Abstract
The self-consistent field theory (SCFT) was employed to numerically study the interaction and interpenetration between two opposing weak polyelectrolyte (PE) brushes formed by grafting weak PE chains onto the surfaces of two long and parallel columns with rectangular-shaped cross-section immersed in a salty aqueous solution. The dependences of the brush heights and the average degree of ionization on various system parameters were also investigated. When the brush separation is relatively large compared with the unperturbed brush height, the degree of interpenetration between the two opposing PE brushes was found to increase with increasing grafting density and bulk degree of ionization. The degree of interpenetration also increases with the bulk salt concentration in the osmotic brush regime. Numerical results further revealed that, at a brush separation comparable to the unperturbed brush height, the degree of interpenetration does not increase further with increasing bulk degree of ionization, bulk salt concentration in the osmotic regime and grafting density. The saturation of the degree of interpenetration with these system parameters indicates that the grafted PE chains in the gap between the two columns retract and tilt in order to reduce the unfavorable electrostatic and steric repulsions between the two opposing PE brushes. Based on salt ion concentrations at the midpoint between the two opposing brushes, a quantitative criterion in terms of the unperturbed brush height and Debye screening length was established to determine the threshold value of the brush separation beyond which they are truly independent from each other.
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Data Availability Statement
The related data (DOI:https://doi.org/10.57760/sciencedb.j00189.00018) of this paper can be accessed in the Science Date Bank database https://www.scidb.cn/en/c/cjps.
References
Halperin, A.; Tirrell, M.; Lodge, T. P. Tethered chains in polymer microstructures. Adv. Polym. Sci. 1991, 100, 30–71.
Rühe, J.; Ballauff, M.; Biesalski, M.; Dziezok, P.; Gröhn, F.; Johannsmann, D. Polyelectrolyte brushes. Adv. Polym. Sci. 2004, 165, 79–150.
Naji, A.; Seidel, C.; Netz, R. R. Theoretical approaches to neutral and charged polymer brushes. Adv. Polym. Sci. 2006, 198, DOI:https://doi.org/10.1007/12-062.
Wu, T.; Gong, P.; Szleifer, I.; Vicek, P.; Subr, V.; Genzer, J. Behavior of surface-anchored poly(acrylic acid) brushes with grafting density gradients on solid substrates: 1. Experiment. Macromolecules 2007, 40, 8756–8764.
Witte, K. N.; Kim, S.; Won, Y. Y. J. Self-consistent field theory study of the effect of grafting density on the height of a weak polyelectrolyte brush. J. Phys. Chem. B 2009, 113, 11076–11084.
Napper, Donald H. Polymeric stabilization of colloidal dispersions. Academic Press, London. 1983, Vol. 7.
Klein, J.; Kamiyama, Y.; Yoshizawa, H.; Israelachvili, J. N.; Fredrickson, G. H.; Pincus, P.; Fetters, L. J. Lubrication forces between surfaces bearing polymer brushes. Macromolecules 1993, 26, 5552–5560.
Sokoloff, J. B. Theory of the observed ultralow friction between sliding polyelectrolyte brushes. J. Chem. Phys. 2008, 129, 014901.
Ouyang, H.; Xia, Z. H.; Zhe, J. Voltage-controlled flow regulating in nanofluidic channels with charged polymer brushes. Microfluid Nanofluid. 2010, 9, 915–922.
Roy, I.; Gupta, M. N. Smart polymeric materials: emerging biochemical applications. Chem. Biol. 2003, 10, 1161–1171.
Patwary, J.; Chen, G.; Das, S. Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density. Microfluid Nanofluid. 2016, 20, 37.
Chen, G.; Das, S. J. Electroosmotic transport in polyelectrolyte-grafted nanochannels with pH-dependent charge density. Appl. Phys. 2015, 117, 185304.
Pincus, P. Colloid stabilization with grafted polyelectrolytes. Macromolecules 1991, 24, 2912–2919.
Borisov, O. V.; Zhulina, E. B.; Birshtein, T. M. Diagram of the states of a grafted polyelectrolyte layer. Macromolecules 1994, 27, 4795–4803.
Netz, R. R.; Andelman, D. Neutral and charged polymers at interfaces. Phys. Rep. 2003, 380, 1–95.
Israëls, R.; Leermakers, F. A. M.; Fleer, G. J.; Zhulina, E. B. Charged polymeric brushes: structure and scaling relations. Macromolecules 1994, 27, 3249–3261.
Zhulina, E. B.; Wolterink, J. K.; Borisov, O. V. Screening effects in a polyelectrolyte brush: self-consistent-field theory. Macromolecules 2000, 33, 4945–4953.
Csajka, F. S.; Seidel, C. Strongly charged polyelectrolyte brushes: a molecular dynamics study. Macromolecules 2000, 33, 2728–2739.
Seidel, C. Strongly stretched polyelectrolyte brushes. Macromolecules 2003, 36, 2536–2543.
Meng, D.; Wang, Q. Stimuli-response of charged diblock copolymer brushes. J. Chem. Phys. 2011, 135, 224904.
Hehmeyer, O. J.; Stevens, M. J. Molecular dynamics simulations of grafted polyelectrolytes on two apposing walls. J. Chem. Phys. 2005, 122, 134909.
Kumar, N. A.; Seidel, C. Interaction between two polyelectrolyte brushes. Phys. Rev. E 2007, 76, 02080.
Wynveen, A.; Likos, C. N. Interactions between planar stiff polyelectrolyte brushes. Phys. Rev. E 2009, 80, 010801.
Linse, P. Interaction between colloids with grafted diblock polyampholytes. J. Chem. Phys. 2007, 126, 114903.
Russano, D.; Carrillo, J. M. Y.; Dobrynin, A. V. Interaction between brush layers of bottle-brush polyelectrolytes: molecular dynamics simulations. Langmuir 2011, 27, 11044–11051.
Sjöström, L.; Akesson, T.; Jönsson, B. J. Interaction and conformation of polyelectrolyte chains adsorbed on neutral surfaces. J. Chem. Phys. 1993, 99, 4739–4747.
Ou, Y. P.; Sokoloff, J. B.; Stevens, M. Comparison of the kinetic friction of planar neutral and polyelectrolyte polymer brushes using molecular dynamics simulations. J. Phys. Rev. E 2012, 85, 011801.
He, S. Z.; Merlitz, H.; Chen, L.; Sommer, J. U.; Wu, C. X. Polyelectrolyte brushes: MD simulation and SCF theory. Macromolecules 2010, 43, 7845–7851.
Malfreyt, P.; Tildesley, D. J. Dissipative particle dynamics simulations of grafted polymer chains between two walls. Langmuir 2000, 16, 4732–4740.
Sirchabesan, M.; Giasson, S. Mesoscale simulations of the behavior of charged polymer brushes under normal compression and lateral shear forces. Langmuir. 2007, 23, 9713–9721.
Ibergay, C.; Malfreyt, P.; Tildesley, D. J. Mesoscale modeling of polyelectrolyte brushes with salt. J. Phys. Chem. B 2010, 114, 7274–7285.
Yang, J.; Cao, D. P. Counterion valence-induced tunnel formation in a system of polyelectrolyte brushes grafted on two apposing walls. J. Phys. Chem. B 2009, 113, 11625–11631.
Abraham, T.; Giasson, S.; Gohy, J. F.; Jérome, R. Direct measurements of interactions between hydrophobically anchored strongly charged polyelectrolyte brushes. Langmuir 2000, 16, 4286–4292.
Balastre, M.; Li, F.; Schorr, P.; Yang, J.; Mays, J. W.; Tirrell, M. V. A study of polyelectrolyte brushes formed from adsorption of amphiphilic diblock copolymers using the surface forces apparatus. Macromolecules 2002, 35, 9480–9486.
Raviv, U.; Giasson, S.; Kampf, N.; Gohy, J. F.; Jérome, R.; Klein, J. Lubrication by charged polymers. Nature 2003, 425, 163–165.
Hayashi, S.; Abe, T.; Higashi, N.; Niwa, M.; Kurihara, K. Polyelectrolyte brush layers studied by surface forces measurement: dependence on pH and salt concentrations and scaling. Langmuir 2002, 18, 3932–3944.
Romet-Lemonne, G.; Daillant, J.; Guenoun, P.; Yang, J.; Mays, J. W. Thickness and density profiles of polyelectrolyte brushes: dependence on grafting density and salt concentration. Phys. Rev. Lett. 2004, 93, 148301.
Ahrens, H.; Förster, S.; Helm, C. A. Charged polymer brushes: counterion incorporation and scaling relations. Phys. Rev. Lett. 1998, 81, 4172–4175.
Weir, M. P.; Heriot, S. Y.; Martin, S. J.; Parnell, A. J.; Holt, S. A.; Webster, J. R. P.; Jones, R. A. L. Voltage-induced swelling and deswelling of weak polybase brushes. Langmuir 2011, 27, 11000–11007.
Liu, G. Q.; Cai, M. R.; Zhou, F.; Liu, W. M. Charged polymer brushes-grafted hollow silica nanoparticles as a novel promising material for simultaneous joint lubrication and treatment. J. Phys. Chem. B 2014, 118, 4920–4931.
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, 163–172.
Wang, C. S.; Xie, R. J.; Liu, S.; Giasson, S. Tribological behavior of surface-immobilized novel biomimicking multihierarchical polymers: the role of structure and surface attachment. Langmuir 2019, 35, 15592–15604.
Zhulina, E. B.; Rubinstein, M. Lubrication by polyelectrolyte brushes. Macromolecules 2014, 47, 5825–5838.
Lin, W. F.; Klein, J. Recent progress in cartilage lubrication. Adv. Mater. 2021, 33, 2005513.
Adibnia, V.; Mirbagheri, M.; Faivre, J.; Robert, J.; Lee, J.; Matyjaszewski, K.; Lee, D. W.; Banquy, X. Bioinspired polymers for lubrication and wear resistance. Prog. Polym. Sci. 2020, 110, 101298.
Jahn, S.; Seror, J.; Klein, J. Annu. Rev. Lubrication of Articular Cartilage. Biomed. Eng. 2016, 18, 235–258.
Lin, W. F.; Klein, J. Direct measurement of surface forces: recent advances and insights. Appl. Phys. Rev. 2021, 8, 031316.
Lin, W. F.; Klein, J. Control of surface forces through hydrated boundary layers. Curr. Opin. in Colloid Interface Sci. 2019, 44, 94–106.
Grest, G. S. Interfacial sliding of polymer brushes: a molecular dynamics simulation. Phys. Rev. Lett. 1996, 26, 4979–4982.
Murat, M.; Grest, G. S. Interaction between grafted polymeric brushes: a molecular-dynamics study. Phys. Rev. Lett. 1989, 63, 1074–1077.
Kreer, T.; Müser, M. H.; Binder, K.; Klein, J. Frictional drag mechanisms between polymer-bearing surfaces. Langmuir 2001, 17, 7804–7813.
Sandberg, D. J.; Carrillo, J. M. Y.; Dobrynin, A. V. Molecular dynamics simulations of polyelectrolyte brushes: from single chains to bundles of chains. Langmuir 2007, 23, 12716–12728.
Cao, Q.; Zuo, C.; He, H. Shearing and compression behavior of end-grafted polyelectrolyte brushes with mono- and trivalent counterions: a molecular dynamics simulation. Modell. Simul. Mater. Sci. Eng. 2010, 18, 7.
Liberelle, B.; Giasson, S. Friction and normal interaction forces between irreversibly attached weakly charged polymer brushes. Langmuir. 2008, 24, 1550–1559.
Goujon, F.; Malfreyt, P.; Tildesley, D. Dissipative particle dynamics simulations in the grand canonical ensemble: applications to polymer brushes. Chem. Phys. Chem. 2004, 5, 457–464.
Raviv, U.; Klein, J. Fluidity of Bound Hydration Layers. Science 2002, 297, 1540–1543.
Raviv, U.; Giasson, S.; Kampf, N.; Gohy, J. F.; Jerome, R.; Klein, J. Normal and frictional forces between surfaces bearing polyelectrolyte brushes. Langmuir 2008, 24, 8678–8687.
Duan, M. Y.; Chen, G. Swelling and shrinking of two opposing polyelectrolyte brushes. Phys. Rev. E 2023, DOI: https://doi.org/10.1103/PhysRevE.107.024502.
Witte, K. N.; Won, Y. Y. Self-consistent-field analysis of mixed polyelectrolyte and neutral polymer brushes. Macromolecules 2006, 39, 7757–7768.
Shi, A. C.; Noolandi, J. Theory of inhomogeneous weakly charged polyelectrolytes. Macromol. Theory Simul. 1999, 8, 214–229.
Wang, Q.; Taniguchi, T.; Fredrickson, G. H. Self-consistent field theory of polyelectrolyte systems. J. Phys. Chem. B 2004, 108, 6733–6744.
Lewis, T.; Ganesan, V. Mean-field modeling of the encapsulation of weakly acidic molecules in polyelectrolyte dendrimers. J. Phys. Chem. B 2012, 116, 8269–8281.
Kumar, R.; Sumpter, B. G.; Kilbey II, S. M. Charge regulation and local dielectric function in planar polyelectrolyte brushes. J. Chem. Phys. 2012, 136, 234901.
Gong, P.; Genzer, J.; Szleifer, I. Phase behavior and charge regulation of weak polyelectrolyte grafted layers. Phys. Rev. Lett. 2007, 98, 018302.
Kim J. U.; Masten, M. W. Interaction between polymer-grafted particles. Macromolecules 2008, 41, 4435–4443
Kim, J. U.; Masten, M. W. Repulsion exerted on a spherical particle by a polymer brush. Macromolecules 2008, 41, 246–252.
Manning, G. S. Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties. J. Chem. Phys. 1969, 51, 924–933.
Wang, M. L.; Tong, C. A numerical study of two opposing polyelectrolyte brushes by the self-consistent field theory. RSC Adv. 2014, 4, 20769–20780.
Acknowledgments
This work was financially supported by the National Natural Science Foundation of China (No. 21774067) and The Foundation of Key Laboratory of Flexible Electronics of Zhejiang Province (No. 2023FE004). C. T. acknowledges the support from K. C. Wong Magna at Ningbo University.
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Wang, BN., Ding, HD., Chen, ZK. et al. Numerical Study of Two Opposing Weak Polyelectrolyte Brushes by the Self-consistent Field Theory. Chin J Polym Sci (2024). https://doi.org/10.1007/s10118-024-3139-z
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DOI: https://doi.org/10.1007/s10118-024-3139-z