The critical coagulation concentration is the electrolyte concentration at which rapid, approximately diffusion-limited colloidal coagulation begins: the electrostatic barrier has become ineffective and nearly every sufficiently close encounter sticks. It is an operational threshold for the specified colloid and electrolyte, not a universal concentration or a guarantee of a mathematically exact zero barrier in every system.
DLVO theory adds short-range attractive Van der Waals forces to repulsive overlap of the electric double layer. Increasing salt concentration raises the ionic strength and shortens the Debye length, screening the repulsion. The repulsive barrier falls, so thermal collisions can carry particles into the primary attractive minimum and cause colloidal coagulation. An intermediate shallow secondary minimum can instead produce weak, potentially reversible association.
The figure's assignments are a: low salt; b: intermediate salt; c: high salt. Curve a has the largest protective barrier, b a lower barrier and secondary minimum, and c no effective repulsive barrier. This explanation assumes the surface charging chemistry does not independently reverse or radically change the surface potential.
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 at a surface gap , a useful schematic form is
Here is the Hamaker constant. For a symmetric monovalent electrolyte with number density of each ionic species, . 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 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.
Figure 1.
Original schematic pair potentials showing how a shorter screening length lowers a repulsive barrier
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