Fluctuations and ordering in macroion suspensions

We propose an analytical approximation for the dependence of the effective charge on the bare charge for spherical and cylindrical macro-ions as a function of the size of the colloid and salt content, for the situation of a unique colloid immersed in a sea of electrolyte (where the definition of an effective charge is non ambiguous). Our approach is based on the Poisson-Boltzmann (PB) meanfield theory. Mathematically speaking, our estimate is asymptotically exact in the limit κa ≫ 1, where a is the radius of the colloid and κ the inverse screening length. In practice, a careful comparison with effective charges parameters obtained by numerically solving the full non-linear PB theory proves that it is good down to κa ∼ 1. This is precisely the limit appropriate to treat colloidal suspensions. A particular emphasis is put on the range of parameters suitable to describe both single and double strand DNA molecules under physiological conditions.

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“…where t λ = T λ bare ℓ B κa + 1/2 (5) and the function T , also useful in spherical geometry (see below), is defined as…”

Section: Effective Charge Dependencementioning

confidence: 99%

Effective charge versus bare charge: an analytical estimate for colloids in the infinite dilution limit

Aubouy

Trizac

Bocquet

2003

J. Phys. A: Math. Gen.

105

139

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“…The phase-behavior has been investigated analytically [85,88,89,90] and by computer simulation [81,82,91,92,93,94]. The solid phase is BCC ordered in the region of low κ and FCC ordered at high κ.…”

Section: The Solid-liquid Phase Behavior Of a Simple Yukawa Fluidmentioning

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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“…(1) also obeys the linearized Poisson-Boltzmann (LPB) equation ∇ 2 Φ = κ 2 Φ, and therefore takes the Yukawa form Φ LPB = Z eff ℓ B exp[κ(a − r)]/[r(1 + κa)], with a the radius of the sphere. Z eff (in e units) is consequently defined here without ambiguity from the far field behaviour of Φ PB (see [4,10,11] for alternative definitions of effective charges). Accordingly, a "non linear" region may be defined (r ∈ [a, r * ]), corresponding to Φ PB larger than unity, where by definition of the cutoff r * , Φ LPB (r * ) is of order 1.…”

mentioning

confidence: 99%

Simple Approach for Charge Renormalization in Highly Charged Macroions

2002

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We revisit the notion of renormalized charge, which is a concept of central importance in the field of highly charged colloidal or polyelectrolyte solutions. Working at the level of a linear Debye-Hückel-like theory only, we propose a versatile method to predict the saturated amount of charge renormalization, which is, however, a nonlinear effect arising at strong electrostatic coupling. The results are successfully tested against nonlinear Poisson-Boltzmann theory for polyions of various shapes (planar, cylindrical, and spherical), both in the infinite dilution limit or in confined geometry, with or without added electrolyte. Our approach, accurate for monovalent microions in solvents such as water, is finally confronted against experimental results on charged colloids and B-DNA solutions.

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Fluctuations and ordering in macroion suspensions

Cited by 15 publications

References 21 publications

Effective charge versus bare charge: an analytical estimate for colloids in the infinite dilution limit

Effective charge versus bare charge: an analytical estimate for colloids in the infinite dilution limit

Many-body interactions and the melting of colloidal crystals

Simple Approach for Charge Renormalization in Highly Charged Macroions

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