Abstract
Brownian dynamics simulations are employed to explore the effects of chain stiffness and trivalent salt concentration on the conformational behavior of spherical polyelectrolyte brush. The rigid brush adopts bundle-like morphology at a wide range of trivalent salt concentration. The number variation of bundles pinned on the colloid surface shows a non-monotonic profile as a function of the chain stiffness. The radial distributions of monomers and ions and the charge ratio between condensed ions and monomers are calculated. The charge inversion is observed for the high salt concentration regardless of chain rigidity. Furthermore, the pair correlation functions of monomer-monomer and monomer-salt cation are used to elucidate the aggregated mechanism of the bundle-like structure.
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References
Pincus, P. Colloid stabilization with grafted polyelectrolyte brushes. Macromolecules 1991, 24(10), 2912–2919.
Kreer, T. Polymer-brush lubrication: a review of recent theoretical advances. Soft Matter 2016, 12(15), 3479–3501.
Li, B.; Yu, B.; Wang, X. L.; Guo, F.; Zhou, F. Correlation between conformation change of polyelectrolyte brushes and lubrication. Chinese J. Polym. Sci. 2015, 33(1), 163–172.
Motornov, M.; Tam, T. K.; Pita, M.; Tokarev, I.; Katz, E.; Minko, S. Switchable selectivity for gating ion transport with mixed polyelectrolyte brushes: approaching ‘smart’ drug delivery systems. Nanotechnology 2009, 20(43), DOI: 10.1088/0957-4484/20/43/434006
Stuart, M. A. C.; Huck, W. T. S.; Genzer, J.; Muller, M.; Ober, C.; Stamm, M.; Sukhorukov, G. B.; Szleifer, I.; Tsukruk, V. V.; Urban, M.; Winnik, F.; Zauscher, S.; Luzinov, I.; Minko, S. Emerging applications of stimuli-responsive polymer materials. Nat. Mater. 2010, 9(2), 101–113.
Binder, K.; Milchev, A. Polymer brushes on flat and curved surfaces: How computer simulations can help to test theories and to interpret experiments. J. Polym. Sci., Part B: Polym. Phys. 2012, 50(50), 1515–1555.
Das, S.; Banik, M.; Chen, G.; Sinhaa, S.; Mukherjeeb, R. Polyelectrolyte brushes: theory, modelling, synthesis and applications. Soft Matter 2015, 11(44), 8550–8583.
Yu, X.; Wang, W.; Li, L.; Guo, X.; Zhou, Z.; Wang, F. Analysis of spherical polyelectrolyte brushes by small angle X-ray scattering. Chinese J. Polym. Sci. 2014, 32(6), 778–785.
Willott, J. D.; Murdoch, T. J.; Webber, G. B.; Wanless, E. J. Physicochemical behaviour of cationic polyelectrolyte brushes. Prog. Polym. Sci. 2017, 64, 52–75.
Guenoun, P.; Muller, F.; Delsanti, M.; Auvray, L.; Chen, Y. J.; Mays, J. W.; Tirrell, M. Rodlike behavior of polyelectrolyte brushes. Phys. Rev. Lett. 1998, 81(18), 3872–3875.
Shen, G.; Tercero, N.; Gaspar, M. A.; Varughese, B.; Shepard, K.; Levicky, R. Charging behavior of single-stranded DNA polyelectrolyte brushes. J. Am. Chem. Soc. 2006, 128(26), 8427–8433.
Kegler, K.; Salomo, M.; Kremer, F. Forces of interaction between DNA-grafted colloids: an optical tweezer measurement. Phys. Rev. Lett. 2007, 98(5), 058304.
Fazli, H.; Golestanian, R.; Hansen, P. L., Kolahchi, M. R. Rod-like polyelectrolyte brushes with mono and multivalent counterions. Europhys. Lett. 2006, 73(3), 429–435.
Likos, C. N.; Blaak, R.; Wynveen, A. Computer simulations of polyelectrolyte stars and brushes. J. Phys.: Condens. Matter 2008, 20(49), 494221.
Wynveen, A.; Likos, C. N. Interactions between planar stiff polyelectrolyte brushes. Phys. Rev. E 2009, 80(1), DOI: 10.1103/PhysRevE.80.010801
Wynveen, A.; Likos, C. N. Interactions between planar polyelectrolyte brushes: effects of stiffness and salt. Soft Matter 2010, 6(1), 163–171.
Cao, Q. Q.; Zuo, C. C.; Li, L. J. Molecular dynamics simulations of end-grafted centipede-like polymers with stiff charged side chains. Eur. Phys. J. E 2010, 32(1), 1–12.
Cao, Q. Q.; Zuo, C. C.; Li, L. J.; Yan, G. Effects of chain stiffness and salt concentration on responses of polyelectrolyte brushes under external electric field. Biomicrofluidics 2011, 5(4), DOI: 10.1063/1.3672190
Cao, Q. Q.; You, H. Polyampholyte brushes grafted on the surface of a spherical cavity: effect of the charged monomer sequence, grafting density, and chain stiffness. Langmuir 2015, 31(23), 6375–6384.
Lieleg, O.; Schmoller, K. M.; Cyron, C. J.; Luan, Y.; Wall, W. A.; Bausch, A. R. Structural polymorphism in heterogeneous cytoskeletal networks. Soft Matter 2009, 5(9), 1796–1803.
Wang, Z.; Sheetz, M. P. The C-terminus of tubulin increases cytoplasmic dynein and kinesin processivity. Biophys. J. 2000, 78(4), 1955–1964.
Fazli, H.; Mohammadinejad, S., Golestanian, R. Salt-induced aggregation of stiff polyelectrolytes. J. Phys.: Condens. Matter 2009, 21(42), DOI: 10.1088/0953-8984/21/42/424111
Sayar, M.; Holm, C. Equilibrium polyelectrolyte bundles with different multivalent counterion concentrations. Phys. Rev. E 2010, 82(3), DOI: 10.1103/PhysRevE.82.031901
Tom, A. M.; Rajesh, R.; Vemparala, S. Aggregation dynamics of rigid polyelectrolytes. J. Chem. Phys. 2016, 144(3), DOI: 10.1063/1.4939870
Li, Y.; Jiang, T.; Wang, L.; Lin, S.; Lin J. Self-assembly of rod-coil-rod triblock copolymers: a route toward hierarchical liquid crystalline structures. Polymer 2016, 103, 64–72.
Li, Y.; Jiang, T.; Lin, S.; Lin, J.; Cai, C.; Zhu, X. Hierarchical nanostructures self-assembled from a mixture system containing rod-coil block copolymers and rigid homopolymers. Sci. Rep. 2015, 5, DOI: 10.1038/srep10137
Guan, Z.; Wang, L.; Lin, J. Interaction pathways between plasma membrane and block copolymer micelles. Biomacromolecules 2017, 18(3), 797–807.
Kremer, K.; Grest, G. S. Dynamics of entangled linear polymer melts: a molecular-dynamics simulation. J. Chem. Phys. 1990, 92(8), 5057–5086.
Yeh, I. C.; Berkowitz, M. L. Ewald summation for systems with slab geometry. J. Chem. Phys. 1999, 111(7), 3155–3162.
Plimpton, S. J. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117(1), 1–19.
Pathria, R. in "Statistical mechanics", 2nd ed. 2006, Elsevier, Singapore: Pte Ltd.
Varghese, A.; Rajesh, R.; Vemparala, S. Aggregation of rod-like polyelectrolyte chains in the presence of monovalent counterions. J. Chem. Phys. 2012, 137(23), DOI: 10.1063/1.4771920
Günther, J. U.; Ahrens, H.; Förster, S.; Helm, C. A. Bundle formation in polyelectrolyte brushes. Phys. Rev. Lett. 2008, 101(25), DOI: 10.1103/PhysRevLett.101.258303
Guptha, V. S.; Hsiao, P. Y. Polyelectrolyte brushes in monovalent and multivalent salt solutions. Polymer 2014, 55(12), 2900–2912.
Liu, L., Pincus, P. A.; Hyeon, C. Heterogenous morphology and dynamics of polyelectrolyte brush condensates in trivalent counterion solution. Macromolecules 2017, 50(4), 1579–1588.
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This work was financially supported by the National Natural Science Foundation of China (No. 21474005) and the Fundamental Research Funds for the Central Universities (No. 3122016L011).
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Hao, QH., Zheng, Z., Xia, G. et al. Brownian Dynamics Simulations of Rigid Polyelectrolyte Chains Grafting to Spherical Colloid. Chin J Polym Sci 36, 791–798 (2018). https://doi.org/10.1007/s10118-018-2042-x
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DOI: https://doi.org/10.1007/s10118-018-2042-x