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The spatially extended ionic atmosphere screening a charged surface beyond the compact Stern layer.

The Stern layer is the compact near-surface layer of specifically adsorbed or closely associated ions. The diffuse layer is the more extended, thermally distributed excess of counterions that screens the surface charge.

For water near $25^{\circ }\mathrm{C}$, the Debye length can be writtenFor $0.01$ M KCl, $I=0.01$ M and ${\lambda }_D\simeq 3.0$ nm. For a fully dissociated 2:2 electrolyte at the same formula-unit concentration, $I=4c=0.04$ M, giving ${\lambda }_D\simeq 1.5$ nm, half as large. These are linear-screening estimates, not sharp boundaries of the diffuse layer.

A charged colloid in a polar electrolyte is surrounded by an 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.

For a mean-field dilute electrolyte, $n_i(r)=n_{i,\infty }\exp [-z_{i}e\psi (r)/(k_{B}T)]$ 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 ${\kappa }^2=e^2{\sum }_i{z}_i^2{n}_{i,\infty }/(ϵk_{B}T)$: 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.

Choose a positively charged plate to match the question's labels $n_{+}$ for co-ions and $n_{-}$ for counterions. Let $x=0$ denote the outer edge of its compact Stern layer, and set the bulk potential to zero.

In the weak-potential Debye–Hückel approximation, the diffuse-layer potential isThe key length is the Debye–Hückel screening length. For a symmetric monovalent electrolyte, the Boltzmann distribution givesPositive co-ions are depleted near the positive plate, while negative counterions accumulate. Both approach the same bulk density as the potential decays. Attraction and repulsion by the surface compete with mixing entropy, so diffuse ions do not simply collapse into one plane. The compact Stern layer represents finite closest approach and specifically associated charge; the diffuse continuum begins outside it. For large potentials the linear exponential potential needs the nonlinear Poisson-Boltzmann equation, though the far-field screening scale remains the same in this simple electrolyte.