Non-linear screening of spherical and cylindrical colloids: the case of 1:2 and 2:1 electrolytes

Details Non-linear screening of spherical and cylindrical colloids: the case of 1:2 and 2:1 electrolytes Non-linear screening of spherical and cylindrical colloids: the case of 1:2 and 2:1 electrolytes

2004-03-10

arxiv.org/abs/cond-mat/0403265v1

Phys. Rev. E 70, 011404 (2004)

Physics

Condensed Matter

Soft Condensed Matter

9 pages, 11 figures

Scientific paper

10.1103/PhysRevE.70.011404

From a multiple scale analysis, we find an analytic solution of spherical and cylindrical Poisson-Boltzmann theory for both a 1:2 (monovalent co-ions, divalent counter-ions) and a 2:1 (reversed situation) electrolyte. Our approach consists in an expansion in powers of rescaled curvature $1/(\kappa a)$, where $a$ is the colloidal radius and $1/\kappa$ the Debye length of the electrolytic solution. A systematic comparison with the full numerical solution of the problem shows that for cylinders and spheres, our results are accurate as soon as $\kappa a>1$. We also report an unusual overshooting effect where the colloidal effective charge is larger than the bare one.

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