Stabilisation of the Resulting Dispersion

When charged colloidal particles in a dispersion approach each other such that the double layers begin to overlap (when particle separation becomes less than twice the double layer extension), then repulsion will occur. The individual double layers can no longer develop unrestrictedly, as the limited space does not allow complete potential decay [10, 11]. The potential v j2 half-way between the plates is no longer zero (as would be the case for isolated particles at 00). For two spherical particles of radius R and surface potential and condition x i 3 (where k is the reciprocal Debye length), the expression for the electrical double layer repulsive interaction is given by Deryaguin and Landau [10] and Verwey and Overbeek [11], 

The above expression shows an exponential decay of G i with h. The higher the value of K (i.e., the higher the electrolyte concentration), the steeper the decay this means that at any given distance h, the double layer repulsion will decrease with an increase of electrolyte concentration. 

Most qualitative aspects of the microscopic theory given by Equations (13.7-13.12) are fully confirmed the only exception concerns the decay of with h at large separations. Owing to the time required for electromagnetic waves to cover the distance between the particles, the h dependence in Equation (13.7) gradually changes to h dependence at large separations, a phenomenon known as retardation. 

The combination of G j and G results in the well-known theory of stability of colloids (DLVO theory) [8,10, 11], 

At long distances of separation, GA Gel, resulting in a shallow minimum (secondary minimum), whereas at very short distances, resulting in a 

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Shell developed a special line of polymer polyols based exclusively on styrene [11], the stabilisation of the resulting dispersion of polystyrene in liquid polyether being given by special NAD [8, 9, 32, 33] and of course not to the graft species, which in the case of polystyrene are practically absent. 

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