science Foundation of China 21320102005the 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 (No. 2016YFA0203301)Ministry of Science and Technology of the People's Republic of China 2016YFA0203301

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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)^1/5N^2/5, 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)^2/5N^1/5. 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~P^3/5 in good solvent, which agrees with the pioneer theories.
- dendrimer,
- mean-field theory,
- self-consistent field theory,
- scaling law
1. [1]
  Astruc, D.; Boisselier, E.; Ornelas, C. Chem. Rev. 2010, 110, 1857. doi: 10.1021/cr900327d
2. [2]
  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.
3. [3]
  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
4. [4]
  Boas, U.; Heegaard, P. M. H. Chem. Soc. Rev. 2004, 33, 43. doi: 10.1039/b309043b
5. [5]
  Zhang, S.; Yang, J.; Liu, M.; Lü, S.; Gao, C.; Wu, C.; Zhu, Z. Acta Chim. Sinica 2016, 74, 401. doi: 10.3969/j.issn.0253-2409.2016.04.003
6. [6]
  Zhang, W.; Xu, N.; Yao, Z.; Li, K.; Zhu, Y.; Chen, L.; Ye, W.; Deng, W. Chin. J. Org. Chem. 2016, 36, 2039.
7. [7]
  Buhleier, G. E.; Wehner, W.; Vögtle, F. Synthesis-Stuttgart. 1978, 2, 155.
8. [8]
  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
9. [9]
  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
10. [10]
  Prosa, T. J.; Bauer, B. J.; Amis, E. J. Macromolecules 2001, 34, 4897. doi: 10.1021/ma0002186
11. [11]
  Pötschke, D.; Ballauf, M.; Lindner, P.; Fischer, M.; Vögtle, F. J. Appl. Cryst. 2000, 33, 605. doi: 10.1107/S0021889899013795
12. [12]
  Rosenfeldt, S.; Dingenouts, N.; Ballauf, M.; Werner, N.; Vögtle, F.; Lindner, P. Macromolecules 2002, 35, 8098. doi: 10.1021/ma020585c
13. [13]
  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
14. [14]
  Prosa, T. J.; Bauer, B. J.; Amis, E. J.; Tomalia, D. A.; Scherrenberg, R. J. Polym. Sci. Part B:Polym. Phys. 1997, 35, 2913.
15. [15]
  Rathgeber, S.; Monkenbusch, M.; Kreitschmann, M.; Urban, V.; Brulet, A. J. Chem. Phys. 2002, 117, 4047. doi: 10.1063/1.1493771
16. [16]
  Qin, T.; Zeng, Y.; Chen, J.; Yu, T.; Li, Y. Acta Chim. Sinica 2017, 75, 99.
17. [17]
  de Gennes, P. G.; Hervet, H. Journal de Physique Lettres 1983, 44, L351. doi: 10.1051/jphyslet:01983004409035100
18. [18]
  Lescanec, R. L.; Muthukumar, M. Macromolecules 1990, 23, 2280. doi: 10.1021/ma00210a026
19. [19]
  Mansfield, M. L.; Klushin, L. I. Macromolecules 1993, 26, 4262. doi: 10.1021/ma00068a029
20. [20]
  Mansfield, M. L.; Jeong, M. Macromolecules 2002, 35, 9794. doi: 10.1021/ma012229k
21. [21]
  Chen, Z. Y.; Cui, S.-M. Macromolecules 1996, 29, 7943. doi: 10.1021/ma9514636
22. [22]
  Murat, M.; Grest, G. S. Macromolecules 1996, 29, 1278. doi: 10.1021/ma951219e
23. [23]
  Boris, D.; Rubinstein, M. Macromolecules 1996, 29, 7251. doi: 10.1021/ma960397k
24. [24]
  Lyulin, A. V.; Davies, G. R.; Adolf, D. B. Macromolecules 2000, 33, 6899. doi: 10.1021/ma0003811
25. [25]
  Sheng, Y.-J.; Jiang, S.; Tsao, H.-K. Macromolecules 2002, 35, 7865. doi: 10.1021/ma025561k
26. [26]
  Götze, I. O.; Likos, C. N. Macromolecules 2003, 36, 8189. doi: 10.1021/ma030137k
27. [27]
  Timoshenko, E. G.; Kuznetsov, Y. A.; Connolly, R. J. Chem. Phys. 2002, 117, 9050. doi: 10.1063/1.1514571
28. [28]
  Bosko, J. T.; Prakash, J. R. Macromolecules 2011, 44, 660. doi: 10.1021/ma102094f
29. [29]
  Cui, W.; Su, C.-F.; Merlitz, H.; Wu, C.-X.; Sommer, J.-U. Macromolecules 2014, 47, 3645. doi: 10.1021/ma500129h
30. [30]
  Kłos, J. S.; Sommer, J.-U. Macromolecules 2013, 46, 3107. doi: 10.1021/ma4001989
31. [31]
  Lewis, T.; Pryamitsyn, V.; Ganesan, V. J. Chem. Phys. 2011, 135, 204902. doi: 10.1063/1.3663382
32. [32]
  Lu, Y.; An, L.; Wang, Z.-G. Macromolecules 2013, 46, 5731. doi: 10.1021/ma400872s
33. [33]
  Mandal, T.; Dasgupta, C.; Maiti, P. K. J. Chem. Phys. 2014, 141, 144901. doi: 10.1063/1.4897160
34. [34]
  Rubio, A. M.; McBride, C.; Freire, J. J. Macromolecules 2014, 47, 5379. doi: 10.1021/ma501127f
35. [35]
  Chen, C.; Tang, P.; Qiu, F.; Shi, A.-C. J. Phys. Chem. B 2016, 120, 5553. doi: 10.1021/acs.jpcb.6b03005
36. [36]
  Chen, W.-R.; Porcar, L.; Liu, Y.; Butler, P. D.; Magid, L. J. Macromolecules 2007, 40, 5887. doi: 10.1021/ma0626564
37. [37]
  Giupponi, G.; Buzza, D. M. A. J. Chem. Phys. 2004, 120, 10290. doi: 10.1063/1.1714829
38. [38]
  Yang, Y. Z.; Qiu, F.; Zhang, H. D.; Yang, Y. L. Macromolecules 2017, 50, 4007. doi: 10.1021/acs.macromol.7b00040
39. [39]
  Flory, P. J. Principles of Polymer Chemistry, Cornell University Press, New York, 1953.
40. [40]
  Matsen, M. W. J. Phys.:Condens. Matter 2002, 14, R21. doi: 10.1088/0953-8984/14/2/201
41. [41]
  Fredrickson, G. The Equilibrium Theory of Inhomogeneous Polymers, Oxford University Press, Oxford, 2006.
42. [42]
  Edwards, S. F. Proc. Phys. Soc. 1965, 85, 613. doi: 10.1088/0370-1328/85/4/301
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