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

  • 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

Figures(8)

  • 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.
  • 加载中
    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

  • 加载中
    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]

      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

    3. [3]

      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

    4. [4]

      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

    5. [5]

      Yanglin Jiang Mingqing Chen Min Liang Yige Yao Yan Zhang Peng Wang Jianping Zhang . Experimental and Theoretical Investigations of Solvent Polarity Effect on ESIPT Mechanism in 4′-N,N-diethylamino-3-hydroxybenzoflavone. Acta Physico-Chimica Sinica, 2025, 41(2): 100012-. doi: 10.3866/PKU.WHXB202309027

    6. [6]

      Qianqian Liu Xing Du Wanfei Li Wei-Lin Dai Bo Liu . Synergistic Effects of Internal Electric and Dipole Fields in SnNb2O6/Nitrogen-Enriched C3N5 S-Scheme Heterojunction for Boosting Photocatalytic Performance. Acta Physico-Chimica Sinica, 2024, 40(10): 2311016-. doi: 10.3866/PKU.WHXB202311016

    7. [7]

      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

    8. [8]

      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

    9. [9]

      Yaling Chen . Basic Theory and Competitive Exam Analysis of Dynamic Isotope Effect. University Chemistry, 2024, 39(8): 403-410. doi: 10.3866/PKU.DXHX202311093

    10. [10]

      Kaifu Zhang Shan Gao Bin Yang . Application of Theoretical Calculation with Fun Practice in Raman Spectroscopy Experimental Teaching. University Chemistry, 2025, 40(3): 62-67. doi: 10.12461/PKU.DXHX202404045

    11. [11]

      Meifeng Zhu Jin Cheng Kai Huang Cheng Lian Shouhong Xu Honglai Liu . Classical Density Functional Theory for Understanding Electrochemical Interface. University Chemistry, 2025, 40(3): 148-152. doi: 10.12461/PKU.DXHX202405166

    12. [12]

      Fei Xie Chengcheng Yuan Haiyan Tan Alireza Z. Moshfegh Bicheng Zhu Jiaguo Yud带中心调控过渡金属单原子负载COF吸附O2的理论计算研究. Acta Physico-Chimica Sinica, 2024, 40(11): 2407013-. doi: 10.3866/PKU.WHXB202407013

    13. [13]

      Hui Li Jia Nie Zhongyuan Lü Hujun Qian Youliang Zhu Fuquan Bai Zexing Qu Ronglin Zhong . Developing a Lecture Mode for Theoretical and Computational Chemistry Curriculum under the “Modernization of Chinese Education” Initiative. University Chemistry, 2025, 40(3): 1-9. doi: 10.3866/PKU.DXHX202402007

    14. [14]

      Xintian Xie Sicong Ma Yefei Li Cheng Shang Zhipan Liu . Application of Machine Learning Potential-based Theoretical Simulations in Undergraduate Teaching Laboratory Course Design. University Chemistry, 2025, 40(3): 140-147. doi: 10.12461/PKU.DXHX202405164

    15. [15]

      Jie ZHAOSen LIUQikang YINXiaoqing LUZhaojie WANG . Theoretical calculation of selective adsorption and separation of CO2 by alkali metal modified naphthalene/naphthalenediyne. Chinese Journal of Inorganic Chemistry, 2024, 40(3): 515-522. doi: 10.11862/CJIC.20230385

    16. [16]

      Ping Cai Yaxian Zhu Tao Hu . Frontier Research and Basic Theory in the Classroom: an Introduction to the Inorganic Chemistry Teaching Case under the Chemistry “101 Plan”. University Chemistry, 2024, 39(10): 84-88. doi: 10.12461/PKU.DXHX202408027

    17. [17]

      Baitong Wei Jinxin Guo Xigong Liu Rongxiu Zhu Lei Liu . Theoretical Study on the Structure, Stability of Hydrocarbon Free Radicals and Selectivity of Alkane Chlorination Reaction. University Chemistry, 2025, 40(3): 402-407. doi: 10.12461/PKU.DXHX202406003

    18. [18]

      Hao XURuopeng LIPeixia YANGAnmin LIUJie BAI . Regulation mechanism of halogen axial coordination atoms on the oxygen reduction activity of Fe-N4 site: A density functional theory study. Chinese Journal of Inorganic Chemistry, 2025, 41(4): 695-701. doi: 10.11862/CJIC.20240302

    19. [19]

      Yiying Yang Dongju Zhang . Elucidating the Concepts of Thermodynamic Control and Kinetic Control in Chemical Reactions through Theoretical Chemistry Calculations: A Computational Chemistry Experiment on the Diels-Alder Reaction. University Chemistry, 2024, 39(3): 327-335. doi: 10.3866/PKU.DXHX202309074

    20. [20]

      Jie ZHAOHuili ZHANGXiaoqing LUZhaojie WANG . Theoretical calculations of CO2 capture and separation by functional groups modified 2D covalent organic framework. Chinese Journal of Inorganic Chemistry, 2025, 41(2): 275-283. doi: 10.11862/CJIC.20240213

Metrics
  • PDF Downloads(9)
  • Abstract views(638)
  • HTML views(78)

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

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Address:Zhongguancun North First Street 2,100190 Beijing, PR China Tel: +86-010-82449177-888
Powered By info@rhhz.net

/

DownLoad:  Full-Size Img  PowerPoint
Return