Electrical double effective thickness

An illustration of the effect of micelle/nanoparticle volume fraction on contact line motion is found in [57]. They used 0.1 M NaCl solution to reduce the electrical double layer thickness surrounding the NaDS micelle. At a given number concentration of micelles, decreasing the size of each micelle decreases the volume fraction greatly, since the volume of each spherical micelle varies as the third power of the radius. Thus, the addition of electrolyte effectively reduced the micellar volume fraction in the aqueous medium. The authors found that the oil droplet that would otherwise become completely detached from the solid surface, came back to reattach itself to the solid when electrolyte was present. They rationalized this finding as being caused by the inability of the weakened structural disjoining forces to counteract the attraction of the oil drop to the solid surface. 

Two additional stabilizing influences will be summarized next that of viscoelastic films and that of solid-particle films. In general, where electrical surface charge is an important determinant of stability, it is easier to formulate a very stable O/W emulsion than a W/O emulsion because the electric double layer thickness is much greater in water than in oil. (This is sometimes incorrectly stated in terms of greater charge being present on droplets in an O/W emulsion.) However, there are ways to effectively stabilize W/O emulsions. 

A linear relationship exists between the ESA or CVP amplitude and the volume fraction of the suspended particles. At relatively high-volume fractions, hydrodynamic and electric double-layer interactions lead to a non-linear dependence of these two effects on volume fraction. Generally, non-linear behavior can be expected when the electric double-layer thickness is comparable to the interparticle spacing. In most aqueous systems, where the electric double layer is thin relative to the particle radius, the electro-acoustic signal will remain linear with respect to volume fraction up to 10% by volume. At volume-fractions that are even higher, particle-particle interactions lead to a reduction in the dynamic mobility. 

Steric stabilization of a colloidal dispersion is achieved by attaching long-chain molecules to colloidal particles (Fig. 3.6). Then when colloidal particles approach one another (for example due to Brownian motion), the limited interpenetration of the polymer chains leads to an effective repnlsion which stabilizes the dispersion against flocculation. Steric stabilization has several advantages compared to charge stabilization. First, the interparticle repulsion does not depend on electrolyte concentration, in contrast to charge-stabilized colloids where the electric double-layer thickness is very sensitive to ionic strength. Second, steric stabilization is effective in both... 

Equation 46 suggests that, maintaining pi constant, q, must depend linearly on if only a first-order electroviscous effect exists, and an increase in the electrolyte concentration implies a decrease in the thickness, 1/k, of the electrical double layer. 

The concept of surface concentration Cg j requires closer definition. At the surface itself the ionic concentrations will change not only as a result of the reaction but also because of the electric double layer present at the surface. Surface concentration is understood to be the concentration at a distance from the surface small compared to diffusion-layer thickness, yet so large that the effects of the EDL are no fonger felt. This condition usually is met at points about 1 nm from the surface. 

Table 1. Effect of buffer concentration c on thickness of the electrical double layer 6 [33]...

Finally, if the thickness of the electrical double layer (diffuse layer) in the droplet is comparable with r, the r dependence of kqbs will be dependent on the TBA+ concentration in the droplet since the spatial distribution of the inner electric potential of the droplet varies with [TBA+TPB ], However, since results analogous with those in Figure 14a ([TBA+TPB ] = 10 mM) have been obtained even at [TBA+TPB"] = 5mM (Aodiffuse layer effect does not contribute to the r effect on kobs at r > 1 /an. 

A quantitative treatment of the effects of electrolytes on colloid stability has been independently developed by Deryagen and Landau and by Verwey and Over-beek (DLVO), who considered the additive of the interaction forces, mainly electrostatic repulsive and van der Waals attractive forces as the particles approach each other. Repulsive forces between particles arise from the overlapping of the diffuse layer in the electrical double layer of two approaching particles. No simple analytical expression can be given for these repulsive interaction forces. Under certain assumptions, the surface potential is small and remains constant the thickness of the double layer is large and the overlap of the electrical double layer is small. The repulsive energy (VR) between two spherical particles of equal size can be calculated by ... 

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