Repulsion double layer

An electrical double layer can be created at the solid/hquid or liquid/hquid interface by charge separation due to the presence of ionogenic groups (e.g. -OH, -COOH) or by adsorption of ionic surfactants at the interface. 

The double layer is characterised by the surface charge (cro), the charge in the Stern layer (o-g), the charge of the diffuse layer era (note that ao = as+ aa) the surface potential ( T)q and the Stern potential Ta ( zeta potential). 

The double layer extension is determined by the electrolyte concentration and the valency of the counter ions, as given by the reciprocal of the Debye-Huckel parameter (1 /k) - referred to as the thickness of the double layer, 

The double layer thickness increases with decreasing electrolyte concentration, 10 mol dm NaCl (1/jc) - 100 nm and 10 mol dm NaCl (1/k) = 10 nm. 

When two particles or droplets with double layers of the same sign approach to a separation h that is smaller than twice the double layer thickness, double layer repulsion occurs, since the two double layers carmot be frdly extended in the confined space. This leads to repulsion energy Gei, which is given by 

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A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

Using the conditions of the Langmuir approximation for the double-layer repulsion, calculate for what size particles in water at 25°C the double-layer repulsion energy should equal kT if the particles are 40 A apart. 

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 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. 

A lack of an explicit concentration value indicates, that the value of iip c did not depend upon the concentration. DR = Double layer repulsion method, H = Hardness measurements, T = Tensammetiy (for details see text). See also list of symbols. 

Prieve, D. C. (1986) Hydrodynamic measurement of double-layer repulsion between colloidal particle and flat plate. Science, 231, 1269-1270. 

Table 7.3 Colloid Stability as Calculated from van der Waals Attraction and Electrostatic Diffuse Double-Layer Repulsion >b)...

In Fig. 7.4 the energies of interaction (double-layer repulsion, VRl and van der Waals attraction, Va, and net total interaction, Vj) were plotted as a function of distance of the separation of the surfaces. As (2a) of Table 7.3 shows, Vr decreases in... 

Figure 2.7. Force-distance profiles at different CTAB surfactant concentrations. Droplet radius = 98 nm. The continuous fines are the best fits obtained with Eqs. (2.14), (2.15) (for double-layer repulsion), and (2.17) (for depletion attraction). (Adapted from [22].)...

O. Mondain-Monval, F. Leal-Calderon, J. PhUlip, and J. Bibette Depletion Forces in the Presence of Electrostatic Double-Layer Repulsion. Phys. Rev. lett. 75, 3364 (1995). 

Interaction Energy Expressions. Previous papers (8,10,12,13) have used exact sphere-plane interaction energy expressions to approximate the sphere-cylinder Interaction. In this work, these exact expressions were replaced with recently published approximate expressions. For the double layer repulsion, this avoided the inconvenience and Inaccuracy of using tabular values ( ) while for the van der Waals attraction, using the approximate solution simplified the programing task. 

The previously mentioned expressions were originally derived by Bell et al. (36) to calculate the double layer repulsion. 

Fig. 1.6 DLVO interactions showing the energetics of colloidal particles as a competition between electrostatic double-layer repulsion and van der Waals attractions. The primary minimum is due to strong short-range electron overlap repulsion (shown in Figure 1.4... 

The contribution of double-layer forces to the osmotic pressure of HIPEs was also investigated [98], These forces arise from the repulsion between adjacent droplets in o/w HIPEs stabilised by ionic surfactants. It was observed that double-layer repulsive forces significantly affected jt for systems of small droplet radius, high volume fraction and low ionic strength of the aqueous continuous phase. The discrepancies between osmotic pressure values observed by Bibette [97] and those calculated by Princen [26] were tentatively attributed to this effect. 

Finally, some studies have been performed on the addition of salt to the aqueous phase of oil-in-water HIPEs [109]. For systems stabilised by ionic surfactants, increasing salt concentration reduces the double-layer repulsion between droplets however, stability is more or less maintained, probably due to steric and polarisation repulsions. Above a sufficiently high salt concentration, emulsions become unstable due to salting-out of the surfactant into the oil-phase. For nonionic surfactants, the situation is similar, except that there are no initial double-layer forces. In addition, Babak [115] found that increasing the electrolyte concentration reduced the barrier to coagulation between emulsion droplets, and therefore increased coalescence. Generally, therefore, stability of o/w HIPEs is not enhanced by salt addition. 

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