FOLLOWUS
College of Chemistry, Beijing Normal University, Beijing 100875, China
00071@bnu.edu.cn
Published:01 September 2024,
Published Online:05 June 2024,
Received:02 March 2024,
Revised:08 April 2024,
Accepted:12 April 2024
Scan for full text
Zhao, K. S. Conformation and counterion distribution of polyelectrolyte in solution as viewed from dielectric approach. Chinese J. Polym. Sci. 2024, 42, 1278–1301
Kong-Shuang Zhao. Conformation and Counterion Distribution of Polyelectrolyte in Solution as Viewed from Dielectric Approach. [J]. Chinese Journal of Polymer Science 42(9):1278-1301(2024)
Zhao, K. S. Conformation and counterion distribution of polyelectrolyte in solution as viewed from dielectric approach. Chinese J. Polym. Sci. 2024, 42, 1278–1301 DOI: 10.1007/s10118-024-3138-0.
Kong-Shuang Zhao. Conformation and Counterion Distribution of Polyelectrolyte in Solution as Viewed from Dielectric Approach. [J]. Chinese Journal of Polymer Science 42(9):1278-1301(2024) DOI: 10.1007/s10118-024-3138-0.
The methods and strategies of analyzing dielectric spectra for typical polyelectrolyte solutions in the RF range are reviewed. Emphasis is placed on gaining insight into internal information about the studying system
including chain conformation
counter-ion distribution
phase transition
and the micro-structure of microgels and polymer networks.
Polyelectrolyte solutions are more variable than uncharged macromolecule due to electrical interaction between charged molecules and surrounding counterions. Therefore
the subject of polyelectrolyte solutions has attracted a wide range of interests in both basic and applied research
and has also been extensively explored. However
the understanding of the molecular dynamics and conformation of polyelectrolytes in solution remains to be deepened
and universal consensus on some key issues have not been reached. Many methods have contributed to solving the above problems in different ways
including dielectric relaxation spectroscopy (DRS). In this perspective
we briefly reviewed the history of dielectric spectroscopic research on polyelectrolyte solution
with emphasis on summarizing our efforts. In particular
we expound the characteristics of DRS and its ability to obtain the internal information of the system of interest. Finally
we evaluate the advantages and limitations of the dielectric method and discussed future prospects of this field.
PolyelectrolyteDielectric relaxation spectroscopyChain conformationThermosensitive microgelPNIPAM microgelSpherical polyelectrolyte brushes
Anderson, C.F.; Record, M.T. Polyelectrolyte Theories and their Applications to DNA.Annu. Rev. Phys. Chem.1982,33, 191−222..
Muthukumar, M. 50thAnniversary perspective: a perspective on polyelectrolyte solutions.Macromolecules 2017 ,50, 9528-9560..
Dobrynin, A.V.; Rubinstein, M. Theory of polyelectrolytes in solutions and at surfaces.Prog. Polym. Sci.2005,30, 1049−1118..
Mandel, M. The physical chemistry of polyelectrolyte solutions.Die Angewandte Makromolekulare Chemie1984,1231124, 63−83..
Förster, S.; Schmidt, M. Polyelectrolytes in Solution. InPhysical Properties of Polymers.Springer, 1995 , 51..
Muthukumar; M. Electrostatic Correlations in Polyelectrolyte Solutions.Polym. Sci. Ser.2016,58, 852−863..
Rubinstein, M.; Papoian, G.A. Polyelectrolytes in biology and soft matter.Soft Matter2012,8, 9265−9267..
Kern, W. Über heteropolare Molekülkolloide. II. Die Viscosität von Lösungen der Polyacrylsäure and ihrer Salze.Z. physik. Chem. A1937,181, 283−300..
Katchalsky, A.; Kunzle, O.; Kuhn, W. Behavior of polyvalent polymeric ions in solution.J. Polym. Sci.1950,5, 283−300..
Rice, S. A.; Nagasawa, M.Polyelectrolyte Solutions. Academic Press, New York, 1961 ..
Katchalsky, A. Polyelectrolytes.Pure Appl.Chem.1971,26, 327−373..
Manning, G. S. Polyelectrolytes.Annu. Rev. Phys. Chem.1972,23, 117−140..
Eisenberg, H.Biological Macromolecules and Polyelectrolytes in Solution. Clarendon Press, Oxford, 1976 ..
De Gennes, P.G. Thermotropic mesophases and mesophase transitions of linear, flexible macromolecules.J. Chem. Phys. 1974 ,55..
Degennes, P. G.; Pincus, P.; Velasco, R. M.; Brochard, F. Remarks on polyelectrolyte conformation.J. Phys.1976,37, 1461−1473..
Dobrynin, A. V.; Colby, R. H.; Rubinstein, M. Scaling theory of polyelectrolyte solutions.Macromolecules1995,28, 1859−1871..
Manning, G. S. Counterion binding in polyelectrolyte theory.Acc. Chem. Res.1979,12, 443−449..
Manning, G. S. Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties.J. Chem. Phys.1969,51, 924−931..
Manning, G, S. Limiting laws and counterion condensation in polyelectrolyte solutions II. Self-diffusion of the small ions.Acc. Chem. Res.1969,51, 934−944..
Flory, P. J.; Rehner, J. Statistical theory of chain configuration and physical properties of high polymers.Ann. N.Y. Acad. Sci.1943,44, 419−429..
Zimm, B.H. Dynamic properties of solutions. Models for chain molecule dynamics in dilute solution.J. Chem. Phys.1956,24, 269−278..
Rouse, P.E.A. Theory of the linear viscoelastic properties of dilute solutions of cooling polymers.J. Chem. Phys.1953,21, 1271−1280..
Manning, G. S. Electrostatic free energies of spheres, cylinders, and planes in counterion condensation theory with some applications.Macromolecules2007,40, 8071−8081..
Oosawa, F.Polyelectrolytes. Marcel Dekker: New York, 1971 ..
Fuoss, R. M.; Lifson, K. S. The potential of an infinite rod-like molecule and the distribution of the counter ions.Proc. Nati. Acad. Sci. U. S. A.1951,37, 579−589..
Solis, F. J.; de la Cruz, M. O. Collapse of flexible polyelectrolytes in multivalent salt solutions.J. Chem. Phys.2000,112, 2030−2035..
Deshkovski, A.; Obukhov, S.; Rubinstein, M. Counterion phase transitions in dilute polyelectrolyte solutions.Phys. Rev. Lett.2001,86, 2341−2344..
Liao, Q.; Dobrynin, A.V.; Rubinstein, M. Molecular dynamics simulations of polyelectrolyte solutions: osmotic coefficient and counterion condensation behavior.Macromolecules2003,36, 3399−3410..
Palencia, M.; Rivas, B.; Pereira, E. Polymer-enhanced ultrafiltration: counterion distribution and its relation with the divalent metal-ion retention properties by sulfonic acid polyelectrolytes.Polym. Bull.2011,67, 1123−1138..
Muthukumar, M. Theory of counter-ion condensation on flexible polyelectrolytes: adsorption mechanism.J. Chem. Phys.2004,120, 9343−9350..
Dobrynin, A. V.; Rubinstein, M. Counterion condensation and phase separation in solutions of hydrophobic polyelectrolytes.Macromolecules2001,34, 1964−1972..
Jeon, J.; Dobrynin, A. V. Necklace globule and counterion condensation.Macromolecules2007,40, 7695−7706..
Liao, Q.; Dobrynin, A. V.; Rubinstein, M. Counterion-correlation-induced attraction and necklace formation in polyelectrolyte solutions: Theory and simulations.Macromolecules2006,39, 1920−1938..
Liao, Q.; Dobrynin, A.V.; Rubinstein, M. Molecular dynamics simulations of polyelectrolyte solutions: nonuniform stretching of chains and scaling behavior.Macromolecules2003,36, 3386−3398..
Gordievskaya, Y. D.; Gavrilov, A.A.; Kramarenko, E. Y. Effect of counterion excluded volume on the conformational behavior of polyelectrolyte chains.Soft Matter2018,14, 1474−1481..
Liu, S.; Muthukumar, M. Langevindynamics simulation of counterion distribution around isolated flexible polyelectrolyte chains.J. Chem. Phys.2002,116, 9975−9982..
Ullner, M.; Staikos, G.; Theodorou, D. N. Monte Carlo simulations of a single polyelectrolyte in solution: activity coefficients of the simple ions and application to viscosity measurements.Macromolecules1998,31, 7921−7933..
Chi, P.; Li, B.; Shi, A. C. Conformation transitions of a polyelectrolyte chain: a replica-exchange Monte-Carlo study.PhRvE2011,84, 021804..
Su, W.; Zhao, K.; Wei, J.; Ngai, T. Dielectric relaxations of poly(N-isopropylacrylamide) microgels near the volume phase transition temperature: impact of cross-linking density distribution on the volume phase transition.Soft Matter2014,10, 8711−8723..
Su, W.; Yang, M.; Zhao, K.; Ngai, T. Influence of charged groups on the structure of microgel and volume phase transition by dielectric analysis.Macromolecules2016,49, 7997−8008..
Khousakoun, E.; Gohy, J.F.; Jérôme, R. Self-association of double-hydrophilic copolymers of acrylic acid and poly(ethylene oxide) macromonomer.Polymer2004,45, 8303−8310..
Essafi, W.; Spiteri, M. N.; Williams, C.; Boue, F. Hydrophobic polyelectrolytes in better polar solvent. Structure and chain conformation as seen by SAXS and SANS.Macromolecules2009,42, 9568−9580..
Essafi, W.; Raissi, W.; Abdelli, A.; Boue, F. Metastability of large aggregates and viscosity, and stability of the pearl necklace conformation after organic solvent treatment of aqueous hydrophobic polyelectrolyte solutions.J. Phys. Chem. B2014,118, 12271−12281..
Hinderberger, D.; Jeschke, G.; Spiess, H. W. Counterion condensation and conformational transitions of polyelectrolytes characterized by EPR spectroscopy.Macromolecules2002,35, 9698−9706..
Hinderberger, D.; Spiess, H. W.; Jeschke, G. Separation of polyelectrolyte chain dynamics and dynamics of counterion attachment by EPR spectroscopy.Macromolecular Symposia2004,211, 71−86..
Hinderberger, D.; Spiess, H. W.; Jeschke, G. Radial counterion distributions in polyelectrolyte solutions determined by EPR spectroscopy.Europhys. Lett.2005,70, 102−108..
Huber, K.; Scheler, U. New experiments for the quantification of counterion condensation.Current Opinion in Colloid & Interface Science2012,17, 64−73..
Prabhu, V. M. Counterion structure and dynamics in polyelectrolyte solutions.Current Opinion in Colloid & Interface Science2005,10, 2−8..
Poe, G.D.; Jarrett, W.L.; Scales, C.W.; McCormick, C.L. Enhanced coil expansion and intrapolymer complex formation of linear poly(methacrylic acid) containing poly(ethylene glycol) grafts.Macromolecules2004,37, 2603−2612..
Benmansour, K.; Mansri, A.; François, J. Oligo(ethylene oxide) side-chain steric screening effects on conductimetric properties of grafted poly(4-vinylpyridinium) salts in aqueous solutions.Polym. Int.2003,52, 1506−1514..
Loh, P.; Deen, G.R.; Vollmer, D.; Fischer, K.; Schmidt, M.; Kundagrami, A.; Muthukumar, M. Collapse of linear polyelectrolyte chains in a poor solvent: when does a collapsing polyelectrolyte collect its counterions.Macromolecules2008,41, 9352−9358..
Zhao, J. Studying the physics of charged macromolecules by single molecule fluorescence spectroscopy.J. Chem. Phys.2020,153, 0903..
Xu, G. F.; Yang, J. F.; Zhao, J. Molecular weight dependence of chain conformation of strong polyelectrolytes.J. Chem. Phys.2018,149, 3329..
Shi, Y.; Peng, H.; Yang, J. F.; Zhao, J. Counterion binding dynamics of a polyelectrolyte.Macromolecules2021,54, 4926−4933..
Chen, K.; Zheng, K. K.; Xu, G. F.; Yang, J. F.; Zhao, J. Diffusive motion of single polyelectrolyte molecules under electrostatic repulsion.Macromolecules2019,52, 3925−3934..
Zhang, G.; Wu, C. Quartz crystal microbalance studies on conformational change of polymer chains at interface.Macromol. Rapid Commun.2009,30, 328−335..
Zhang, G. Z. Study on conformation change of thermally sensitive linear grafted poly(N-isopropylacrylamide) chains by quartz crystal microbalance.Macromolecules2004,37, 6553−6557..
Don, S. C.; Colby, R. H. Solution rheology of a strongly charged polyelectrolyte in good solvent.Macromolecules2008,41, 6505−6510..
Bordi, F.; Cametti, C.; Colby, R. H. Dielectric spectroscopy and conductivity of polyelectrolyte solutions.J. Phys.-Cond. Matter2004,16, R1423−R1463..
Axelrod, N.; Axelrod, E.; Gutina, A.; Puzenko, A.; Ben Ishai, P.; Feldman, Y. Dielectric spectroscopy data treatment: I. Frequency domain.Meas. Sci. Technol.2004,15, 755−764..
Feldman, Y.; Andrianov, A.; Polygalov, E.; Ermolina, I.; Romanychev, G.; Zuev, Y.; Milgotin, B. Time domain dielectric spectroscopy: An advanced measuring system.Rev. Sci. Instrum.1996,67, 3208−3216..
Sachs, S. B.; Raziel, A.; Eisenber, H; Katchalsk, A. Dielectric dispersion properties of aqueous polyelectrolyte solutions.Trans. Faraday Society1969,65, 77−90..
Mandel, M.; Odijk, T. Dielectric properties of polyelectrolyte solutions.Ann. Rev. Phys. Chem1984,35, 75−108..
Mandel, M.; Jenard, A. Dielectric behaviour of aqueous polyelectrolyte solutions. Part 1.Trans. Faraday Society 1963 ,59, 2158-&..
Vandertouw, F.; Mandel, M. Dielectric increment and dielectric dispersion of solutions containing simple charged linear macromolecules: I. Theory.Biophys. Chem.1974,2, 218−230..
Vandertouw, F.; Mandel, M. Dielectric increment and dielectric dispersion of solutions containing simple charged linear macromolecules: II. Experimental results with synthetic polyelectrolytes.Biophys. Chem.1974,2, 231−241..
Mandel, M. The dielectric increments of aqueous polyelectrolyte solutions: a scaling approach.Biophys. Chem.2000,85, 125−139..
Vandijk, W.; Vandertouw, F.; Mandel, M. Influence of counterion exchange on the induced dipole moment and its relaxation for a rodlike polyion.Macromolecules1981,14, 792−795..
Ookubo, N.; Hirai, Y.; Ito, K.; Hayakawa, R. Anisotropic counterion polarizations and their Dynamics in aqueous polyelectrolytes as studied by frequency-domain electric birefringence relaxation spectroscopy.Macromolecules1989,22, 1359−1366..
Ito, K.; Yagi, A.; Ookubo, N.; Hayakawa, R. Crossover behavior in high-frequency dielectric relaxation of linear polyions in dilute and semidilute solutions.Macromolecules1990,23, 857−862..
Ito, K.; Hayakawa, R. Theory on the relation between the dielectric relaxation and the polyion mobility relaxation in polyelectrolyte solutions.Macromolecules1991,24, 3857−3865..
Bordi, F.; Cametti, C.; Gili, T. Reduction of the contribution of electrode polarization effects in the radiowave dielectric measurements of highly conductive biological cell suspensions.Bioelectrochemistry2001,54, 53−61..
Cametti, C.; Zuzzi, S. Radiowave dielectric properties of sodium maleate copolymers in aqueous solutions in light of a scaling approach.J. Phys. Chem. B2010,114, 7140−7147..
Bordi, F.; Cametti, C.; Sennato, S.; Zuzzi, S.; Dou, S.; Colby, R. H. Dielectric scaling in polyelectrolyte solutions with different solvent quality in the dilute concentration regime.Phys. Chem. Chem. Phys.2006,8, 3653−3658..
Bordi, F.; Cametti, C.; Paradossi, G. Conformational changes of xanthan in salt-free aqueous solutions: a low-frequency electrical conductivity study.J. Phys. Chem.1996,100, 7148−7154..
Bordi, F.; Cametti, C.; Paradossi, G. Conformational transition in aqueous solution of poly(L-glutamlc acid). A low-frequency electrical conductivity study.J. Phys. Chem.1992,96, 913−918..
Bordi, F.; Colby, R.H.; Cametti, C.; De Lorenzo, L.; Gili, T. Electrical conductivity of polyelectrolyte solutions in the semidilute and concentrated regime: the role of counterion condensation.J. Phys. Chem. B2002,106, 6887−6893..
Bordi, F.; Cametti, C.; Motta, A. Scaling behavior of the high-frequency dielectric properties of poly-L-lysine aqueous solutions.Macromolecules2000,33, 1910−1916..
Bordi, F.; Cametti, C.; Gili, T.; Colby, R.H. Dielectric relaxations in aqueous polyelectrolyte solutions: a scaling approach and the role of the solvent quality parameter.Langmuir2002,18, 6404−6409..
Truzzolillo, D.; Cametti, C.; Sennato, S. Dielectric properties of differently flexible polyions: a scaling approach.Phys. Chem. Chem. Phys.2009,11, 1780−1786..
Watanabe, H. Viscoelasticity and dynamics of entangled polymers.Prog. Polym. Sci.1999,24, 1253−1403..
Lian, Y.W.; Zhao, K.S.; Yang, L.K. Dielectric analysis of poly(diallyldimethylammonium chloride) aqueous solution coupled with scaling approach.Phys. Chem. Chem. Phys.2010,12, 6732−6741..
Liu, C.Y.; Zhao, K.S. Dielectric relaxations in chitosan solution with varying concentration and temperature: analysis coupled with a scaling approach and thermodynamical functions.Soft Matter2010,6, 2742−2750..
Liu, C. Y.; Zhao, K. S. Effects of concentration and temperature on the dynamic behavior of PAA-g-PEO aqueous solutions with different counterion species: a dielectric sprctroscopy study.J. Phys. Chem. B2012,116, 763−774..
Li, J. L.; Zhao, K. S. The chain conformation and relaxation dynamics of poly(acrylic acid)-graft-poly(ethylene oxide)-graft-dodecyl in water: effect of side-chains and distribution of counterions.Phys. Chem. Chem. Phys.2015,17, 4175−4183..
Li, J. L.; Zhao, K. S. Effect of side-chain on conformation of poly(acrylic acid) and its dielectric behaviors in aqueous solution: hydrophobic and hydrogen-bonding interactions and mechanism of relaxations.J. Phys. Chem. B2013,117, 11843−11852..
Li, J. L.; Zhao, K. S.; Liu, C.Y. Dielectric relaxations of poly(acrylic acid)-graft-poly(ethylene oxide) aqueous solution: Analysis coupled with scaling approach and hydrogen-bonding complex.Phys. Rev. E2013,87, 042603..
Zhou, X. L.; Zhao, K. S. How side chains affect conformation and electrical properties of poly(acrylic acid) in solution.Phys. Chem. Chem. Phys.2017,19, 20559−20572..
Zhou, X. L.; Zhao, K. S. Chain conformation of poly(acrylic acid)-graft-poly(ethylene oxide)-graft-dodecyl in solution: an anomalous counter-ions condensation.Soft Matter2018,14, 1130−1141..
Zhou, X. L.; Zhao, K. S. Effect of grafting density on conformation of poly(acrylic acid) in solution by dielectric spectroscopy.Soft Matter2018,14, 7190−7203..
Zhou, X. L.; Zhao, K. S. Conformational transition of polyelectrolytes in mixed solvent by dielectric spectroscopy: Electrostatic and hydrophobic interactions.J. Polym. Scie., Part B: Polym. Phys.2019,57, 1716−1724..
Yang, M.; Liu, C. Y.; Lian, Y. W.; Zhao, K. S.; Zhu, D.; Zhou, J. F. Relaxations and phase transitions during the collapse of a dense PNIPAM microgel suspension-thorough insight using dielectric spectroscopy.Soft Matter2017,13, 2663−2676..
Yang, M.; Liu, C. Y.; Zhao, K. S. Concentration dependent phase behavior and collapse dynamics of PNIPAM microgel by dielectric relaxation.Phys. Chem. Chem. Phys.2017,19, 15433−15443..
Yang, M.; Su, W.J.; Zhao, K.S. Quantification of solvent water and hydration dynamic of thermo-sensitive microgel by dielectric spectroscopy.J. Polym. Sci., Part B: Polym. Phys.2017,55, 1859−1864..
Yang, M.; Zhao, K.S. Anomalous volume phase transition temperature of thermosensitive semi-interpenetrating polymer network microgel suspension by dielectric spectroscopy.J. Phys. Chem. B2015,119, 13198−13207..
Yang, M.; Zhao, K. S. Influence of the structure on the collapse of poly(N-isopropylacrylamide)-basedmicrogels: an insight by quantitative dielectric analysis.Soft Matter2016,12, 4093−4102..
Wu, H. Y.; Zhao, K. S. Dielectric relaxation of spherical polyelectrolyte brushes: movement of counterions and electrical properties of the brush layer.Langmuir2015,31, 8566−8576..
Guo, X. X.; Zhao, K. S. Dielectric analysis based on spherical-shell model for cationic and anionic spherical polyelectrolyte brushes.J. Phys.-Conden. Matter2017,29, 295101..
Guo, X. X.; Zhao, K. S. Insight into the electrical properties and chain conformation of spherical polyelectrolyte brushes by dielectric spectroscopy.J. Phys.: Condens. Matter2017,29, 055102..
Meng, H. Y.; Zhao, K. S. Dielectric analysis of different spherical polyelectrolyte brushes: influence of pH and mass fraction on movement of counterions and electrical properties for different SPBs.Colloids and Surfaces A-Physicochemical and Engineering Aspects2016,508, 205−217..
Mashimo, S.; Miura, N.; Shinyashiki, N.; Ota, T. Dielectric study on molecular motions of poly(glutamic acid) in aqueous solution over a frequency range of 105−1010Hz.Macromolecules1993,26, 6859−6863..
Bordi, F.; Cametti, C.; Paradossi, G. High-frequency dielectric relaxation measurements of side-chain dynamics of branched chitosan derivatives in aqueous solutions.Macromolecules1993,26, 3363−3368..
Havriliak, S.; Negami, S. A Complex plane analysis of alpha -dispersions in some polymer systems.J. Polym. Sci., Part C: Polym. Symp.1966,14, 99..
Flory, P. J. Molecular configuration of polyelectrolytes.J. Chem. Phys.1953,21, 162−163..
Kuhn, W.; Kunzle, O.; Katchalsky, A. Verhalten polyvalenter fadenmolekelionen in losung.Helv. Chim. Acta1948,31, 1994−2037..
Odijk, T. Possible scaling relations for semidilute polyelectrolyte solutions.Macromolecules1979,12, 688−693..
Dobrynin, A. V.; Rubinstein, M. Hydrophobic polyelectrolytes.Macromolecules1999,32, 915−922..
Rubinstein, M.; Colby, R. H.; Dobrynin, A. V. Dynamics of semidilute polyelectrolyte solutions.Phys. Rev. Lett.1994,73, 2776−2779..
Okonski, C. T. Electric properties of macromolecules. V. Theory of ionic polarization in polyelectrolytes.J. Phys. Chem.1960,64, 605−619..
Fixman, M. Charged macromolecules in external fields. 2. Preliminary remarks on the cylinder.Macromolecules1980,13, 711−716..
Nagamine, Y.; Ito, K.; Hayakawa, R. Low- and high-frequency electric birefringence relaxations in linear polyelectrolyte solutions.Langmuir1999,15, 4135−4138..
Lian, Y. W.; Li, Z.; Liu, Z. B.; Xie, J.; Zhao, K. S. The chain conformation, relaxation dynamics and thermodynamics of poly(acrylamide-co-diallyldimethylammonium chloride) solution: Dielectric analysis coupled with scaling approach.Colloids and Surfaces A-Physicochemical and Engineering Aspects2016,490, 343−353..
Hao, J. K.; Yuan, G. C.; He, W. D.; Cheng, H.; Han, C. C.; Wu, C. Interchain hydrogen-bonding-induced association of poly(acrylic acid)-graft-poly(ethylene oxide) in water.Macromolecules2010,43, 2002−2008..
Lu, C. Y. D. Theory of the polyelectrolyte dielectric function.Phys. Rev. E 2011 ,84..
Wu, C.; Zhou, S. Q. Laser light scattering study of the phase transition of poly(N-isopropylacrylamide) in water. 1. Single chain.Macromolecules1995,28, 8381−8387..
Masci, G.; Cametti, C. Dielectric properties of thermo-reversible hydrogels: the case of a dextran copolymer grafted with poly(N-isopropylacrylamide).J. Phys. Chem. B2009,113, 11421−11428..
Guo, X.; Ballauff, M. Spherical polyelectrolyte brushes: Comparison between annealed and quenched brushes.PhRvE 2001 ,64..
Wittemann, A.; Drechsler, M.; Talmon, Y.; Ballauff, M. High elongation of polyelectrolyte chains in the osmotic limit of spherical polyelectrolyte brushes: a study by cryogenic transmission electron microscopy.J. Am. Chem. Soc.2005,127, 9688−9689..
Jimenez, M.L.; Delgado, A.V.; Ahualli, S.; Hoffmann, M.; Witteman, A.; Ballauff, M. Giant permittivity and dynamic mobility observed for spherical polyelectrolyte brushes.Soft Matter2011,7, 3758−3762..
Yan, L. T.; Xu, Y. Y.; Ballauff, M.; Mueller, A. H. E.; Boeker, A. Influence of counterion valency on the conformational behavior of cylindrical polyelectrolyte brushes.J. Phys. Chem. B2009,113, 5104−5110..
Ji, C. D.; Zhou, C.; Zhao, B. T.; Yang, J. F.; Zhao, J. Effect of counterion binding to swelling of polyelectrolyte brushes.Langmuir2021,37, 5554−5562..
Ohshima, H. Donnan potential and surface potential of a spherical soft particle in an electrolyte solution.J. Colloid Interface Sci.2008,323, 92−97..
Masci, G.; De Santis, S.; Cametti, C. Dielectric properties of micellar aggregates due to the self-assembly of thermoresponsive diblock copolymers.J. Phys. Chem. B2011,115, 2196−2204..
Masci, G.; De Santis, S.; Cametti, C. Assemblies of thermoresponsive diblock copolymers: micelle and vesicle formation investigated by means of dielectric relaxation spectroscopy.J. Phys. Chem. B2012,116, 2121−2130.
Cametti, C. Dielectric properties of soft-particles in aqueous solutions.Soft Matter2011,7, 5494−5506..
0
Views
90
Downloads
0
CSCD
Publicity Resources
Related Articles
Related Author
Related Institution