Abstract
A generic coarse-grained bead-and-spring model, mapped onto comb-shaped polycarboxylate-based (PCE) superplasticizers, is developed and studied by Langevin molecular dynamics simulations with implicit solvent and explicit counterions. The agreement on the radius of gyration of the PCEs with experiments shows that our model can be useful in studying the equilibrium sizes of PCEs in solution. The effects of ionic strength, side-chain number, and side-chain length on the conformational behavior of PCEs in solution are explored. Single-chain equilibrium properties, including the radius of gyration, end-to-end distance and persistence length of the polymer backbone, shape-asphericity parameter, and the mean span dimension, are determined. It is found that with the increase of ionic strength, the equilibrium sizes of the polymers decrease only slightly, and a linear dependence of the persistence length of backbone on the Debye screening length is found, in good agreement with the theory developed by Dobrynin. Increasing side-chain numbers and/or side-chain lengths increases not only the equilibrium sizes (radius of gyration and mean span) of the polymer as a whole, but also the persistence length of the backbone due to excluded volume interactions.
Similar content being viewed by others
References
Voycheck, C. L.; Tan, J. S.; Hara, M. Polyelectrolytes: Science and technology. Marcel Dekker, Inc., New York, 1993, p. 250.
Holm, C.; Joanny, J. F.; Kremer, K.; Netz, R. R.; Reineker, P.; Seidel, C.; Vilgis, T. A.; Winkler, R. G. Polyelectrolyte theory. in Polyelectrolytes with defined molecular architecture II. Berlin, Heidelberg, 2004, p. 67.
Chremos, A.; Douglas, J. F. Influence of higher valent ions on flexible polyelectrolyte stiffness and counter-ion distribution. J. Chem. Phys.2016, 144, 164904–164913.
Stevens, M. J.; Mcintosh, D.; Saleh, O. Simulations of stretching a strong, flexible polyelectrolyte. Macromolecules0012, 45, 5757–5765.
Toan, N. M.; Thirumalai, D. On the origin of the unusual behavior in the stretching of single-stranded DNA. J. Chem. Phys.2012, 136, 235103–235108.
Elder, R. M.; Jayaraman, A. Coarse-grained simulation studies of effects of polycation architecture on structure of the polycation and polycation-polyanion complexes. Macromolecules2012, 45, 8083–8096.
Bayramoglu, B.; Faller, R. Coarse-grained modeling of polystyrene in various environments by iterative Boltzmann inversion. Macromolecules2012, 45, 9205–9249.
Carrillo, J. M. Y.; Dobrynin, A. V. Polyelectrolytes in salt solutions: Molecular dynamics simulations. Macromolecules2011, 44, 5798–5816.
Carrillo, J. M. Y.; Dobrynin, A. V. Detailed molecular dynamics simulations of a model NaPSS in water. J. Phys. Chem. B2010, 114, 9391–9399.
Saleh, O.; Mcintosh, D.; Pincus, P.; Ribeck, N. Nonlinear low-force elasticity of single-stranded DNA molecules. Phys. Rev. Lett.2009, 102, 068301.
Chang, R.; Yethiraj, A. Dilute solutions of strongly charged flexible polyelectrolytes in poor solvents: Molecular dynamics simulations with explicit solvent. Macromolecules2006, 39, 821–828.
Liao, Q.; Dobrynin, A. V.; Rubinstein, M. Counterion-correlation-induced attraction and necklace formation in polyelectrolyte solutions: Theory and simulations. Macromolecules2006, 39, 1920–1938.
Dobrynin, A. V.; Rubinstein, M. Theory of polyelectrolytes in solutions and at surfaces. Prog. Polym. Sci.2005, 30, 1049–1118.
Limbach, H. J.; Holm, C. Single-chain properties of polyelectrolytes in poor solvent. J. Phys. Chem. B2003, 107, 8041–8055.
Micka, U.; Holm, C.; Kremer, K. Strongly charged, flexible polyelectrolytes in poor solvents: Molecular dynamics simulations. Langmuir1999, 15, 4033–4044.
Stevens, M. J.; Kremer, K. The nature of flexible linear polyelectrolytes in salt free solution: A molecular dynamics study. J. Chem. Phys.1995, 103, 1669.
Dobrynin, A. V. Theory and simulations of charged polymers: From solution properties to polymeric nanomaterials. Curr. Opin. Colloid In.2008, 13, 376–388.
Khokhlov, A. R.; Khalatur, P. G. Solution properties of charged hydrophobic/hydrophilic copolymers. Curr. Opin. Colloid In.2005, 10, 22–29.
Burak, Y.; Ariel, G.; Andelman, D. Onset of DNA aggregation in presence of monovalent and multivalent counterions. Biophys. J.2003, 85, 2100–2110.
Deming, T. J. Synthesis of side-chain modified polypeptides. Chem. Rev.2015, 116, 786–808.
Zhang, Y.; Lu, H.; Lin, Y.; Cheng, J. Water-soluble polypeptides with elongated, charged side chains adopt ultrastable helical conformations. Macromolecules2011, 44, 6641–6644.
Wang, Y.; Zheng, M.; Meng, F.; Zhang, J.; Peng, R.; Zhong, Z. Branched polyethylenimine derivatives with reductively cleavable periphery for safe and efficient in vitro gene transfer. Biomacromolecules2011, 12, 1032–1040.
Lu, H.; Wang, J.; Bai, Y.; Lang, J. W.; Liu, S.; Lin, Y.; Cheng, J. Ionic polypeptides with unusual helical stability. Nat. Commun.2011, 2, 206.
Alonso, M. M.; Palacios, M.; Puertas, F. Compatibility between polycarboxylate-based admixtures and blended-cement pastes. Cem. Concr. Compos.2013, 35, 151–162.
Malferrari, D.; Fermani, S.; Galletti, P.; Goisis, M.; Tagliavini, E.; Falini, G. Shaping calcite crystals by means of comb polyelectrolytes having neutral hydrophilic teeth. Langmuir2013, 29, 1938–1947.
Reese, J.; Plank, J. Adsorption of polyelectrolytes on calcium carbonate-which thermodynamic parameters are driving this process. J. Am. Ceram. Soc.2011, 94, 3515–3522.
Yamada, K.; Takahashi, T.; Hanehara, S.; Matsuhisa, M. Effects of the chemical structure on the properties of polycarboxylate-type superplasticizer. Cem. Concr. Res.2000, 30, 197–207.
Ran, Q.; Qiao, M.; Liu, J. Influence of Ca2+ on the performance of poly(acrylic acid)-g-poly(ethylene glycol) comb-like copolymers in cement suspensions. Iran Polym. J.2014, 23, 663–669.
Shu, X.; Ran, Q.; Liu, J.; Zhao, H.; Zhang, Q.; Wang, X.; Yang, Y.; Liu, J. Tailoring the solution conformation of polycarboxylate superplasticizer toward the improvement of dispersing performance in cement paste. Constr. Build. Mater2016, 116, 289–298.
Flatt, J. F.; Schober, I.; Raphael, E.; Plassard, C.; Lesniewska, E. Conformation of adsorbed comb copolymer dispersants. Langmuir2008, 25, 845–855.
Ran, Q.; Somasundaran, P.; Miao, C.; Liu, J; Wu, S.; Shen, J. Effect of the length of the side chains of comb-like copolymer dispersants on dispersion and rheological properties of concentrated cement suspensions. J. Colloid Interface Sci.2009, 336, 624–633.
Winnefeld, F.; Becker, S.; Pakusch, J.; Götz, T. Effects of the molecular architecture of comb-shaped superplasticizers on their performance in cementitious systems. Cem. Concr. Compos.2007, 29, 251–262.
Kirby, G. H.; Lewis, J. A. Comb polymer architecture effects on the rheological property evolution of concentrated cement suspensions. J. Am. Ceram. Soc.2004, 87, 1643–1652.
Sappidi, P.; Muralidharan, S. S.; Natarajan, U. Conformations and hydration structure of hydrophobic polyelectrolyte atactic poly(ethac rylic acid) in dilute aqueous solution as a function of neutralization. Mol. Simul.2014, 40, 295–305.
Tong, K. F.; Song, X. F.; Sun, S. Y.; Xu, Y. X.; Yu, J. G. Molecular dynamics study of linear and comb-like polyelectrolytes in aqueous solution: Effect of Ca2+ ions. Mol. Phys.2014, 112, 2176–2183.
Zidar, J.; Lim, G. S.; Cheong, D. W.; Klähn, M. Protein-like dynamics of polycarbonate polymers in water. J. Phys. Chem. B2014, 119, 316–329.
Sulatha, M. S.; Natarajan, U. Molecular dynamics simulations of PAA-PMA polyelectrolyte copolymers in dilute aqueous solution: Chain conformations and hydration properties. Ind. Eng. Chem. Res.2012, 51, 10833–10839.
Sulatha, M. S.; Natarajan, U. Origin of the difference in structural behavior of poly(acrylic acid) and poly(methacrylic acid) in aqueous solution discerned by explicit-solvent explicit-ion MD simulations. Ind. Eng. Chem. Res.2011, 50, 11785–11796.
Maskey, S.; Pierce, F.; Perahia, D.; Grest, G. S. Conformational study of a single molecule of poly para phenylene ethynylenes in dilute solutions. J. Chem. Phys.2011, 134, 244906–244914.
Tribello, G. A.; Liew, C. C.; Parrinello, M. Binding of calcium and carbonate to polyacrylates. J. Phys. Chem. B0099, 113, 7081–7085.
Ju, S. P.; Lee, W. J.; Huang, C. I.; Cheng, W. Z.; Chung, Y. T. Structure and dynamics of water surrounding the poly(methacrylic acid): A molecular dynamics study. J. Chem. Phys.2007, 126, 224901–224912.
Molnar, F.; Rieger, J. “Like-charge attraction” between anionic polyelectrolytes: Molecular dynamics simulations. Langmuir2005, 21, 786–789.
Hehmeyer, O. J.; Arya, G.; Panagiotopoulos, A. Z.; Szleifer, I. Monte Carlo simulation and molecular theory of tethered polyelectrolytes. J. Chem. Phys.2007, 126, 244902.
Luque-Caballero, G.; Martín-Molina, A.; Quesada-Pérez, M. Polyelectrolyte adsorption onto like-charged surfaces mediated by trivalent counterions: A Monte Carlo simulation study. J. Chem. Phys.2014, 140, 174701.
Yu, S.; Larson, R. G. Monte-Carlo simulations of PAMAM dendrimer-DNA interactions. Soft Matter2014, 10, 5325–5336.
Turesson, M.; Labbez, C.; Nonat, A. Calcium mediated polyelectrolyte adsorption on like-charged surfaces. Langmuir2011, 27, 13572–13581.
Chremos, A.; Douglas, J. F. Counter-ion distribution around flexible polyelectrolytes having different molecular architecture. Soft Matter2016, 12, 2932–2941.
Ghelichi, M.; Qazvini, N. T. Self-organization of hydrophobic-capped triblock copolymers with a polyelectrolyte midblock: A coarse-grained molecular dynamics simulation study. Soft Matter2016, 12, 4611–4620.
Ghelichi, M.; Eikerling, M. H. Conformational properties of comblike polyelectrolytes: A coarse-grained MD study. J. Phys. Chem. B2016, 120, 2859–2867.
Turesson, M.; Nonat, A.; Labbez, C. Stability of negatively charged platelets in calcium-rich anionic copolymer solutions. Langmuir2014, 30, 6713–6720.
Liu, Z.; Shang, Y.; Feng, J.; Peng, C.; Liu, H.; Hu, Y. Effect of hydrophilicity or hydrophobicity of polyelectrolyte on the interaction between polyelectrolyte and surfactants: Molecular dynamics simulations. J. Phys. Chem. B2012, 116, 5516–5526.
Spaeth, J. R.; Kevrekidis, I. G.; Panagiotopoulos, A. Z. A comparison of implicit-and explicit-solvent simulations of self-assembly in block copolymer and solute systems. J. Chem. Phys.2011, 134, 164902.
Reddy, G.; Yethiraj, A. Solvent effects in polyelectrolyte adsorption: Computer simulations with explicit and implicit solvent. J. Chem. Phys.2010, 132, 074903.
Košovan, P.; Limpouchová, Z.; Procházka, K. Conformational behavior of comb-like polyelectrolytes in selective solvent: Computer simulation study. J. Phys. Chem. B0077, 111, 8605–8611.
Hsiao, P. Y.; Luijten, E. Salt-induced collapse and reexpansion of highly charged flexible polyelectrolytes. Phys. Rev. Lett.2006, 97, 148301–148305.
Liao, Q.; Dobrynin, A. V.; Rubinstein, M. Molecular dynamics simulations of polyelectrolyte solutions: Nonuniform stretching of chains and scaling behavior. Macromolecules0003, 36, 3386–3398.
Wynveen, A.; Likos, C. N. Interactions between planar polyelectrolyte brushes: Effects of stiffness and salt. Soft Matter2010, 6, 163–171.
Baratlo, M.; Fazli, H. Brushes of flexible, semiflexible, and rodlike diblock polyampholytes: Molecular dynamics simulation and scaling analysis. Phys. Rev. E2010, 81, 011801.
Baratlo, M.; Fazli, H. Molecular dynamics simulation of semiflexible polyampholyte brushes—The effect of charged monomers sequence. Eur. Phys. J.2009, 29, 131–138.
Csajka, F. S.; Netz, R. R.; Seidel, C.; Joanny, J. F. Collapse of polyelectrolyte brushes: Scaling theory and simulations. Eur. Phys. J.2001, 4, 505–513.
Seidel, C. Strongly stretched polyelectrolyte brushes. Macromolecules2000, 36, 2536–2543.
Merlitz, H.; He, G. L.; Wu, C. X.; Sommer, J. U. Nanoscale brushes: How to build a smart surface coating. Phys. Rev. Lett.2009, 102, 115702.
Merlitz, H.; He, G. L.; Wu, C. X.; Sommer, J. U. Surface instabilities of monodisperse and densely grafted polymer brushes. Macromolecules2008, 41, 5070–5072.
Carrillo, J. M. Y.; Dobrynin, A. V. Morphologies of planar polyelectrolyte brushes in a poor solvent: Molecular dynamics simulations and scaling analysis. Langmuir2009, 25, 13158–13168.
Guptha, V. S.; Hsiao, P. Y. Polyelectrolyte brushes in monovalent and multivalent salt solutions. Polymer2014, 55, 2900–2912.
Giraudeau, C.; D’Espinose De Lacaillerie, J. B.; Souguir, Z.; Nonat, Z.; Flatt, R. J. Surface and intercalation chemistry of polycarboxylate copolymers in cementitious systems. J. Am. Ceram. Soc.2009, 92, 2471–2488.
Lee, H.; Venable, R. M.; MacKerell Jr, A. D.; Pastor, R. W. Molecular dynamics studies of polyethylene oxide and polyethylene glycol: Hydrodynamic radius and shape anisotropy. Biophys. J.2008, 95, 1590–1599.
Gay, C.; Raphael, E. Comb-like polymers inside nanoscale pores. Adv. Colloid Inter. Sci.2001, 94, 229–236.
Pedersen, J. S.; Sommer, C. Temperature dependence of the virial coefficients and the chi parameter in semi-dilute solutions of PEG. In Scattering methods and the properties of polymer materials. Berlin, Heidelberg, 2005, pp. 70–78.
Diehl, H. W.; Eisenriegler, E. Universal shape ratios for open and closed random walks: Exact results for all d. J. Phys. A: Math. Gen.1989, 22, L87.
Wang, Y.; Teraoka, I.; Hansen, F. Y.; Peters, G. H.; Hassager, O. Mean span dimensions of ideal polymer chains containing branches and rings. Macromolecules2010, 44, 403–412.
Hsu, H. P.; Paul, W.; Binder, K. Standard definitions of persistence length do not describe the local “intrinsic” stiffness of real polymer chains. Macromolecules2010, 43, 3094–3102.
Dobrynin, A. V. Electrostatic persistence length of semiflexible and flexible polyelectrolytes. Macromolecules2005, 38, 9304–9314.
Dorfman, K. D.; King, S. B.; Olson, D. W.; Thomas, J. D. P.; Tree, D. R. Beyond gel electrophoresis: Microfluidic separations, fluorescence burst analysis and DNA stretching. Chem. Rev.2012, 113, 2584–2667.
Paturej, J.; Sheiko, S. S.; Panyukov, S.; Rubinstein, M. Molecular structure of bottlebrush polymers in melts. Sci. Adv.2016, 2, 1601478–1601480.
Birshtein, T. M.; Borisov, O. V.; Zhulina, Y. B.; Khokhlov, A. R; Yurasova, T. A. Conformations of comb-like macromolecules. Polym. Sci.1987, 29, 1293–1300.
Feuz, L.; Leermakers, F. A. M.; Textor, M.; Borisov, O. Bending rigidity and induced persistence length of molecular bottle brushes: A self-consistent-field theory. Macromolecules2005, 38, 8891–8901.
Acknowledgments
This work was financially supported by the National Key Research and Development Program of China (No. 2017YFB0310100).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, JH., Lu, LQ., Zhao, HX. et al. Conformational Properties of Comb-shaped Polyelectrolytes with Negatively Charged Backbone and Neutral Side Chains Studied by a Generic Coarse-grained Bead-and-Spring Model. Chin J Polym Sci 38, 371–381 (2020). https://doi.org/10.1007/s10118-020-2350-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10118-020-2350-9