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Onuki A. Ions and dipoles in electric field: nonlinear polarization and field-dependent chemical reaction. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:3. [PMID: 38206545 DOI: 10.1140/epje/s10189-023-00398-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2023] [Accepted: 12/17/2023] [Indexed: 01/12/2024]
Abstract
We investigate electric-field effects in dilute electrolytes with nonlinear polarization. As a first example of such systems, we add a dipolar component with a relatively large dipole moment [Formula: see text] to an aqueous electrolyte. As a second example, the solvent itself exhibits nonlinear polarization near charged objects. For such systems, we present a Ginzburg-Landau free energy and introduce field-dependent chemical potentials, entropy density, and stress tensor, which satisfy general thermodynamic relations. In the first example, the dipoles accumulate in high-field regions, as predicted by Abrashikin et al.[Phys.Rev.Lett. 99, 077801 (2007)]. Finally, we consider the case, where Bjerrum ion pairs form a dipolar component with nonlinear polarization. The Bjerrum dipoles accumulate in high-field regions, while field-induced dissociation was predicted by Onsager [J. Chem. Phys.2, 599 (1934)]. We present an expression for the field-dependent association constant K(E), which depends on the field strength nonmonotonically.
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Affiliation(s)
- Akira Onuki
- Department of Physics, Kyoto University, Kyoto, 606-8502, Japan.
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2
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Härtel A, Bültmann M, Coupette F. Anomalous Underscreening in the Restricted Primitive Model. PHYSICAL REVIEW LETTERS 2023; 130:108202. [PMID: 36962045 DOI: 10.1103/physrevlett.130.108202] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Revised: 12/19/2022] [Accepted: 02/08/2023] [Indexed: 06/18/2023]
Abstract
Underscreening is a collective term for charge correlations in electrolytes decaying slower than the Debye length. Anomalous underscreening refers to phenomenology that cannot be attributed alone to steric interactions. Experiments with concentrated electrolytes and ionic fluids report anomalous underscreening, which so far has not been observed in simulation. We present Molecular Dynamics simulation results exhibiting anomalous underscreening that can be connected to cluster formation. A theory that accounts for ion pairing confirms the trend. Our results challenge the classic understanding of dense electrolytes impacting the design of technologies for energy storage and conversion.
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Affiliation(s)
- Andreas Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Moritz Bültmann
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Fabian Coupette
- Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
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3
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Goodwin ZA, Kornyshev AA. Cracking Ion Pairs in the Electrical Double Layer of Ionic Liquids. Electrochim Acta 2022. [DOI: 10.1016/j.electacta.2022.141163] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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4
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Onuki A. Long-range correlations of polarization and number densities in dilute electrolytes. J Chem Phys 2020; 153:234501. [DOI: 10.1063/5.0030763] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Akira Onuki
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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5
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Okamoto R, Koga K, Onuki A. Theory of electrolytes including steric, attractive, and hydration interactions. J Chem Phys 2020; 153:074503. [PMID: 32828079 DOI: 10.1063/5.0015446] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
We present a continuum theory of electrolytes composed of a waterlike solvent and univalent ions. First, we start with a density functional F for the coarse-grained solvent, cation, and anion densities, including the Debye-Hückel free energy, the Coulombic interaction, and the direct interactions among these three components. These densities fluctuate obeying the distribution ∝exp(-F/kBT). Eliminating the solvent density deviation in F, we obtain the effective non-Coulombic interactions among the ions, which consist of the direct ones and the solvent-mediated ones. We then derive general expressions for the ion correlation, the apparent partial volume, and the activity and osmotic coefficients up to linear order in the average salt density ns. Second, we perform numerical analysis using the Mansoori-Carnahan-Starling-Leland model [J. Chem. Phys. 54, 1523 (1971)] for three-component hardspheres. The effective interactions sensitively depend on the cation and anion sizes due to competition between the steric and hydration effects, which are repulsive between small-large ion pairs and attractive between symmetric pairs. These agree with previous experiments and Collins' rule [Biophys. J. 72, 65 (1997)]. We also give simple approximate expressions for the ionic interaction coefficients valid for any ion sizes.
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Affiliation(s)
- Ryuichi Okamoto
- Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan
| | - Kenichiro Koga
- Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan
| | - Akira Onuki
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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McEldrew M, Goodwin ZAH, Bi S, Bazant MZ, Kornyshev AA. Theory of ion aggregation and gelation in super-concentrated electrolytes. J Chem Phys 2020; 152:234506. [DOI: 10.1063/5.0006197] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Affiliation(s)
- Michael McEldrew
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Zachary A. H. Goodwin
- Department of Physics, CDT Theory and Simulation of Materials, Imperial College of London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Department of Chemistry, Imperial College of London, Molecular Sciences Research Hub, White City Campus, Wood Lane, London W12 0BZ, United Kingdom
- Thomas Young Centre for Theory and Simulation of Materials, Imperial College of London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Sheng Bi
- State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology (HUST), Wuhan, Hubei 430074, China
| | - Martin Z. Bazant
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Alexei A. Kornyshev
- Department of Chemistry, Imperial College of London, Molecular Sciences Research Hub, White City Campus, Wood Lane, London W12 0BZ, United Kingdom
- Thomas Young Centre for Theory and Simulation of Materials, Imperial College of London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Institute of Molecular Science and Engineering, Imperial College of London, South Kensington Campus, London SW7 2AZ, United Kingdom
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7
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Avni Y, Adar RM, Andelman D. Charge oscillations in ionic liquids: A microscopic cluster model. Phys Rev E 2020; 101:010601. [PMID: 32069538 DOI: 10.1103/physreve.101.010601] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2019] [Indexed: 06/10/2023]
Abstract
In spite of their enormous applications as alternative energy storage devices and lubricants, room-temperature ionic liquids (ILs) still pose many challenges from a pure scientific viewpoint. We develop an IL microscopic theory in terms of ionic clusters, which describes the IL behavior close to charged interfaces. The full structure factor of finite-size clusters is considered and allows us to retain fine and essential details of the system as a whole. Beside the reduction in the screening, it is shown that ionic clusters cause the charge density to oscillate near charged boundaries, with alternating ion-size thick layers, in agreement with experiments. We distinguish between short-range oscillations that persist for a few ionic layers close to the boundary, as opposed to long-range damped oscillations that hold throughout the bulk. The former can be captured by finite-size ion pairs, while the latter is associated with larger clusters with a pronounced quadrupole (or higher) moment. The long-wavelength limit of our theory recovers the well-known Bazant-Storey-Kornyshev (BSK) equation in the linear regime, and elucidates the microscopic origin of the BSK phenomenological parameters.
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Affiliation(s)
- Yael Avni
- Raymond and Beverly Sackler School of Physics and Astronomy, and Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
| | - Ram M Adar
- Raymond and Beverly Sackler School of Physics and Astronomy, and Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
| | - David Andelman
- Raymond and Beverly Sackler School of Physics and Astronomy, and Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel
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Adar RM, Safran SA, Diamant H, Andelman D. Screening length for finite-size ions in concentrated electrolytes. Phys Rev E 2019; 100:042615. [PMID: 31771021 DOI: 10.1103/physreve.100.042615] [Citation(s) in RCA: 43] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2019] [Indexed: 11/07/2022]
Abstract
The classical Debye-Hückel (DH) theory clearly accounts for the origin of screening in electrolyte solutions and works rather well for dilute electrolyte solutions. While the Debye screening length decreases with the ion concentration and is independent of ion size, recent surface-force measurements imply that for concentrated solutions, the screening length exhibits an opposite trend; it increases with ion concentration and depends on the ionic size. The screening length is usually defined by the response of the electrolyte solution to a test charge but can equivalently be derived from the charge-charge correlation function. By going beyond DH theory, we predict the effects of ion size on the charge-charge correlation function. A simple modification of the Coulomb interaction kernel to account for the excluded volume of neighboring ions yields a nonmonotonic dependence of the screening length (correlation length) on the ionic concentration, as well as damped charge oscillations for high concentrations.
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Affiliation(s)
- Ram M Adar
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
| | - Samuel A Safran
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Haim Diamant
- Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
| | - David Andelman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
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9
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Ludwig NB, Dasbiswas K, Talapin DV, Vaikuntanathan S. Describing screening in dense ionic fluids with a charge-frustrated Ising model. J Chem Phys 2018; 149:164505. [DOI: 10.1063/1.5043410] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nicholas B. Ludwig
- The James Franck Institute, The University of Chicago, Chicago, Illinois 60615, USA
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60615, USA
| | - Kinjal Dasbiswas
- The James Franck Institute, The University of Chicago, Chicago, Illinois 60615, USA
| | - Dmitri V. Talapin
- The James Franck Institute, The University of Chicago, Chicago, Illinois 60615, USA
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60615, USA
| | - Suriyanarayanan Vaikuntanathan
- The James Franck Institute, The University of Chicago, Chicago, Illinois 60615, USA
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60615, USA
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10
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Adar RM, Markovich T, Levy A, Orland H, Andelman D. Dielectric constant of ionic solutions: Combined effects of correlations and excluded volume. J Chem Phys 2018; 149:054504. [PMID: 30089391 DOI: 10.1063/1.5042235] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
The dielectric constant of ionic solutions is known to reduce with increasing ionic concentrations. However, the origin of this effect has not been thoroughly explored. In this paper, we study two such possible sources: long-range Coulombic correlations and solvent excluded-volume. Correlations originate from fluctuations of the electrostatic potential beyond the mean-field Poisson-Boltzmann theory, evaluated by employing a field-theoretical loop expansion of the free energy. The solvent excluded-volume, on the other hand, stems from the finite ion size, accounted for via a lattice-gas model. We show that both correlations and excluded volume are required in order to capture the important features of the dielectric behavior. For highly polar solvents, such as water, the dielectric constant is given by the product of the solvent volume fraction and a concentration-dependent susceptibility per volume fraction. The available solvent volume decreases as a function of ionic strength due the increasing volume fraction of ions. A similar decrease occurs for the susceptibility due to the correlations between the ions and solvent, reducing the dielectric response even further. Our predictions for the dielectric constant fit well with experiments for a wide range of concentrations for different salts in different temperatures, using a single fit parameter related to the ion size.
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Affiliation(s)
- Ram M Adar
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
| | - Tomer Markovich
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Amir Levy
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Henri Orland
- Institut de Physique Théorique, CE-Saclay CEA, F-91191 Gif-sur-Yvette Cedex, France
| | - David Andelman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
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11
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Adar RM, Markovich T, Andelman D. Bjerrum pairs in ionic solutions: A Poisson-Boltzmann approach. J Chem Phys 2018; 146:194904. [PMID: 28527430 DOI: 10.1063/1.4982885] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ionic solutions are often regarded as fully dissociated ions dispersed in a polar solvent. While this picture holds for dilute solutions, at higher ionic concentrations, oppositely charged ions can associate into dimers, referred to as Bjerrum pairs. We consider the formation of such pairs within the nonlinear Poisson-Boltzmann framework and investigate their effects on bulk and interfacial properties of electrolytes. Our findings show that pairs can reduce the magnitude of the dielectric decrement of ionic solutions as the ionic concentration increases. We describe the effect of pairs on the Debye screening length and relate our results to recent surface-force experiments. Furthermore, we show that Bjerrum pairs reduce the ionic concentration in bulk electrolyte and at the proximity of charged surfaces, while they enhance the attraction between oppositely charged surfaces.
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Affiliation(s)
- Ram M Adar
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
| | - Tomer Markovich
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
| | - David Andelman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
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12
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13
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Offeddu GS, Mela I, Jeggle P, Henderson RM, Smoukov SK, Oyen ML. Cartilage-like electrostatic stiffening of responsive cryogel scaffolds. Sci Rep 2017; 7:42948. [PMID: 28230077 PMCID: PMC5322396 DOI: 10.1038/srep42948] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2016] [Accepted: 01/17/2017] [Indexed: 11/24/2022] Open
Abstract
Cartilage is a structural tissue with unique mechanical properties deriving from its electrically-charged porous structure. Traditional three-dimensional environments for the culture of cells fail to display the complex physical response displayed by the natural tissue. In this work, the reproduction of the charged environment found in cartilage is achieved using polyelectrolyte hydrogels based on polyvinyl alcohol and polyacrylic acid. The mechanical response and morphology of microporous physically-crosslinked cryogels are compared to those of heat-treated chemical gels made from the same polymers, as a result of pH-dependent swelling. In contrast to the heat-treated chemically-crosslinked gels, the elastic modulus of the physical cryogels was found to increase with charge activation and swelling, explained by the occurrence of electrostatic stiffening of the polymer chains at large charge densities. At the same time, the permeability of both materials to fluid flow was impaired by the presence of electric charges. This cartilage-like mechanical behavior displayed by responsive cryogels can be reproduced in other polyelectrolyte hydrogel systems to fabricate biomimetic cellular scaffolds for the repair of the tissue.
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Affiliation(s)
- G. S. Offeddu
- Nanoscience Centre, Department of Engineering, University of Cambridge, Cambridge CB3 0FF, UK
- Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, UK
| | - I. Mela
- Department of Pharmacology, University of Cambridge, Cambridge CB2 1PD, UK
| | - P. Jeggle
- Department of Pharmacology, University of Cambridge, Cambridge CB2 1PD, UK
| | - R. M. Henderson
- Department of Pharmacology, University of Cambridge, Cambridge CB2 1PD, UK
| | - S. K. Smoukov
- Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, UK
| | - M. L. Oyen
- Nanoscience Centre, Department of Engineering, University of Cambridge, Cambridge CB3 0FF, UK
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14
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Kokot G, Bespalova MI, Krishnan M. Measured electrical charge of SiO 2 in polar and nonpolar media. J Chem Phys 2017; 145:194701. [PMID: 27875880 DOI: 10.1063/1.4967401] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present measurements of the net electrical surface charge of silicon dioxide (SiO2) in contact with solvents of dielectric constants between 5 and 80. Our experimental approach relies on observing the thermal motion of single silica particles confined in an electrostatic fluidic trap created by SiO2 surfaces. We compare the experimentally measured functional form of the trapping potential with that from free energy calculations and thereby determine the net surface charge in the system. Our findings clearly demonstrate that contrary to popular perception, even in the absence of surfactants, the net electrical charge of ionizable surfaces in contact with apolar solvents can be large enough to lead to significant repulsive forces. A charge regulation model for SiO2 surfaces with a single tunable parameter explains our measurements. This model may find general applicability in estimating the net charge of ionizable surfaces, given system parameters such as the dissociation or association constants of the ionizable groups and the pH, ionic strength, and dielectric constant of the solvent phase.
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Affiliation(s)
- G Kokot
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH 8057 Zurich, Switzerland
| | - M I Bespalova
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH 8057 Zurich, Switzerland
| | - M Krishnan
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH 8057 Zurich, Switzerland
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15
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Naji A, Ghodrat M, Komaie-Moghaddam H, Podgornik R. Asymmetric Coulomb fluids at randomly charged dielectric interfaces: Anti-fragility, overcharging and charge inversion. J Chem Phys 2014; 141:174704. [DOI: 10.1063/1.4898663] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ali Naji
- School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
| | - Malihe Ghodrat
- School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
| | - Haniyeh Komaie-Moghaddam
- School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
| | - Rudolf Podgornik
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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16
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Heinen M, Palberg T, Löwen H. Coupling between bulk- and surface chemistry in suspensions of charged colloids. J Chem Phys 2014; 140:124904. [DOI: 10.1063/1.4869338] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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17
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Naji A, Kanduč M, Forsman J, Podgornik R. Perspective: Coulomb fluids—Weak coupling, strong coupling, in between and beyond. J Chem Phys 2013; 139:150901. [DOI: 10.1063/1.4824681] [Citation(s) in RCA: 133] [Impact Index Per Article: 12.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Electrodynamics of lipid membrane interactions in the presence of zwitterionic buffers. Biophys J 2011; 101:362-9. [PMID: 21767488 DOI: 10.1016/j.bpj.2011.05.062] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2011] [Revised: 05/10/2011] [Accepted: 05/27/2011] [Indexed: 11/22/2022] Open
Abstract
Due to thermal motion and molecular polarizability, electrical interactions in biological systems have a dynamic character. Zwitterions are dipolar molecules that typically are highly polarizable and exhibit both a positive and a negative charge depending on the pH of the solution. We use multilamellar structures of common lipids to identify and quantify the effects of zwitterionic buffers that go beyond the control of pH. We use the fact that the repeat spacing of multilamellar lipid bilayers is a sensitive and accurate indicator of the force balance between membranes. We show that common buffers can in fact charge up neutral membranes. However, this electrostatic effect is not immediately recognized because of the concomitant modification of dispersion (van der Waals) forces. We show that although surface charging can be weak, electrostatic forces are significant even at large distances because of reduced ionic screening and reduced van der Waals attraction. The zwitterionic interactions that we identify are expected to be relevant for interfacial biological processes involving lipid bilayers, and for a wide range of biomaterials, including amino acids, detergents, and pharmaceutical drugs. An appreciation of zwitterionic electrodynamic character can lead to a better understanding of molecular interactions in biological systems and in soft materials in general.
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Paillusson F, Trizac E. Interaction regimes for oppositely charged plates with multivalent counterions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011407. [PMID: 21867171 DOI: 10.1103/physreve.84.011407] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2011] [Indexed: 05/31/2023]
Abstract
Within a mean-field treatment of the interaction between two oppositely charged plates in a salt-free solution, the distance at which a transition from an attractive to a repulsive regime appears can be computed analytically. The mean-field description, however, breaks down under strong Coulombic couplings, which can be achieved at room temperature with multivalent counterions and highly charged surfaces. Making use of the contact theorem and simple physical arguments, we propose explicit expressions for the equation of state in several situations at short distances. The possibility of Bjerrum pair formation is addressed and is shown to have profound consequences on the interactions. To complete the picture, we consider the large-distance limit, from which schematic phase diagram discriminating attractive from repulsive regions can be proposed.
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Affiliation(s)
- Fabien Paillusson
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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20
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Kanduč M, Naji A, Forsman J, Podgornik R. Dressed counterions: polyvalent and monovalent ions at charged dielectric interfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011502. [PMID: 21867173 DOI: 10.1103/physreve.84.011502] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2011] [Revised: 03/30/2011] [Indexed: 05/31/2023]
Abstract
We investigate the ion distribution and overcharging at charged interfaces with dielectric inhomogeneities in the presence of asymmetric electrolytes containing polyvalent and monovalent ions. We formulate an effective "dressed counterion" approach by integrating out the monovalent salt degrees of freedom and show that it agrees with results of explicit Monte Carlo simulations. We then apply the dressed counterion approach within the framework of the generalized strong-coupling theory, valid for polyvalent ions at low concentrations, which enables an analytical description for salt effects as well as dielectric inhomogeneities in the limit of strong Coulomb interactions. Limitations and applicability of this theory are examined by comparing the results with simulations.
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Affiliation(s)
- Matej Kanduč
- Department of Physics, Technical University of Munich, D-85748 Garching, Germany
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21
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Kanduc M, Naji A, Forsman J, Podgornik R. Dressed counterions: strong electrostatic coupling in the presence of salt. J Chem Phys 2010; 132:124701. [PMID: 20370139 DOI: 10.1063/1.3361672] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We reformulate the theory of strong electrostatic coupling in order to describe an asymmetric electrolyte solution of monovalent salt ions and polyvalent counterions using field-theoretical techniques and Monte Carlo simulations. The theory is based on an asymmetric treatment of the different components of the electrolyte solution. The weak coupling Debye-Hückel approach is used in order to describe the monovalent salt ions while a strong coupling approach is used to tackle the polyvalent counterions. This combined weak-strong coupling approach effectively leads to dressed interactions between polyvalent counterions and thus directly affects the correlation attraction mediated by polyvalent counterions between like-charged objects. The general theory is specifically applied to a system composed of two uniformly charged plane-parallel surfaces in the presence of salt and polyvalent counterions. In the strong coupling limit for polyvalent counterions, the comparison with Monte Carlo simulations shows good agreement for large enough values of the electrostatic coupling parameter. We delineate two limiting laws that in fact encompass all the Monte Carlo data.
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Affiliation(s)
- Matej Kanduc
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
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