The effects of grafting density and charge fraction on the properties of ring polyelectrolyte brushes: a molecular dynamics simulation study

  • Qing-Hai HaoEmail author
  • Li-Xiang Liu
  • Gang Xia
  • Li-Yan Liu
  • Bing MiaoEmail author
Original Contribution


Using molecular dynamics simulations, the flexible ring polyelectrolyte chains tethered to a planar substrate and immersed in good solvents are investigated systematically. Two sets of simulations are performed to explore the effects of grafting density and charge fraction, respectively. Both the monovalent and trivalent counterions are considered. The height of the brush H follows a scaling relation with grafting density (~σgν) and charge fraction (~fν). The values of the exponents are different from those of the linear counterparts. Through a careful analysis on the distributions of monomers and counterions, pair correlation functions of monomer-monomer and monomer-counterion, as well as the fractions of trivalent counterions in four states, the equilibrium structures of the ring PE brushes are examined in detail. Furthermore, a brief comparison with the ‘equivalent’ linear brush is carried out. Also, our results can serve as a guide for improving the performance of ring polyelectrolyte brushes as unique surface modifiers.

Graphical abstract



Molecular dynamics simulation Ring polyelectrolyte brushes Grafting density Charge fraction 


Funding information

Financial support was provided by the National Natural Science Foundation of China (NSFC) (Grant Nos. 21674005, 21544007, 21774131) and the Fundamental Research Funds for the Central Universities (Grant No. 3122018L007).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Cohen Stuart MA, Huck WTS, Genzer J, Müller M, Ober C, Stamm M, Sukhorukov GB, Szleifer I, Tsukruk VV, Urban M, Winnik F, Zauscher S, Luzinov I, Minko S (2010). Nat Mater 9:101CrossRefGoogle Scholar
  2. 2.
    Das S, Banik M, Chen G, Sinha S, Mukherjee R (2015). Soft Matter 11:8550PubMedCrossRefGoogle Scholar
  3. 3.
    Kinjo T, Yoshida H, Washizu H (2018). Colloid Polym Sci 296:1CrossRefGoogle Scholar
  4. 4.
    Pincus P (1991). Macromolecules 24:2912CrossRefGoogle Scholar
  5. 5.
    Motornov M, Tam TK, Pita M, Tokarev I, Katz E, Minko S (2009). Nanotechnology 20:434006PubMedCrossRefGoogle Scholar
  6. 6.
    Kreer T (2016). Soft Matter 12:3479PubMedCrossRefGoogle Scholar
  7. 7.
    Benetti EM, Divandari M, Ramakrishna SN, Morgese G, Yan WQ, Trachsel L (2017). Chem Eur J 23:12433PubMedCrossRefGoogle Scholar
  8. 8.
    Cao DP, Wu JZ (2006). Langmuir 22:2712PubMedCrossRefGoogle Scholar
  9. 9.
    Zhulina EB, Leermakers FAM, Borisov OV (2016). Macromolecules 49:8758CrossRefGoogle Scholar
  10. 10.
    Qiu WJ, Li BH, Wang Q (2018). Soft Matter 14:1887PubMedCrossRefGoogle Scholar
  11. 11.
    Li L, Yan B, Zhang L, Tian Y, Zeng HB (2015). Chem Commun 51:15780CrossRefGoogle Scholar
  12. 12.
    Wei T, Zhou YY, Zhan WJ, Zhang ZB, Zhu XL, Yu Q, Chen H (2017). Colloids Surf B: Biointerfaces 159:527PubMedCrossRefGoogle Scholar
  13. 13.
    Morgese G, Trachsel L, Romio M, Divandari M, Ramakrishna SN, Benetti EM (2016). Angew Chem Int Ed 55:15583CrossRefGoogle Scholar
  14. 14.
    Morgese G, Trachsel L, Romio M, Divandari M, Ramakrishna SN, Benetti EM (2017). Angew Chem Int Ed 56:2236CrossRefGoogle Scholar
  15. 15.
    Divandari M, Morgese G, Trachsel L, Romio M, Dehghani ES, Rosenboom JG, Paradisi C, Zenobi-Wong M, Ramakrishna SN, Benetti EM (2017). Macromolecules 50:7760CrossRefGoogle Scholar
  16. 16.
    Morgese G, Shaghasemi BS, Causin V, Zenobi-Wong M, Ramakrishna SN, Reimhult E, Benetti EM (2017). Angew Chem Int Ed 56:4507CrossRefGoogle Scholar
  17. 17.
    Erbas A, Paturej J (2015). Soft Matter 11:3139PubMedCrossRefGoogle Scholar
  18. 18.
    Reith D, Milchev A, Virnau P, Binder K (2011). Europhys Lett 95:28003CrossRefGoogle Scholar
  19. 19.
    Reith D, Milchev A, Virnau P, Binder K (2012). Macromolecules 45:4381CrossRefGoogle Scholar
  20. 20.
    Milchev A, Binder K (2013). Macromolecules 46:8724CrossRefGoogle Scholar
  21. 21.
    He SZ, Holger M, Su CF, Wu CX (2013). Chin Phys B 22:016101CrossRefGoogle Scholar
  22. 22.
    Wan WB, Lv HH, Holger M, Wu CX (2016). Chin Phys B 25:106101CrossRefGoogle Scholar
  23. 23.
    Pei HW, Liu XL, Liu H, Zhu YL, Lu ZY (2017). Phys Chem Chem Phys 19:4710PubMedCrossRefGoogle Scholar
  24. 24.
    Jones RL, Spontak RJ (1995). J Chem Phys 103:5137CrossRefGoogle Scholar
  25. 25.
    Jones RL, Spontak RJ (1994). J Chem Phys 101:5179CrossRefGoogle Scholar
  26. 26.
    Gulati HS, Hall CK, Jones RL, Spontak RJ (1996). J Chem Phys 105:7712CrossRefGoogle Scholar
  27. 27.
    Goren T, Spencera ND, Crockett R (2014). RSC Adv 4:21497CrossRefGoogle Scholar
  28. 28.
    Kremer K, Grest GS (1990). J Chem Phys 92:5057CrossRefGoogle Scholar
  29. 29.
    Guptha VS, Hsiao PY (2014). Polymer 55:2900CrossRefGoogle Scholar
  30. 30.
    Jackson NE, Brettmann BK, Vishwanath V, Tirrell M, de Pablo JJ (2017). ACS Macro Lett 6:155CrossRefGoogle Scholar
  31. 31.
    Hao QH, Xia G, Miao B, Tan HG, Niu XH, Liu LY (2018). Macromolecules 51:8513CrossRefGoogle Scholar
  32. 32.
    Yu J, Jackson NE, Xu X, Morgenstern Y, Kaufman Y, Ruths M, de Pablo JJ, Tirrell M (2018). Science 360:1434PubMedCrossRefGoogle Scholar
  33. 33.
    Frenkel D, Smit B (2002) Understanding molecular simulations. Academic Press, New YorkGoogle Scholar
  34. 34.
    Ballenegger V, Arnold A, Cerdà JJ (2009). J Chem Phys 131:094107PubMedCrossRefGoogle Scholar
  35. 35.
    Plimpton SJ (1995). J Comput Phys 117:1CrossRefGoogle Scholar
  36. 36.
    Cao Q, Zuo C, He H, Li L (2009). Macromol Theory Simul 18:441CrossRefGoogle Scholar
  37. 37.
    Cao Q, Zuo C, Li L, He H (2010). Model Simul Mater Sci Eng 18:075001CrossRefGoogle Scholar
  38. 38.
    Csajka FS, Seidel C (2000). Macromolecules 33:2728CrossRefGoogle Scholar
  39. 39.
    Farina R, Laugel N, Pincus P, Tirrell M (2013). Soft Matter 9:10458CrossRefGoogle Scholar
  40. 40.
    Yu J, Mao J, Yuan G, Satija S, Jiang Z, Chen W, Tirrell M (2016). Macromolecules 49:5609CrossRefGoogle Scholar
  41. 41.
    Netz RR, Andelman D (2003). Phys Rep 380:1CrossRefGoogle Scholar
  42. 42.
    Alexander S (1977). J Physiol Paris 38:983Google Scholar
  43. 43.
    Milner ST, Witten TA, Cates ME (1988). Macromolecules 21:2610CrossRefGoogle Scholar
  44. 44.
    Zhulina EB, Borisov OV, Pryamitsyn VA, Birshtein TM (1991). Macromolecules 24:140CrossRefGoogle Scholar
  45. 45.
    Brettmann B, Pincus P, Tirrell M (2017). Macromolecules 50:1225CrossRefGoogle Scholar
  46. 46.
    Brettmann BK, Laugel N, Hoffmann N, Pincus P, Tirrell M (2015). J Polym Sci A Polym Chem 54:284CrossRefGoogle Scholar
  47. 47.
    Nap RJ, Solveyra EG, Szleifer I (2018). Biomater Sci 6:1048PubMedPubMedCentralCrossRefGoogle Scholar
  48. 48.
    Manning GS (1969). J Chem Phys 51:3249CrossRefGoogle Scholar
  49. 49.
    Miao B, Vilgis TA (2012). Macromol Theory Simul 21:582CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of ScienceCivil Aviation University of ChinaTianjinChina
  2. 2.Center of Materials Science and Optoelectronics Engineering, College of Materials Science and Opto-Electronic TechnologyUniversity of Chinese Academy of SciencesBeijingChina

Personalised recommendations