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

Emmanuel Trizac·Miguel Aubouy·Lyderic Bocquet
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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.

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Emmanuel Trizac, Miguel Aubouy, Lyderic Bocquet. 2002-10-21. Analytical estimate of effective charges at saturation in Poisson-Boltzmann cell models. https://doi.org/10.1088/0953-8984%2F15%2F1%2F339

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