Analytical estimate of effective charges at saturation in Poisson-Boltzmann cell models

Abstract

We propose a simple approximation scheme to compute the effective charge of highly charged colloids (spherical or cylindrical with infinite length). Within non-linear Poisson-Boltzmann theory, we start from an expression of the effective charge in the infinite dilution limit which is asymptotically valid for large salt concentrations; this result is then extended to finite colloidal concentration, approximating the salt partitioning effect which relates the salt content in the suspension to that of a dializing reservoir. This leads to an analytical expression of the effective charge as a function of colloid volume fraction and salt concentration. These results compare favorably with the effective charges {\em at saturation} (i.e. in the limit of large bare charge) computed numerically following the standard prescription proposed by Alexander {\it et al.} within the cell model.

arXiv comment5 pages, 2 figures, to appear in Journal of Physics : Condensed Matter

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• Screening of Spherical Colloids beyond Mean Field -- A Local Density Functional Approach
• Effective interactions, structure, and pressure in charge-stabilized colloidal suspensions: Critical assessment of charge renormalization methods
• Saturation of Electrostatic Potential: Exactly Solvable 2D Coulomb Models