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

Abstract

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.

9 pages, 11 figures

References in corpus (1)

• A density functional theory study of electric potential saturation: planar geometry

Cited by in corpus (1)

• Description beyond the mean field approximation of an electrolyte confined between two planar metallic electrodes