Electric double-layer repulsion, related

The theory has certain practical limitations. It is useful for o/w (od-in-water) emulsions but for w/o (water-in-oil) systems DLVO theory must be appHed with extreme caution (16). The essential use of the DLVO theory for emulsion technology Hes in its abdity to relate the stabdity of an o/w emulsion to the salt content of the continuous phase. In brief, the theory says that electric double-layer repulsion will stabdize an emulsion, when the electrolyte concentration in the continuous phase is less than a certain value. 

As a related matter it is easily understood that addition of salts at a certain concentration destabilizes an emulsion. It may be concluded that if an emulsion remains stable at electrolyte contents higher than those cited in the preceding paragraphs, the stabiUty is not the result of electric double-layer repulsion, which may be useful information to find the optimum manner for destabilization. 

Ionic compounds such as halides, carboxylates or polyoxoanions, dissolved in (generally aqueous) solution can generate electrostatic stabilization. The adsorption of these compounds and their related counter ions on the metallic surface will generate an electrical double-layer around the particles (Fig. 1). The result is a coulombic repulsion between the particles. If the electric potential associated with the double layer is high enough, then the electrostatic repulsion will prevent particle aggregation [27,30]. 

The physicochemical forces between colloidal particles are described by the DLVO theory (DLVO refers to Deijaguin and Landau, and Verwey and Overbeek). This theory predicts the potential between spherical particles due to attractive London forces and repulsive forces due to electrical double layers. This potential can be attractive, or both repulsive and attractive. Two minima may be observed The primary minimum characterizes particles that are in close contact and are difficult to disperse, whereas the secondary minimum relates to looser dispersible particles. For more details, see Schowalter (1984). Undoubtedly, real cases may be far more complex Many particles may be present, particles are not always the same size, and particles are rarely spherical. However, the fundamental physics of the problem is similar. The incorporation of all these aspects into a simulation involving tens of thousands of aggregates is daunting and models have resorted to idealized descriptions. 

In order to explain this effect it was assumed that micelles can be formed by fusion of two smaller aggregates and can disappear by fission into two small particles [116]. The aggregates formed by ionic surfactants are charged particles. At low concentrations they are stable in relation to coagulation because of repulsive electrostatic forces. When the concentration of counterions increases, the electric double layer around the aggregates shrinks, the repulsive electrostatic forces between the aggregates decrease, and the reversible fusion and fission processes can proceed... 

The interaction between two charged particles in a polar media is related to the osmotic pressure created by the increase in ion concentration between the particles where the electrical double-layers overlap. The repulsion can be calculated by solving the Poisson-Boltzmann equation, which describes the potential, or ion concentration, between two overlapping double-layers. The full theory is quite complicated, although a simplified expression for the double-layer interaction energy, V dl( ) between two spheres, can be written as follows ... 

A remarkable point about eq. (41) is that it contains neither the electric surface potential or z) nor the plate distance 2d, but only the electric potential midway between the plates ( or u). But the relation between z, u, and d being rather complicated (cf. Chapter IV), it is impossible to integrate eq. (41), for, a given value of pQ, with respect to the distance. Hence there is no advantage in using this force equation to evaluate the repulsive potential Vr, for a system of two plane double layers, on the basis of the complete differential equation (3). 

They result from the interaetion of the double electric layers. For identical particles, they are repulsive. When two partieles approach one another, the diffuse parts of the double layers repel. If they are eompressed too much, the Stem layers also enter into interaction. The ealculation of the interaetion potential energy Vr, based on the duration of colhsions and the relaxation times of the layers, is complex. If the overlapping of the layers is weak, the approximate expression of the potential interaction energy is given by the relation ... 

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