Charge renormalization, osmotic pressure, and bulk modulus of colloidal crystals: Theory

Alexander, S.; Chaikin, P. M.; Grant, P. M.; Morales, G. J.; Pincus, P.; Hone, Daniel

doi:10.1063/1.446600

Cited by 932 publications

(915 citation statements)

References 15 publications

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“…different from its structural charge ! "# [4,5]. The counterion condensation for colloids bears strong similarities with that derived for polymers and known as the Oosawa--Manning condensation [6].…”

Section: -Introductionmentioning

confidence: 99%

Polyelectrolyte assisted charge titration spectrometry: Applications to latex and oxide nanoparticles

Mousseau

Vitorazi

Herrmann

et al. 2016

Journal of Colloid and Interface Science

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Abstract:The electrostatic charge density of particles is of paramount importance for the control of the dispersion stability. Conventional methods use potentiometric, conductometric or turbidity titration but require large amount of samples. Here we report a simple and cost--effective method called polyelectrolyte assisted charge titration spectrometry or PACTS. The technique takes advantage of the propensity of oppositely charged polymers and particles to assemble upon mixing, leading to aggregation or phase separation. The mixed dispersions exhibit a maximum in light scattering as a function of the volumetric ratio , and the peak position !"# is linked to the particle charge density according to ~ ! !"# where ! is the particle diameter. The PACTS is successfully applied to organic latex, aluminum and silicon oxide particles of positive or negative charge using poly(diallyldimethylammonium chloride) and poly(sodium 4--styrenesulfonate). The protocol is also optimized with respect to important parameters such as pH and concentration, and to the polyelectrolyte molecular weight. The advantages of the PACTS technique are that it requires minute amounts of sample and that it is suitable to a broad variety of charged nano--objects.

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Section: -Introductionmentioning

confidence: 99%

Polyelectrolyte assisted charge titration spectrometry: Applications to latex and oxide nanoparticles

Mousseau

Vitorazi

Herrmann

et al. 2016

Journal of Colloid and Interface Science

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“…An additional condition is that the concentration of potential determining ions is constant. Potential determining ions in this case are those ions that escape from the Gouy layer leaving the surface to have a renormalized charge [10]. The absence of a term proportional to R in Eq.…”

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confidence: 99%

“…[10] if R 1. Reported experimental values of j j are close to 6 kT for micelles [12] and highly charged colloids [13] in aqueous media, but also smaller values have been observed depending upon (bare) charge density and ionic strength [8,14,15].…”

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confidence: 99%

Charge Regulation as a Stabilization Mechanism for Shell-Like Assemblies of Polyoxometalates

et al. 2007

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We show that the equilibrium size of single-layer shells composed of polyoxometalate macroions is inversely proportional to the dielectric constant of the medium in which they are dispersed. This behavior is consistent with a stabilization mechanism based on Coulomb repulsion combined with charge regulation. We estimate the cohesive energy per bond between macroions on the shells to be approximately ÿ6kT. This number is extracted from analysis based on a charge regulation model in combination with a model for defects on a sphere. The value of the cohesive bond energy is in agreement with the model-independent critical aggregate concentration. This observation points to a new class of thermodynamically stable shell-like objects. We point out the possible relevance our findings have for certain surfactant systems.

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“…In fact, it has outstanding effects in the general electrostatics of soft matter, affecting the stability of colloids [42][43], or the self-assembly of biomolecules [44], as well as the compaction of genetic material [45]. The phenomenon also occurs in pure salt-free or low-salt regimes at finite volume fractions [46], and it has provided explanation to such findings as the independence of electrokinetic properties like electrophoretic mobility with particle charge [13][14][15]19], or the presence of a relaxation process linked to this condensate region in radiofrequency electric fields [23].…”

Section: Introductionmentioning

confidence: 99%

General electrokinetic model for concentrated suspensions in aqueous electrolyte solutions: Electrophoretic mobility and electrical conductivity in static electric fields

Carrique

Roa

Arroyo

et al. 2015

Journal of Colloid and Interface Science

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In recent years different electrokinetic cell models for concentrated colloidal suspensions in aqueous electrolyte solutions have been developed. They share some of its premises with the standard electrokinetic model for dilute colloidal suspensions, in particular, neglecting both the specific role of the so-called added counterions (i.e., those released by the particles to the solution as they get charged), and the realistic chemistry of the aqueous solution on such electrokinetic phenomena as electrophoresis and electrical conductivity.These assumptions, while having been accepted for dilute conditions (volume fractions of solids well below 1 %, say), are now questioned when dealing with concentrated suspensions.In this work, we present a general electrokinetic cell model for such kind of systems, including the mentioned effects, and we also carry out a comparative study with the standard treatment (the standard solution only contains the ions that one purposely adds, without ionic contributions from particle charging or water chemistry). We also consider an intermediate model that neglects the realistic aqueous chemistry of the solution but accounts for the correct contribution of the added counterions. The results show the limits of applicability of the classical assumptions and allow one to better understand the relative role of the added counterions and ions stemming from the electrolyte in a realistic aqueous solution, on electrokinetic properties. For example, at low salt concentrations the realistic effects of the aqueous solution are the dominant ones, while as salt concentration is increased, it is this that progressively takes the control of the electrokinetic response for low to moderate volume fractions. As expected, if the solids concentration is high enough the added counterions will play the dominant role (more important the higher the particle surface charge), no matter the salt concentration if it is not too high. We hope this work can help in setting up the real limits of applicability of the standard cell model for concentrated suspensions by a quantitative 4 analysis of the different effects that have been classically disregarded, showing that in many cases they can be determinant to get rigorous predictions.

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Charge renormalization, osmotic pressure, and bulk modulus of colloidal crystals: Theory

Cited by 932 publications

References 15 publications

Polyelectrolyte assisted charge titration spectrometry: Applications to latex and oxide nanoparticles

Polyelectrolyte assisted charge titration spectrometry: Applications to latex and oxide nanoparticles

Charge Regulation as a Stabilization Mechanism for Shell-Like Assemblies of Polyoxometalates

General electrokinetic model for concentrated suspensions in aqueous electrolyte solutions: Electrophoretic mobility and electrical conductivity in static electric fields

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