One method is to give every particle a sufficiently large surface charge density of the same sign. For example, attach ionizable sulfonate groups covalently to the surface. Dissociation leaves negatively charged surface groups and releases mobile positive counterions into the water. A surfactant with a strongly bound head group can provide another charging route, provided it does not desorb during the experiment.
Each charged particle is surrounded by an electric double layer. As two such particles approach, overlap of these ionic clouds raises the electrostatic and ionic free energy, producing repulsion. In a dilute electrolyte, the range is set by the Debye–Hückel screening length,
For identical weakly charged spheres a representative screened Coulomb pair potential is
Its sum with the Van der Waals force attraction is the DLVO theory pair potential. Choose the charging level so that the repulsive barrier is many high; particles then rarely reach the primary attractive well during the observation time. This is kinetic stabilization rather than removal of all attraction.
Deionized water is useful because low added ionic strength gives a long-ranged repulsion. It does not mean that the charged dispersion contains no ions: the surface's own counterions are unavoidable and contribute to screening. Surface dissociation, contamination and particle concentration therefore matter even without added salt. An alternative valid route is a dense, firmly attached layer of water-soluble polyethylene glycol, producing steric stabilization without relying on a large electrostatic barrier.
In a magnesium chloride chemical solution, the principal pair interactions are hard sphere exclusion, repulsion of overlapping electric double layers, and attractive Van der Waals forces. The positive surface attracts chloride counterions and repels magnesium coions; mobile ions screen the bare Coulomb's law interaction. The competition between screened electrostatic repulsion and Van der Waals force attraction is described by DLVO theory.
For well-separated identical weakly charged spheres, the approximate repulsive pair potential energy, at centre separation , is
It is a screened Coulomb pair potential. An attractive Hamaker constant adds a negative short-range contribution, while overlap is forbidden. Very near contact, solvation and molecular surface structure can also matter. No polymer-induced interaction should be assumed before polymer is added in part (f).
A screened Coulomb pair potential models the effective electrostatic interaction of particles in an electrolyte. For identical weakly charged spheres of radius , charge , and Debye–Hückel screening length , a common pairwise approximation is for . The near-contact interaction can require more detailed boundary conditions or nonlinear screening. Charge, screening length and temperature all matter to a resulting phase diagram.