Stabilization, electrostatic diffuse-layer

Barkey, Tobias and Muller formulated the stability analysis for deposition from well-supported solution in the Tafel regime at constant current [48], They used dilute-solution theory to solve the transport equations in a Nernst diffusion layer of thickness S. The concentration and electrostatic potential are given in this approximation... 

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

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 ... 

At low concentrations of dissolved organic matter (DOM) (<0.01 mg of C/L) and at low ionic strength (10-3 M), the hematite particles are positively charged at this pH and are stabilized electrostatically by interacting diffuse layers with characteristic (Debye) lengths of 10 nm. As the ionic strength is increased to 10 1 M at these low DOM concentrations, the diffuse layers are compressed to 1 nm, and attractive van der Waals forces promote attachment in classical Derjaguin-Landau-Verwey-Overbeek (DLVO) destabilization by what has been termed double-layer compression. 

The speculation continues here into estuarine waters, bounded in this analysis at both inlet and outlet by waters that can, in the presence of suitable NOM, yield stable colloids. Diffuse layer thicknesses in these waters are small, on the order of 1 nm at 7 = 0.1. There can be sufficient salt in these waters to prevent classical DLVO electrostatic stabilization this is the conventional view. There may also be insufficient salt to form a thick layer of adsorbed NOM by screening of intra- and intermolecular repulsive interactions of the molecules of NOM. The result would then be a region of ionic strength or salinity in an estuary within which colloidal particles have a minimum stability and a maximum sticking probability. This possibility is shown by the proposed relationship between a and ionic strength shown in Figure 12. 

The electrostatic interaction between diffuse layers of ions surrounding particles is one of the most thoroughly theoretically developed factors of colloid stability. The theory of electrostatic factor is, essentially, the basis for the quantitative description of coagulation by electrolytes. This theory was developed in the Soviet Union by B.V. Derjaguin and L.D. Landau in 1935 -1941, and independently by the Dutch scientists E.Verwey and T. Overbeek, and is presently known by the initial letters of their names as the DL VO theory [44,45]. The DLVO theory is based on comparison of molecular interaction between the dispersed particles in dispersion medium and the electrostatic interaction between diffuse layers of ions, with Brownian motion of particles taken into account (in the simplest version of theory this is done on a qualitative level). 

The repulsive forces arise from the electromagnetic interactions of the charged layer surrounding the particles, the so-called electrical double layer. On the surface of the particles, a charged layer may be formed due to selective adsorption of ions. This part of the double layer is immobile and consists of tightly adsorbed ions in direct contact with the particle surface. In the solution adjacent to the particle, a second layer, in which the ions are more diffusely distributed, penetrates into the liquid. This part of the double layer is termed the diffusion layer. The extent of this diffusion layer depends on the electrolyte concentration increasing electrolyte concentration causes this diffuse double layer to shrink closer in to the particle, so that the electrostatic potential falls off more quickly with distance. The process by which the particles are stabilized by the repulsive forces of the electrical double layers is known as electrostatic stabilization. 

Simple ions and molecule dispersants are most mainly used in aqueous suspensions. They are inorganic compounds, including salts, acids, and bases, which are also known as electrolytes. Selective adsorption of one type of ions onto the particle surface coupled with the formation of a diffuse layer of the counterions, i.e., ions with opposite charge, provides electrostatic stabilization, due to the repulsion between the double layers. The stability of the suspensions is influenced through control the repulsion force between the particles, by the valence and radius of the counterions. According to the Schulze-Hardy mle, the higher the valence of the counterions, the more effective they will be, while for ions with the same valence, the smaller the ions the more effective the dispersants are. 

Tle(h) - Ionic molecules in water give rise to double layers at the fluid-fluid and at the fluid-solid interfaces that consist of a compact surface charged layer and a diffuse layer of counterions (see Figure 2). As a film thins, the counterions of the two double layers approach each other and repulsion of these double layers takes place. This repulsion stabilizes the film by preventing further thinning and creates the electrostatic component of the disjoining pressure. 

The first example (Fig. 5.70a) involves dipping a solid into an aqueous salt solution, thus, creating a soHd-liquid interface. Either cations or anions will be preferentially adsorbed on the smface, and the result is an excess surface charge. The coimter-charge is distributed in the zone of the solution adjacent to the interface the extent of this zone is determined by the Debye length (see Eq. (5.203)). It is inversely proportional to the square root of charge carrier concentration in the bulk solution. A rigid double-layer is formed in a concentrated solution in dilute solution a diffuse layer is formed with appreciable extension (typical numbers are several tens of nanometres). Such electrostatic effects are responsible for the kinetic stability of dispersed systems in colloid chemistry . 

In a qualitative way, colloids are stable when they are electrically charged (we will not consider here the stability of hydrophilic colloids - gelatine, starch, proteins, macromolecules, biocolloids - where stability may be enhanced by steric arrangements and the affinity of organic functional groups to water). In a physical model of colloid stability particle repulsion due to electrostatic interaction is counteracted by attraction due to van der Waal interaction. The repulsion energy depends on the surface potential and its decrease in the diffuse part of the double layer the decay of the potential with distance is a function of the ionic strength (Fig. 3.2c and Fig. 

The micellar surface has a high charge density and the stability of the aggregate is heavily dependent on the binding of counterions to the surface. From the solution of the Poisson-Boltzmann equation one finds that a large fraction (0.4—0.7) of the counterions is in the nearest vicinity of the micellar surface300. These ions could be associated with the Stern layer, but it seems simpler not to make a distinction between the ions of the Stern layer and those more diffusely bound. They are all part of the counterions and their distribution is primarily determined by electrostatic effects. 

The details of the influence that electrostatic surface forces on the stability of foam films is discussed in Section 3.3. As already mentioned, the electrostatic disjoining pressure is determined (at constant electrolyte concentration) by the potential of the diffuse electric layer at the solution/air interface. This potential can be evaluated by the method of the equilibrium foam film (Section 3.3.2) which allows to study the nature of the charge, respectively, the potential. Most reliable results are derived from the dependence foam film thickness on pH of the surfactant solution at constant ionic strength. The effect of the solution pH is clearly pronounced the potential of the diffuse electric layer drops to zero at certain critical pH value. We have named it pH isoelectric (pH ). As already mentioned pH is an intrinsic parameter for each surfactant and is related to its electrochemical behaviour at the solution/air interface. Furthermore, it is possible to find conditions under which the electrostatic interactions in foam films could be eliminated when the ionic strength is not very high. 

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