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The change from a positive surface potential to a negative potential outside the compact layer is consistent with specific phosphate adsorption that overcompensates the positive oxide charge. The negative compact-layer charge then has a diffuse excess of positive counterions. This charge reversal is an interfacial-chemistry interpretation, not something a single monotone double-layer profile with an unchanged positive boundary charge could generate by screening alone. Surface potential and zeta potential at a slip plane are distinct observables.

The Stern model separates the specifically adsorbed compact layer from a diffuse layer. In a spherical diffuse layer, a Poisson-Boltzmann equation description isAt sufficiently small $|z_{i}e\psi |/k_{B}T$, the Debye–Hückel approximation gives ${\nabla }^2\psi ={\kappa }^2\psi$. If $a_s$ is the outer compact-layer radius, its decaying solution isFor a locally flat surface, the geometric factor tends to unity. Thus the far-field negative potential approaches zero from below over the Debye–Hückel screening length. Neither $+120$ nor $-70\mathrm{mV}$ is safely in the low-potential linear regime at room temperature, so the simple exponential is a far-field approximation, not a globally valid fit. The phosphate layer requires adsorption chemistry or an equivalent specified boundary model.

DLVO theory adds attractive Van der Waals forces and electric double layer repulsion to obtain an effective colloid pair potential. For two identical spheres of radius $b$ at a surface gap $h\ll b$, a useful schematic form isHere $A_H$ is the Hamaker constant. For a symmetric monovalent electrolyte with number density $n$ of each ionic species, ${\kappa }_D^2=2n{e}^2/(ϵk_{B}T)$. The exponential is a simplified screened repulsion; its amplitude depends on electric potential at the surface, charge regulation and geometry. Constant-charge and constant-potential boundary conditions need not produce the same close-approach law.

A primary attractive minimum near contact may be separated from dispersed configurations by an energy barrier; a shallower secondary minimum can produce loose reversible aggregation. A barrier much larger than $k_{B}T$ can give long-lived kinetic stabilization without making the dispersed state the global free-energy minimum. Adding salt shortens the Debye–Hückel screening length and can lower the barrier, allowing colloidal coagulation. Changing pH can alter surface ionization, so screening alone does not determine stability.

One can vary salt concentration while holding particle concentration, temperature and pH fixed, then follow particle aggregation using light scattering or microscopy. A solvent-only control and an independently measured surface-charge indicator help distinguish a change of screening from adsorption or charge reversal. Classical DLVO theory omits steric stabilization, hydration forces and strong ionic correlations; the formal attraction diverging at contact is cut off by molecular-scale physics.