Electrostatic interactions of charged bodies from the weak- to the strong-coupling regime

Hatlo, Marius M.; Lue, Leo

doi:10.1209/0295-5075/89/25002

Cited by 73 publications

(121 citation statements)

References 28 publications

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“…The high-temperature (weak-coupling) limit of general Coulomb systems is described by the Poisson-Boltzmann (PB) mean-field theory [7] which basically does not depend on dimension. Formulating the Coulomb system as a field theory, the A relevant progress has been made in the last decade in the opposite low-temperature (strong-coupling, SC) limit [6,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Within a field-theoretical treatment [15,16], the leading SC behavior stems from a singleparticle picture and next correction orders correspond to a virial/fugacity expansion in inverse powers of the coupling constant.…”

Section: Introductionmentioning

confidence: 99%

Counter-ions at charged walls: Two-dimensional systems

Šamaj

Trizac

2011

Eur. Phys. J. E

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We study equilibrium statistical mechanics of classical point counter-ions, formulated on 2D Euclidean space with logarithmic Coulomb interactions (infinite number of particles) or on the cylinder surface (finite particle numbers), in the vicinity of a single uniformly charged line (one single doublelayer), or between two such lines (interacting double-layers). The weak-coupling Poisson-Boltzmann theory, which applies when the coupling constant Γ is small, is briefly recapitulated (the coupling constant is defined as Γ ≡ βe 2 where β is the inverse temperature, and e the counter-ion charge). The opposite strong-coupling limit (Γ → ∞) is treated by using a recent method based on an exact expansion around the ground-state Wigner crystal of counter-ions. The weak-and strong-coupling theories are compared at intermediary values of the coupling constant Γ = 2γ (γ = 1, 2, 3), to exact results derived within a 1D lattice representation of 2D Coulomb systems in terms of anti-commuting field variables. The models (density profile, pressure) are solved exactly for any particles numbers N at Γ = 2 and up to relatively large finite N at Γ = 4 and 6. For the one-line geometry, the decay of the density profile at asymptotic distance from the line undergoes a fundamental change with respect to the mean-field behavior at Γ = 6. The like-charge attraction regime, possible in the strong coupling limit but precluded at mean-field level, survives for Γ = 4 and 6, but disappears at Γ = 2.

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Section: Introductionmentioning

confidence: 99%

Counter-ions at charged walls: Two-dimensional systems

Šamaj

Trizac

2011

Eur. Phys. J. E

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“…Such correlations lead to a breakdown of the mean-field approximation, and a non-local theory [47,48] that can account for strong fluctuations in the electrostatic potential is required to improve upon the standard continuum theory [49].…”

Section: Discussionmentioning

confidence: 99%

The influence of excluded volume and excess ion polarisability on the capacitance of the electric double layer

Minton

Lue

2016

Molecular Physics

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This version is available at https://strathprints.strath.ac.uk/55894/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. We apply a modified Poisson-Boltzmann theory which permits ions of different sizes and excess polarizabilities to the study of these properties' effects on the differential capacitance of the electric double layer. For a planar electrode, we find an analytical expression for the differential capacitance, which is examined in the limits of low and high applied potential. In the low potential limit, a reduction of the solution relative permittivity caused by the ion polarizability causes the differential capacitance to decrease above a certain concentration, relative to the Gouy-Chapman-Stern theory. A similar effect is observed for the excluded volume, but only if the ions are of different sizes. In the high potential limit, the differential capacitance decreases inversely with the square root of the applied voltage. In a mixed electrolyte, asymmetries in both ion size and excess polarizability alter the surface adsorption of species: at high potentials, smaller ions displace larger ions and less polarizable ions displace more polarizable ions. The extent of the displacement agrees favorably with experimental data. A further consequence of this displacement is the appearance of a second peak in the differential capacitance, which is enhanced by excess ion polarizability.

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“…On the other hand, particle based approaches, such as virial expansions, work well for short-wavelength correlations. In the splitting approximation 24,25 , we divide the fluctuations of the system into short-wavelength and long-wavelength contributions and treat each of these within different approximation schemes. This leads to a theory which works well for both the weak coupling and strong coupling limits, as well as for intermediate coupling strengths.…”

Section: Theorymentioning

confidence: 99%

“…This leads to a theory which works well for both the weak coupling and strong coupling limits, as well as for intermediate coupling strengths. Technically, we divide the Green's function of the electrostatic interactions into short-wavelength G s and long-wavelength G l contributions as 24,25,26 :…”

Section: Theorymentioning

confidence: 99%

“…Also rod-like dipoles and spherical quadrupoles between charged surfaces have also been studied 20,21 . The description of systems of rod-like ions has been extended to the intermediate and strong coupling regimes, where the interionic correlations alone can lead to an attraction between like-charged surfaces 24,25,26 . In systems with highly charged macroions and mobile multivalent ions, correlations between the charges need to be introduced 27,28,29 .…”

Section: Introductionmentioning

confidence: 99%

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A field theoretic approach to the electric interfacial layer — Mixture of trivalent rod-like and monovalent point-like ions between charged walls

Bohinc

Lue

2015

Mod. Phys. Lett. B

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This version is available at https://strathprints.strath.ac.uk/55179/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. In this work, we study the interaction between charged particles immersed in a solution of oppositely charged, rod-like counterions and point-like co-ions. The system is modeled by a field theoretic approach, which was extended to treat mixtures of rod-and point-like ions. The theory is applicable from the weak to the intermediate through to the strong coupling regimes. In the weak coupling limit, the force between the charged surfaces are only repulsive. In the intermediate coupling regime, the rod-like ions can induce attractive force between the charged surfaces. In the strong coupling limit, the inter-ionic charge correlations dominate the attractive forces at short separations between the charged surfaces.

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Electrostatic interactions of charged bodies from the weak- to the strong-coupling regime

Cited by 73 publications

References 28 publications

Counter-ions at charged walls: Two-dimensional systems

Counter-ions at charged walls: Two-dimensional systems

The influence of excluded volume and excess ion polarisability on the capacitance of the electric double layer

A field theoretic approach to the electric interfacial layer — Mixture of trivalent rod-like and monovalent point-like ions between charged walls

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