Repulsion, electric double-layer

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances 

The presence of the large repulsive potential barrier between the secondary minimum and contact prevents flocculation. One can thus see why increasing ionic strength of a solution promotes flocculation. The net potential per unit area between two planar surfaces is given approximately by the combination of Eqs. V-31 and VI-22  

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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. 

The relative value of the two potentials reveals the destabdization action of salts added to the emulsion. Addition of an electrolyte to the continuous phase causes a reduction of the electric double-layer repulsion potential, whereas the van der Waals potential remains essentially unchanged. Hence, the reduced electric double-layer potential causes a corresponding reduction of the maximum in the total potential, and at a certain concentration of electrolyte the maximum barrier height is reduced to a level at which the stabdity is lost. 

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. 

Electrical Double Layer repulsion affected by counter ions such as salts in solution availability of hydrophobic and hydrophilic groups. 

Electrical double-layer repulsion between two flat surfaces (unit, energy)... 

Flotation of Naturally Hydrophobic Minerals. Flotation response of naturally hydrophobic minerals correlates very well with elec-trokinetic measurements. Figure 3 shows that the flotation of coal correlates well with zeta potential of demineralized coal (5.). The flotation rate is maximum where the zeta potential is zero and it decreases with increase in the magnitude of the zeta potential. Similar observations were made earlier by Chander and Fuerstenau (6 ) for the flotation of molybdenite. The decrease in flotation rate with increase in zeta potential is because of the electrical double layer repulsion between the charged particle and the air bubble. 

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. 

The stability of many protected colloidal dispersions cannot be explained solely on the basis of electric double layer repulsion and van der Waals attraction other stabilising mechanisms must be investigated. Steric stabilisation is a name which is used (somewhat loosely) to describe several different possible stabilising mechanisms involving adsorbed macromolecules. These include the following ... 

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)... 

Electrical double layer repulsions (see page 212) Interparticle repulsion due to the overlap of similarly charged electric double layers is an important stabilising mechanism in O/W emulsions. 

When ionic emulsifying agents are used, lateral electric double layer repulsion may prevent the formation of a close-packed film. This film-expanding effect can be minimised by using a mixed ionic plus non-ionic film220 (see above) and/or by increasing the electrolyte concentration in the aqueous phase221. 

Figure 10.4 shows the results of some measurements on aqueous sodium oleate films. The sensitivity of the equilibrium film thickness to added electrolyte reflects qualitatively the expected positive contribution of electric double layer repulsion to the disjoining pressure. However, this sensitivity to added electrolyte is much less than that predicted from electric double layer theory and at high electrolyte concentration an equilibrium film thickness of c. 12 nm is attained which is almost independent of the magnitude of the disjoining pressure. To account for this observation, Deryagin and Titijevskaya have postulated the existence of hydration layers... 

If the balance of van der Waals attraction, electric double layer repulsion, capillary pressure, structure propagation, etc., favours an equilibrium film thickness, random fluctuations in film thickness will, in any case, tend to be neutralised. 

High electric double layer repulsion - increases disjoining pressure and reduces the rates of film thinning and rupture. 

Addition of soluble macromolecules (polymers) in the colloidal dispersion can stabilize the colloidal particles due to the adsorption of the polymers to the particle surfaces. The soluble polymers are often called protective agents or colloids. If the protective agents are ionic and have the same charge as the particles, the electrical double-layer repulsive forces will be increased and thus the stability of the colloidal particles will be enhanced. In addition, the adsorbed polymers may help weaken the van der Waals attraction forces among particles. However, the double-layer repulsion and the van der Waals attraction cannot account for the entire stabilization of the particle dispersions. 

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

Fig. 14.5. Experimental rejection (o) and theoretical prediction of the critical pressure for filtration of BSA in 0.001 M NaCI solution at pH 9 at a membrane of mean pore diameter 84 nm. Rejection is high below the critical pressure as electrical double layer repulsion prevents the protein (effective spherical diameter 6nm) from entering the membrane pores. As the critical pressure is approached, hydrodynamic forces increase and drive the...

Fig. 14.6. Filtration flux as a function of time of filtration for the filtration of O.Oi g/L silica particles in 0.001 M NaCI solution at pH 6 at a membrane of mean pore diameter 84 nm. The particle size was very close to the pore size. The critical transmembrane pressure for these conditions was calculated as 130 kPa. Operation below this pressure gives only a gradual decline in filtration flux with time. Operation above this pressure gives an initially higher filtration flux which declines rapidly with time. In the latter case the intial hydrodynamic force exceeds the electrical double layer repulsion between the membrane and the particles, causing the particles to block the membrane pores.

Electric double-layer repulsion—this repulsion acts to prevent collisions and aggregation. 

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].)...

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],... 

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