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Radhakrishnan K, Singh SP. Explicit characterization of counterion dynamics around a flexible polyelectrolyte. Phys Rev E 2022; 105:044501. [PMID: 35590562 DOI: 10.1103/physreve.105.044501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Accepted: 03/04/2022] [Indexed: 06/15/2023]
Abstract
The article presents a comprehensive study of counterion dynamics around a generic linear polyelectrolyte chain with the help of coarse-grained computer simulations. The ion-chain coupling is discussed in the form of binding time, mean-square displacement (MSD) relative to the chain, local ion transport coefficient, and spatiotemporal correlations in the effective charge. We have shown that a counterion exhibits subdiffusive behavior 〈δR^{2}〉∼t^{δ}, δ≈0.9 w.r.t. chain's center of mass. The MSD of ions perpendicularly outward from the chain segment exhibits a smaller subdiffusive exponent compared to the one along the chain backbone. The effective diffusivity of ion is the lowest in chain's close proximity, extending up to the length-scale of radius of gyration R_{g}. Beyond R_{g} at larger distances, they attain diffusivity of free ion with a smooth cross-over from the adsorbed regime to the free ion regime. We have shown that the effective diffusivity drastically decreases for the multivalent ions, while the crossover length scale remains the same. Conversely, with increasing salt concentration the coupling-length scale reduces, while the diffusivity remains unaltered. The effective diffusivity of adsorbed-ion reveals an exponential reduction with electrostatic interaction strength. We further corroborate this from the binding time of ions on the chain, which also grows exponentially with the coupling strength of the ion-polymer duo. Moreover, the binding time of ions exhibits a weak dependence with salt concentration for the monovalent salt, while for multivalent salts the binding time decreases dramatically with concentration. Our work also elucidates fluctuations in the effective charge per site, where it exhibits strong negative correlations at short length-scales.
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Affiliation(s)
- Keerthi Radhakrishnan
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
| | - Sunil P Singh
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
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Mohanty PS, Nöjd S, Bergman MJ, Nägele G, Arrese-Igor S, Alegria A, Roa R, Schurtenberger P, Dhont JKG. Dielectric spectroscopy of ionic microgel suspensions. SOFT MATTER 2016; 12:9705-9727. [PMID: 27808335 DOI: 10.1039/c6sm01683a] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
The determination of the net charge and size of microgel particles as a function of their concentration, as well as the degree of association of ions to the microgel backbone, has been pursued in earlier studies mainly by scattering and rheology. These methods suffer from contributions due to inter-particle interactions that interfere with the characterization of single-particle properties. Here we introduce dielectric spectroscopy as an alternative experimental method to characterize microgel systems. The advantage of dielectric spectroscopy over other experimental methods is that the polarization due to mobile charges within a microgel particle is only weakly affected by inter-particle interactions. Apart from electrode polarization effects, experimental spectra on PNIPAM-co-AA [poly(N-isopropylacrylamide-co-acrylic acid)] ionic microgel particles suspended in de-ionized water exhibit three well-separated relaxation modes, which are due to the polarization of the mobile charges within the microgel particles, the diffuse double layer around the particles, and the polymer backbone. Expressions for the full frequency dependence of the electrode-polarization contribution to the measured dielectric response are derived, and a theory is proposed for the polarization resulting from the mobile charges within the microgel. Relaxation of the diffuse double layer is modeled within the realm of a cell model. The net charge and the size of the microgel particles are found to be strongly varying with concentration. A very small value of the diffusion coefficient of ions within the microgel is found, due to a large degree of chemical association of protons to the polymer backbone.
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Affiliation(s)
- P S Mohanty
- Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden and School of Applied Sciences, KIIT University, Bhubaneswar 751024, India
| | - S Nöjd
- Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden
| | - M J Bergman
- Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden
| | - G Nägele
- Institute of Complex Systems ICS-3, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany. and Heinrich-Heine Universität Düsseldorf, Department of Physics, D-40225 Düsseldorf, Germany and JARA-SOFT, 52425 Jülich, Germany
| | - S Arrese-Igor
- Centro de Física de Materiales (CSIC-UPV/EHU), Materials Physics Center, 20018 San Sebastián, Spain
| | - A Alegria
- Centro de Física de Materiales (CSIC-UPV/EHU), Materials Physics Center, 20018 San Sebastián, Spain and Universidad del País Vasco (UPV/EHU), Departamento de Física de Materiales, 20080 San Sebastián, Spain
| | - R Roa
- Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, 14109 Berlin, Germany
| | - P Schurtenberger
- Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden
| | - J K G Dhont
- Institute of Complex Systems ICS-3, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany. and Heinrich-Heine Universität Düsseldorf, Department of Physics, D-40225 Düsseldorf, Germany and JARA-SOFT, 52425 Jülich, Germany
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Kim WK, Netz RR. Barrier-induced dielectric counterion relaxation at super-low frequencies in salt-free polyelectrolyte solutions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:120. [PMID: 26590150 DOI: 10.1140/epje/i2015-15120-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2015] [Accepted: 10/20/2015] [Indexed: 06/05/2023]
Abstract
Based on the thermally activated diffusion of counterions over the barrier of the electrostatic binding potential, we construct a scaling theory for the slow dielectric response in dilute and semi-dilute polyelectrolyte solutions. The theory is based on an analytic evaluation of the mean-escape time of a single counterion from the surface of a polyelectrolyte chain and uses a variational expression for the electrostatic potential of a charged cylinder including counterion condensation. This mean-escape time shows a range of characteristic power-law dependencies on the polyelectrolyte length and the polyelectrolyte monomer concentration. The existence of this novel dielectric mode at super-low frequencies reflects the wide spectrum of experimental findings for the super-low-frequency dielectric relaxation mode and thereby helps to reconcile conflicting interpretations of experimental data in terms of conventional scaling laws. We also devise a scaling theory for the counterion condensation of finite-length polyelectrolyte chains at finite concentration, which allows us to include polyelectrolyte charge renormalization in dilute as well as semi-dilute solutions in a unified theoretical framework.
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Affiliation(s)
- Won Kyu Kim
- Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany.
| | - Roland R Netz
- Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany
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Zhou C, Riehn R. Collapse of DNA under alternating electric fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012714. [PMID: 26274209 PMCID: PMC5014398 DOI: 10.1103/physreve.92.012714] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2014] [Indexed: 05/04/2023]
Abstract
Recent studies have shown that double-stranded DNA can collapse in the presence of a strong electric field. Here we provide an in-depth study of the collapse of DNA under weak confinement in microchannels as a function of buffer strength, driving frequency, applied electric-field strength, and molecule size. We find that the critical electric field at which DNA molecules collapse (tens of kV/m) is strongly dependent on driving frequency (100-800 Hz) and molecular size (20-160 kbp), and weakly dependent on the ionic strength (8-60 mM). We argue that an apparent stretching at very high electric fields is an artifact of the finite frame time of video microscopy.
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Affiliation(s)
- Chunda Zhou
- Department of Physics, North Carolina State University, Raleigh, NC 27695-8202
| | - Robert Riehn
- Department of Physics, North Carolina State University, Raleigh, NC 27695-8202
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