= Solution
A charged colloid in a polar <electrolyte> is surrounded by an \b[<electric double layer>]. For a negatively charged surface, <counterions> are positive and <co-ions> negative; their distributions reverse for a positive surface. A compact <Stern layer> contains specifically adsorbed or closely approaching ions, followed by a diffuse layer where electrostatic attraction competes with thermal motion. Mobile charge integrated over the surroundings balances the particle charge in an overall neutral system.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2017/paper-2-double-layer.png]
{title=Compact and diffuse countercharge screen a negatively charged colloidal surface}
{source=paper-2-double-layer.py}
For a mean-field dilute <electrolyte>, $n_i(r)=n_{i,\infty}\exp[-z_ie\psi(r)/(k_BT)]$ with <Poisson's equation> relates charge <density> and potential. At weak potential, the diffuse potential outside a sphere decays approximately as $\psi(r)\propto e^{-\kappa(r-a)}/r$. The inverse screening length obeys $\kappa^2=e^2\sum_i z_i^2n_{i,\infty}/(\epsilon k_BT)$: added salt shortens the <Debye length>. The <zeta potential> is the potential at the hydrodynamic slip plane, not necessarily the surface potential. The simple model neglects ion size, correlations and chemical charge regulation; a polar solvent with almost no dissociated ions need not provide a short screening length.
Back to article page
