Electrical double layer repulsive interaction

For two spherical particles of radius R and surface potential and condition kR < 3, the expression for the electrical double layer repulsive interaction is given... 

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],... 

In another method, Roberts and Tabor201 measured the electric double layer repulsion between a transparent rubber sphere and a plane glass surface separated by surfactant solution. As the surfaces were brought together, the double-layer interaction caused a distortion of the rubber surface which was monitored interferometrically. 

Figure 8.it Schematic interaction energy diagrams for stericaliy stabilised particles (a) in the absence of electric double layer repulsion (V" = VA + Vs), (b) with electric double layer repulsion V = Vr + VA + Vs)... 

FIGURE 4.34 Schematic energy interaction diagrams for two sterically stabilized particles (a) without electrical double-layer repulsion (b) with electrical double-layer repulsion. 

It appears that the data obtained in the above manner prove to be reliable for inferring the charge-potential relationship. Therefore, Fig 3.45 provides convincing evidence that in the case considered double layer repulsive interaction under the conditions of constant charge of the diffuse electric layer is operative. If so, the first integration of Eq. (3.90) predicts that... 

Fig. 6.16. Interaction energies versus the mterparticle distances H for sterically stabilized particles (a) without electrical double layer repulsion (AGt = AGd + AGpoi,sO (b) with electrical double layer repulsion (AGj = AGd AGd + AGpoi,sd- For comparison the curves in the absence of AGd are also plotted. (After Pugh, Chap. 4 in Ref. [5].)...

Electrical Double Layer Repulsion. Double layer interaction theory has been extensively investigated independraitly by Deryagin and Landau, and Verwey and Overbeek, DVLO theory. There are many reviews on the application of DVLO theory to colloids [Shaw, 1989]. One expression for the repulsive energy between two small spheres is ... 

Even if the adsorbed stabilizing agent is non-ionic it will influence the electtostatic interactions by causing a displacement of the Stern plane away from the particle surface. This will increase the range of electric double layer repulsion and thus enhance the stability. 

Here we consider the total interaction between two charged particles in suspension, surrounded by tlieir counterions and added electrolyte. This is tire celebrated DLVO tlieory, derived independently by Derjaguin and Landau and by Verwey and Overbeek [44]. By combining tlie van der Waals interaction (equation (02.6.4)) witli tlie repulsion due to the electric double layers (equation (C2.6.lOI), we obtain... 

The interaction between two double layers was first considered by Voropaeva et a/.145 These concepts were used to measure the friction between two solids in solution. Friction is proportional to the downward thrust of the upper body upon the lower. However, if their contact is mediated by the electrical double layer associated with each interface, an electric repulsion term diminishes the downward thrust and therefore the net friction. The latter will thus depend on the charge in the diffuse layer. Since this effect is minimum at Eam0, friction will be maximum, and the potential at which this occurs marks the minimum charge on the electrode. 

The situations would be totally different when the two surfaces are put in electrolyte solutions. This is because of formation of the electrical double layers due to the existence of ions in the gap between solid surfaces. The electrical double layers interact with each other, which gives rise to a repulsive pressure between the two planar surfaces as... 

A force-distance curve between layers of the ammonium amphiphiles in water is shown in Figure 8. The interaction is repulsive and is attributed to the electric double-layer... 

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