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Effective charge versus bare charge for colloids in the infinite dilution limit

M. Aubouy·E. Trizac·L. Bocquet
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Abstract

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) mean-field theory. Mathematically speaking, our estimate is asymptotically exact in the limit $κa\gg 1$, 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 $κa\sim 1$. 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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M. Aubouy, E. Trizac, L. Bocquet. 2003-01-07. Effective charge versus bare charge for colloids in the infinite dilution limit. https://doi.org/10.1088/0305-4470%2F36%2F22%2F302

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