Abstract
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.
Similar content being viewed by others
References
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 9:101
Das S, Banik M, Chen G, Sinha S, Mukherjee R (2015). Soft Matter 11:8550
Kinjo T, Yoshida H, Washizu H (2018). Colloid Polym Sci 296:1
Pincus P (1991). Macromolecules 24:2912
Motornov M, Tam TK, Pita M, Tokarev I, Katz E, Minko S (2009). Nanotechnology 20:434006
Kreer T (2016). Soft Matter 12:3479
Benetti EM, Divandari M, Ramakrishna SN, Morgese G, Yan WQ, Trachsel L (2017). Chem Eur J 23:12433
Cao DP, Wu JZ (2006). Langmuir 22:2712
Zhulina EB, Leermakers FAM, Borisov OV (2016). Macromolecules 49:8758
Qiu WJ, Li BH, Wang Q (2018). Soft Matter 14:1887
Li L, Yan B, Zhang L, Tian Y, Zeng HB (2015). Chem Commun 51:15780
Wei T, Zhou YY, Zhan WJ, Zhang ZB, Zhu XL, Yu Q, Chen H (2017). Colloids Surf B: Biointerfaces 159:527
Morgese G, Trachsel L, Romio M, Divandari M, Ramakrishna SN, Benetti EM (2016). Angew Chem Int Ed 55:15583
Morgese G, Trachsel L, Romio M, Divandari M, Ramakrishna SN, Benetti EM (2017). Angew Chem Int Ed 56:2236
Divandari M, Morgese G, Trachsel L, Romio M, Dehghani ES, Rosenboom JG, Paradisi C, Zenobi-Wong M, Ramakrishna SN, Benetti EM (2017). Macromolecules 50:7760
Morgese G, Shaghasemi BS, Causin V, Zenobi-Wong M, Ramakrishna SN, Reimhult E, Benetti EM (2017). Angew Chem Int Ed 56:4507
Erbas A, Paturej J (2015). Soft Matter 11:3139
Reith D, Milchev A, Virnau P, Binder K (2011). Europhys Lett 95:28003
Reith D, Milchev A, Virnau P, Binder K (2012). Macromolecules 45:4381
Milchev A, Binder K (2013). Macromolecules 46:8724
He SZ, Holger M, Su CF, Wu CX (2013). Chin Phys B 22:016101
Wan WB, Lv HH, Holger M, Wu CX (2016). Chin Phys B 25:106101
Pei HW, Liu XL, Liu H, Zhu YL, Lu ZY (2017). Phys Chem Chem Phys 19:4710
Jones RL, Spontak RJ (1995). J Chem Phys 103:5137
Jones RL, Spontak RJ (1994). J Chem Phys 101:5179
Gulati HS, Hall CK, Jones RL, Spontak RJ (1996). J Chem Phys 105:7712
Goren T, Spencera ND, Crockett R (2014). RSC Adv 4:21497
Kremer K, Grest GS (1990). J Chem Phys 92:5057
Guptha VS, Hsiao PY (2014). Polymer 55:2900
Jackson NE, Brettmann BK, Vishwanath V, Tirrell M, de Pablo JJ (2017). ACS Macro Lett 6:155
Hao QH, Xia G, Miao B, Tan HG, Niu XH, Liu LY (2018). Macromolecules 51:8513
Yu J, Jackson NE, Xu X, Morgenstern Y, Kaufman Y, Ruths M, de Pablo JJ, Tirrell M (2018). Science 360:1434
Frenkel D, Smit B (2002) Understanding molecular simulations. Academic Press, New York
Ballenegger V, Arnold A, Cerdà JJ (2009). J Chem Phys 131:094107
Plimpton SJ (1995). J Comput Phys 117:1
Cao Q, Zuo C, He H, Li L (2009). Macromol Theory Simul 18:441
Cao Q, Zuo C, Li L, He H (2010). Model Simul Mater Sci Eng 18:075001
Csajka FS, Seidel C (2000). Macromolecules 33:2728
Farina R, Laugel N, Pincus P, Tirrell M (2013). Soft Matter 9:10458
Yu J, Mao J, Yuan G, Satija S, Jiang Z, Chen W, Tirrell M (2016). Macromolecules 49:5609
Netz RR, Andelman D (2003). Phys Rep 380:1
Alexander S (1977). J Physiol Paris 38:983
Milner ST, Witten TA, Cates ME (1988). Macromolecules 21:2610
Zhulina EB, Borisov OV, Pryamitsyn VA, Birshtein TM (1991). Macromolecules 24:140
Brettmann B, Pincus P, Tirrell M (2017). Macromolecules 50:1225
Brettmann BK, Laugel N, Hoffmann N, Pincus P, Tirrell M (2015). J Polym Sci A Polym Chem 54:284
Nap RJ, Solveyra EG, Szleifer I (2018). Biomater Sci 6:1048
Manning GS (1969). J Chem Phys 51:3249
Miao B, Vilgis TA (2012). Macromol Theory Simul 21:582
Funding
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).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hao, QH., Liu, LX., Xia, G. et al. The effects of grafting density and charge fraction on the properties of ring polyelectrolyte brushes: a molecular dynamics simulation study. Colloid Polym Sci 298, 21–33 (2020). https://doi.org/10.1007/s00396-019-04579-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00396-019-04579-2