Simple Approach for Charge Renormalization in Highly Charged Macroions

Trizac, Emmanuel; Bocquet, Lydéric; Aubouy, Miguel

doi:10.1103/physrevlett.89.248301

Cited by 125 publications

(158 citation statements)

References 19 publications

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“…The pioneering work on colloidal charge renormalization is the paper by Alexander et al [71] whose method is based on the Poisson-Boltzmann cell model. The most efficient way to calculate Alexander's effective charge has been described by Bocquet et al [79,80]: Solving the PB equation within the spherical cell model, one obtains the potential φ R at the cell edge located at r = R and thus the effective screening factor κ 2 eff = κ 2 cosh φ R which is used to calculate Alexander's effective charge [79],…”

Section: Effective Force Calculationsmentioning

confidence: 99%

Many-body interactions and the melting of colloidal crystals

Dobnikar

Chen

Rzehak

et al. 2003

The Journal of Chemical Physics

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We study the melting behavior of charged colloidal crystals, using a simulation technique that combines a continuous mean-field Poisson-Boltzmann description for the microscopic electrolyte ions with a Brownian-dynamics simulation for the mesoscopic colloids. This technique ensures that many-body interactions between the colloids are fully taken into account, and thus allows us to investigate how many-body interactions affect the solid-liquid phase behavior of charged colloids.Using the Lindemann criterion, we determine the melting line in a phase-diagram spanned by the colloidal charge and the salt concentration. We compare our results to predictions based on the established description of colloidal suspensions in terms of pairwise additive Yukawa potentials, and find good agreement at high-salt, but not at low-salt concentration. Analyzing the effective pairinteraction between two colloids in a crystalline environment, we demonstrate that the difference in the melting behavior observed at low salt is due to many-body interactions. If the salt concentration is high, we find configuration-independent pair-forces of perfect Yukawa form with effective charges and screening constants that are in good agreement with well-established theories. At low added salt, however, the pair-forces are Yukawa-like only at short distances with effective parameters that depend on the analyzed colloidal configuration. At larger distances, in contrast, the pair-forces decay to zero much faster than they would following a Yukawa force law. This is explained with a screening effect of the macroions. Based on these findings, we suggest a simple model potential for colloids in suspension which has the form of a Yukawa potential, truncated after the first coordination shell of a colloid in a crystal. Using this potential in a one-component simulation, we find a melting line that shows good agreement with the one derived from the full PoissonBoltzmann-Brownian-dynamics simulation.2

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Section: Effective Force Calculationsmentioning

confidence: 99%

Many-body interactions and the melting of colloidal crystals

Dobnikar

Chen

Rzehak

et al. 2003

The Journal of Chemical Physics

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“…is the effective charge of species i, defined from the far-field (large r) behavior of φ i [23]. Since all species obey the same differential equation, but with different boundary conditions, it follows that their effective charge is given by a unique two-parameter function f…”

Section: The Renormalized Jellium: Principles and Resolutionmentioning

confidence: 99%

“…As a consequence, our method allows to treat very simply the effect of packing fraction, since the more time consuming part of the calculation is that of the right hand-side of The quantity Y denotes the bare charge of the macroion under study, so that the upper curve, showing f (X, ∞) corresponds to the saturation value studied in Ref. [23]. Practically, f (X, Y ) a/ℓB is the effective jellium charge of a sphere having radius a, bare charge Y a/ℓB, at a packing fraction X/f (X, Y ) (mono-component case).…”

Section: B Self Consistent Resolutionmentioning

confidence: 99%

“…For highly charged colloids [yet in the mean-field regime, where a Poisson-Boltzmann description may hold], the strong interactions between the colloids and the micro-ions induce an accumulation of the latter in the vicinity of the colloids. This in turn induces a renormalization of the colloidal effective charge [1,3,[22][23][24]. If the colloidal bare charge Z bare is large, the effective charge become independent of Z bare ; this is the saturation phenomenon [25], a signature of mean-field, where the effective charge becomes Z sat , which only depends on the density and salt content.…”

Section: Introductionmentioning

confidence: 99%

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Renormalized jellium model for colloidal mixtures

2016

Self Cite

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In an attempt to quantify the role of polydispersity in colloidal suspensions, we present an efficient implementation of the renormalized jellium model for a mixture of spherical charged colloids. The different species may have different size, charge and density. Advantage is taken from the fact that the electric potential pertaining to a given species obeys a Poisson's equation that is species independent; only boundary conditions do change from a species to the next. All species are coupled through the renormalized background (jellium) density, that is determined self-consistently. The corresponding predictions are compared to the results of Monte Carlo simulations of binary mixtures, where Coulombic interactions are accounted for exactly, at the primitive model level (structureless solvent with fixed dielectric permittivity). An excellent agreement is found.

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“…[1,2,3,4,5]. This concept is based on the assumption that, at a finite temperature, the electric potential induced by a "guest" (say colloidal) charged particle, immersed in an infinite electrolyte, exhibits, at large distances from this particle, basically the screening form given by the high-temperature linear Debye-Hückel (DH) theory.…”

Section: Introductionmentioning

confidence: 99%

Renormalization of a Hard-Core Guest Charge Immersed in a Two-Dimensional Electrolyte

Šamaj

2006

J Stat Phys

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This paper is a continuation of a previous one [L.Šamaj, J. Stat. Phys. 120:125 (2005)] dealing with the renormalization of a guest charge immersed in a two-dimensional logarithmic Coulomb gas of pointlike ± unit charges, the latter system being in the stabilityagainst-collapse regime of reduced inverse temperatures 0 ≤ β < 2. In the previous work, using a sine-Gordon representation of the Coulomb gas, an exact renormalized-charge formula was derived for the special case of the pointlike guest charge Q, in its stability regime β|Q| < 2. In the present paper, we extend the renormalized-charge treatment to the guest charge with a hard core of radius σ, which allows us to go beyond the stability border β|Q| = 2. In the limit of the hard-core radius much smaller than the correlation length of the Coulomb-gas species and at a strictly finite temperature, due to the counterion condensation in the extended region β|Q| > 2, the renormalized charge Q ren turns out to be a periodic function of the bare charge Q with period 1. The renormalized charge therefore does not saturate at a specific finite value as |Q| → ∞, but oscillates between two extreme values. In the high-temperature Poisson-Boltzmann scaling regime of limits β → 0 and Q → ∞ with the product βQ being finite, one reproduces correctly the monotonic dependence of βQ ren on βQ in the guest-charge stability region β|Q| < 2 and the Manning-Oosawa type of counterion condensation with the uniform saturation of βQ ren at the value 4/π in the region β|Q| ≥ 2.

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Simple Approach for Charge Renormalization in Highly Charged Macroions

Cited by 125 publications

References 19 publications

Many-body interactions and the melting of colloidal crystals

Many-body interactions and the melting of colloidal crystals

Renormalized jellium model for colloidal mixtures

Renormalization of a Hard-Core Guest Charge Immersed in a Two-Dimensional Electrolyte

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