Counterion condensation in micellar and colloidal solutions

Ramanathan, G. V.

doi:10.1063/1.453837

Cited by 66 publications

(64 citation statements)

References 13 publications

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“…One early study (Zimm and Lebret, 1983) suggested that although likely with cylindrical and planar surfaces, counterion condensation does not occur with particles of spherical geometry. The present findings and those by Loux (1985) are consistent with observations by Ramanathan (1988) that condensation does occur on spherical particles when the particle radius is large relative to the dimensions of the diffuse layer. From another perspective, when the term k*r is large, a spherical particle can be viewed as an ''infinite plane'' without edge effects and hence, also can experience counterion condensation.…”

supporting

confidence: 82%

Extending the diffuse layer model of surface acidity behavior: I. Model development

Loux

2006

Chemical Speciation & Bioavailability

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Considerable disenchantment exists within the environmental research community concerning our current ability to accurately model surface -complexation -mediated low -porewater -concentration ionic contaminant partitioning with natural surfaces. Several authors attribute this unacceptable variation to uncertainties in our understanding of surface acidity behavior. In support of this contention, many authors are not satisfied with our ability to model surface acidity behavior in controlled, pure phase laboratory systems. The present work was designed to more closely examine the theoretical aspects of those variable energies likely to be contributing to the excess free energies associated with surface acidity behavior. Conclusions from the work include: (1) the excess free energy term associated with chargeypotential relationships is given by: DG excess;sigmaypsi ¼ DG electrostatic þ DG hydration þ DG dipole þ DG Debye Huckel , (2) the excess free energy terms included in effective acidity constant behavior includes a charging energy term: DG excess;pK ¼ DG excess;sigmaypsi þ DG charging , (3) under conditions where ÀDG excess;sigmaypsi 4RT, DG excess;sigmaypsi % DG excess;pK % DG electrostatic þ DG hydration (thereby supporting historical methodologies), (4) under conditions where ÀDG excess;sigmaypsi % RT, DG excess is better approximated by: DG excess;sigmaypsi % DG electrostatic þ DG hydration and DG excess;pK % DG excess;sigmaypsi þ DG charging , (5) DG charging becomes increasingly significant with decreased counterion condensation, and (6) asymmetric behavior in the charge dependency of effective acidity constant behavior is predicted -particularly when charging energies become significant.

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supporting

confidence: 82%

Extending the diffuse layer model of surface acidity behavior: I. Model development

Loux

2006

Chemical Speciation & Bioavailability

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“…(12) still yields a reasonable estimate for Z sat eff (κa), specially for high values of the parameter κa. In the limit of small κa, both expressions (12) and (14) differ notably from the PB saturation charge which diverges, as shown by Ramanathan [28], as:…”

Section: A Planar Casementioning

confidence: 98%

Effective charge saturation in colloidal suspensions

Bocquet

Trizac

Aubouy

2002

The Journal of Chemical Physics

141

182

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Because micro-ions accumulate around highly charged colloidal particles in electrolyte solutions, the relevant parameter to compute their interactions is not the bare charge, but an effective (or renormalized) quantity, whose value is sensitive to the geometry of the colloid, the temperature or the presence of added-salt. This non-linear screening effect is a central feature in the field of colloidal suspensions or polyelectrolyte solutions. We propose a simple method to predict effective charges of highly charged macro-ions, that is reliable for mono-valent electrolytes (and counter-ions) in the colloidal limit (large size compared to both screening length and Bjerrum length). Taking reference to the non linear Poisson-Boltzmann theory, the method is successfully tested against the geometry of the macro-ions, the possible confinement in a Wigner-Seitz cell, and the presence of added salt. Moreover, our results are corroborated by various experimental measures reported in the literature. This approach provides a useful route to incorporate the non-linear effects of charge renormalization within a linear theory for systems where electrostatic interactions play an important role.

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“…At intermediate salt concentration, κ D a 1, the behavior is non-monotonic (and will not be detailed here), while for κ D a 1 [but not smaller than exp(−l B /2a)], Q eff saturates at a value, Ramanathan (1986Ramanathan ( , 1988) that does not depend on Q itself:…”

Section: The Non-linear Pb Solution: Counter-ion Only and Manning Conmentioning

confidence: 99%