FOLLOWUS
a.School of Physics, Zhejiang University, Hangzhou 310027, China
b.Department of Physics, Jiangxi Agricultural University, Nanchang 330045, China
c.College of Electronics and Information Engineering, Shanghai University of Electric Power, Shanghai 200090, China
ke.li@shiep.edu.cn (K.L.)
lxzhang@zju.edu.cn (L.X.Z)
Received:24 December 2024,
Revised:23 January 2025,
Accepted:2025-01-31,
Published Online:11 March 2025,
Published:2025-02
Scan QR Code
Wu, J. X.; Yang, Z. Y.; Li, K.; Zhang, L. X. Salt effects on sliding dynamics of charged ring on diblock polyelectrolyte chain in catenane. Chinese J. Polym. Sci. https://doi.org/10.1007/s10118-025-3311-0
Jia-Xin Wu, Zhi-Yong Yang, Ke Li, et al. Salt Effects on Sliding Dynamics of Charged Ring on Diblock Polyelectrolyte Chain in Catenane[J/OL]. Chinese journal of polymer science, 2025, 431-11.
Wu, J. X.; Yang, Z. Y.; Li, K.; Zhang, L. X. Salt effects on sliding dynamics of charged ring on diblock polyelectrolyte chain in catenane. Chinese J. Polym. Sci. https://doi.org/10.1007/s10118-025-3311-0 DOI:
Jia-Xin Wu, Zhi-Yong Yang, Ke Li, et al. Salt Effects on Sliding Dynamics of Charged Ring on Diblock Polyelectrolyte Chain in Catenane[J/OL]. Chinese journal of polymer science, 2025, 431-11. DOI: 10.1007/s10118-025-3311-0.
Molecular dynamics simulations were performed to investigate the sliding dynamics of a small charged ring chain along rigid cyclic diblock polyelectrolyte in catenane immersed in salt solution. We found that both the mean-square displacement
$$ {g}_{3} \left(t\right) $$
http://notExist.jpg
http://notExist.jpg
http://notExist.jpg
and diffusion coefficient
D
of ring are influenced by the salt type
electrostatic interac
tion strength
A
and salt concentration
$$ {c}_{{\mathrm{s}}} $$
http://notExist.jpg
http://notExist.jpg
http://notExist.jpg
.
$$ D $$
http://notExist.jpg
http://notExist.jpg
http://notExist.jpg
first decreases and then increases as
$$ A $$
http://notExist.jpg
http://notExist.jpg
http://notExist.jpg
increases when
$$ A $$
http://notExist.jpg
http://notExist.jpg
http://notExist.jpg
is not large. At large
$$ A $$
http://notExist.jpg
http://notExist.jpg
http://notExist.jpg
$$ D $$
http://notExist.jpg
http://notExist.jpg
http://notExist.jpg
decreases with an increase in
$$ A $$
http://notExist.jpg
http://notExist.jpg
http://notExist.jpg
owing to the polyelectrolyte charge reversal caused by the aggregation of ions near it. Meanwhile
$$ {g}_{3} \left(t\right) $$
http://notExist.jpg
http://notExist.jpg
http://notExist.jpg
exhibited intermediate oscillating behavior at moderate
$$ A $$
http://notExist.jpg
http://notExist.jpg
http://notExist.jpg
in monovalent cation salt solution. The sliding dynamics of ring can be attributed to the free energy landscape for diffusion. According to the potential of mean force (PMF) of ring chain
we found that our simulation results agreed well with the theoretical results of Lifson-Jackson formula. This study can provide a practical model for the diffusion of charged particles in different dielectric and periodic media
and provides a new perspective for regulating the sliding dynamics of mechanically interlocked molecules in electrolyte solutions.
Gibson, H. W.;Bheda, M. C.;Engen, P. T. Rotaxanes, catenanes, polyrotaxanes, polycatenanes and related materials. Prog. Polym. Sci. 1994 , 19 , 843−945..
Stoddart, J. F. Mechanically interlocked molecules (MIMs)−molecular shuttles, switches, and machines (Nobel Lecture). Angew. Chem., Int. Ed. 2017 , 56 , 11094−11125..
Sauvage, J. P. From chemical topology to molecular machines (Nobel Lecture). Angew. Chem., Int. Ed. 2017 , 56 , 11080−11093..
Chakraborty, D.; Modak, R.; Howlader, P.; Mukherjee, P. S. Denovo approach for the synthesis of water-soluble interlocked and non-interlocked organic cages. Chem. Commun. 2021 , 57 , 3995−3998..
Chakraborty, D.; Mukherjee, P. S. Recent trends in organic cage synthesis: push towards water-soluble organic cages. Chem. Commun. 2022 , 58 , 5558−5573..
Lu, Y.; Liu, D.; Lin, Y. J.; Li, Z. H.; Hahn, F. E.; Jin, G. X. An “All-in-One” synthetic strategy for linear metalla[4 ] catenanes. J. Am. Chem. Soc. 2021 , 143 , 12404−12411..
Cui, Z.; Gao, X.; Lin, Y. J.; Jin, G. X. Stereoselective self assembly of complex chiral radial[5 ] catenanes using half sandwich rhodium/iridium building blocks. J. Am. Chem. Soc. 2022 , 144 , 2379−2386..
Wasserman, E. The preparation of interlocking rings: a catenane. J. Am. Chem. Soc. 1960 , 82 , 4433−4434..
Harrison, I. T.; Harrison, S. Synthesis of a stable complex of a macrocycle and a threaded chain. J. Am. Chem. Soc. 1967 , 89 , 5723−5724..
Kato, K.; Yasuda, T.; Ito, K. Viscoelastic properties of slide-ring gels reflecting sliding dynamics of partial chains and entropy of ring components. Macromolecules 2013 , 46 , 310−316..
Zhou, H. Y.; Han, Y.; Chen, C. F. pH-Controlled motions in mechanically interlocked molecules. Mater. Chem. Front . 2020 , 4 , 12−28..
Lewis, J. E.; G alli, M.; Goldup, S. M. Properties and emerging applications of mechanically interlocked ligands. Chem. Commun. 2016 , 53 , 298−312..
Jamieson, E. M. G.; Modicom, F.; Goldup, S. M. Chirality in rotaxanes and catenanes. Chem. Soc. Rev. 2018 , 47 , 5266−5311..
Erbas-Cakmak, S.; Leigh, D. A.; McTernan, C. T.; Nussbaumer, A. L. Artificial molecular machines. Chem. Rev. 2015 , 115 , 10081−10206..
Araki, J.; Ito, K. Recent advances in the preparation of cyclodextrin-based polyrotaxanes and their applications to soft materials. Soft Matter 2007 , 3 , 1456−1473..
Okumura, Y.; Ito, K. The polyrotaxane gel: a topological gel by figure-of-eight cross-links. Adv. Mater. 2001 , 13 , 485−487..
Yasuda, Y.; Toda, M.; Mayumi, K.; Yokoyama, H.; Morita, H.; Ito, K. Sliding dynamics of ring on polymer in rotaxane: a coarse-grained molecular dynamics simulation study. Macromolecules 2019 , 52 , 3787−3793..
Mayumi, K. Molecular dynamics and structure of polyrotaxane in solution. Polym. J. 2021 , 53 , 581−586..
Wang, J.; Ye, L.; Zhang, A.; Feng, Z. Novel triblock copolymers comprising a polyrotaxane middle block flanked by PNIPAAm blocks showing both thermo- and solvent-response. J. Mater. Chem. 2011 , 21 , 3243−3250..
Ohya, Y.; Takamido, S.; Nagahama, K.; Ouchi, T.; Katoono, R.; Yui, N. Polyrotaxane composed of Poly-l-lactide and α-Cyclodextrin exhibiting protease-triggered hydrolysis. Biomacromolecules 2009 , 10 , 2261−2267..
Huang, J.; Ren, L.; Chen, Y. pH-/Temperature-sensitive supramolecular micelles based on cyclodextrin polyrotaxane. Polym. Int . 2008 , 57 , 714-721..
Tong, X.; Zhang, X.; Ye, L.; Zhang, A. Y.; Feng, Z. G. Synthesis and characterization of block copolymers comprising a polyrotaxane middle block flanked by two brush-like PCL blocks. Soft Matter 2009 , 5 , 1848−1855..
Gavrilov, A. A.; Chertovich, A. V.; Kramarenko, E. Y. Conformational behavior of a single polyelectrolyte chain with bulky counterions. Macromolecules 2016 , 49 , 1103−1110..
Manning, G. S. Limiting laws and counterion condensation in polyelectrolyte solutions I. colligative properties. J. Chem. Phys. 1969 , 51 , 924−933..
Manning, G. S. Limiting laws and counterion condensation in polyelectrolyte solutions. IV. the approach to the limit and the extraordinary stability of the charge fraction. Biophys. Chem. 1977 , 7 , 95−102..
Yang, Z. Y.; Wu, J. X.; Li, K.; Zhou, X. L.; Lu, D.; Zhang, L. X. Sliding dynamics of a small charged ring chain on the diblock polyelectrolyte in poly[2 ] catenane in the presence of counterions. J. Phys. Chem. B 2023 , 127 , 10189−10200..
Dobrynin, A. V.; Rubinstein, M. Theory of polyelectrolytes in solutions and at surfaces. Prog. Polym. Sci. 2005 , 30 , 1049−1118..
Colby, R. H. Structu re and linear viscoelasticity of flexible polymer solutions: comparison of polyelectrolyte and neutral polymer solutions. Rheol. Acta 2010 , 49 , 425−442..
Dobrynin, A. V. Theory and simulations of charged polymers:from solution properties to polymeric nanomaterials. Curr. Opin. Colloid Interface Sci. 2008 , 13 , 376−388..
Bloomfield, V. A. DNA condensation. Curr. Opin. Struct. Biol. 1996 , 6 , 334−341..
Luo, Q.; Wei, Z. C.; Duan, H. Y.; Jin, L.; Kankanamage, R. N. T.; Shuster, S.; Suib, S. L.; Rusling, J. F.; He, J. Templated synthesis of crystalline mesoporous CeO 2 with organosilane-containing polymers: balancing porosity, crystallinity, and catalytic activity. Mater. Futures 2022 , 1 , 025302..
Hagita, K.; Murashima, T.; Sakata, N. Mathematical classification and rheological properties of ring catenane structures. Macromolecules 2022 , 55 , 166−177..
Murashima, T.; Hagita, K.; Kawakatsu, T. Topological transition in multicyclic chains with structural symmetry induci ng stress-overshoot phenomena in multicyclic/linear blends under biaxial elongational flow. Macromlecules 2022 , 55 , 9358−9372..
Haverson, J. D.; Lee, W. B.; Grest, G. S.; Grosberg, A. Y.; Kremer, K. Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. statics. J. Chem. Phys. 2011 , 134 , 204904..
Kremer, K.; Grest, G. S. Dynamics of entangled linear polymer melts: a molecular-dynamics simulation. J. Chem. Phys. 1990 , 92 , 5057−5986..
Tom, A. M.; Vemparala, S.; Rajesh, R.; Brilliantov, N. V. Mechanism of chain collapse of strongly charged polyelectrolytes. Phys. Rev. Lett. 2016 , 117 , 147801..
Tom, A. M.; Rajesh, R.; Vemparala, S. Aggregation of flexible polyelectrolytes: phase diagram and dynamics. J. Chem. Phys. 2017 , 147 , 144903..
Tom, A. M.; Vemparala, S.; Rajesh, R.; Brilliantov, N. V. Regimes of electrostatic collapse of a highly charged polyelectrolyte in a poor solvent. Soft Matter 2017 , 13 , 1 862−1872..
Tom, A. M.; Rajesh, R.; Vemparala, S. Aggregation dynamics of rigid polyelectrolytes. J. Chem. Phys. 2016 , 144 , 034904..
Liu, S.; Ghosh, K.; Muthukumar, M. Polyelectrolyte solutions with added salt: a simulation study. J. Chem. Phys. 2003 , 119 , 1813−1823..
Mecerreyes, D. Polymeric ionic liquids: broadening the properties and applications of polyelectrolytes. Prog. Polym. Sci. 2011 , 36 , 1629−1648..
Lu, K.; Rudzinski, J. F.; Noid, W. G.; Milner, S. T.; Maranas, J. K. Scaling behavior and local structure of ion aggregates in single-ion conductors. Soft Matter 2014 , 10 , 978−989..
Breitsprecher, K.; Košovan, P.; Holm, C. Coarse-grained simulations of an ionic liquid-based capacitor: I. density, ion size, and valency effects. J. Phys.: Condens. Matter 2014 , 26 , 284108..
Brackley, C. A.; Johnson, J. ; Michieletto, D.; Morozov, A. N.; Nicodemi, M.; Cook, P. R.; Marenduzzo, D. Nonequilibrium chromosome looping via molecular slip links. Phys. Rev. Lett. 2017 , 119 , 138101..
Ghelichi, M.; Malek, K.; Eikerling, M. H. Ionomer self-assembly in dilute solution studied by coarse-grained molecular dynamics. Macromolecules 2016 , 49 , 1479−1489..
Luty, B. A.; Davis, M. E.; Tironi, I. G.; Gunsteren, W. F. V. A comparison of particle-particle, particle-mesh and ewald methods for calculating electrostatic interactions in periodic molecular systems. Mol. Simulat. 1994 , 14 , 11−20..
LAMMPS package, http://lammps.org/.
Bedrov, D.; Smith, G. D.; Smith, J. S. Matrix-induced nanoparticle interactions in a polymer melt: a molecular dynamics simulation study. J. Chem. Phys. 2003 , 119 , 10438−10447..
Souaille, M.; Roux, B. Extension to the weighted histogram analysis method: combining umbrella sampling with free energy calculations. Comput. Phys. Commun. 2001 , 135 , 40−57..
Deng, Z. Y.; Jiang, Y. W.; He, L. L.; Zhang, L. X. Aggregation-dispersion transition for nanoparticles in semiflexible ring polymer nanocomposite melts. J. Phys. Chem. B 2016 , 120 , 11574−11581..
Chandler, D. Introduction to modern statistical mechanics, Oxford University Press, Oxford, UK, 1987, p. 55−134.
Smoluchowski, M. V. Über brownsche molekularbewegung unter einwirkung äußerer kräfte und deren zusammenhang mit der verallgemeinerten diffusionsgleichung. Ann. Phys . 1916 , 353 , 1103−1112..
Kalnin, J. R.; Berezhkovskii, A. M. Note: on the relation between Lifson-Jackson and Derrida formulas for effective diffusion coefficient. J. Chem. Phys. 2013 , 139 , 196101..
Makhnovskii, Y. A. Effect of particle size oscillations on drift and diffusion along a periodically corrugated channel. Phys. Rev. E 2019 , 99 , 032102..
Dagdug, L.; Vazquez, M. V.; Berezhkovskii, A. M.; Bezrukov, S. M. Unbiased diffusion in tubes with corrugated walls. J. Chem. Phys. 2010 , 133 , 034707..
Lifson, S.; Jackson, J. L. On the self-diffusion of ions in a polyelectrolyte solution. J. Chem. Phys. 1962 , 36 , 2410−2415..
0
Views
0
Downloads
0
CSCD
Publicity Resources
Related Articles
Related Author
Related Institution