The Coulombic Attraction Theory of Colloid Stability

We presume that the electric charge of the plate particle is distributed uniformly on the surface. Thus, if the nth plate, whose center of mass is situated at Xn, has the thickness 2an, the charge-distribution function is given by 

Because this result has been obtained by solving a generalized Poisson-Boltzmann equation with the linearization approximation, it is necessary to compare it with the DLVO theory in the limit where the Debye approximation holds. In this case, Verwey and Overbeek [2], working in cgs (centimeter-gram-second) units, derived the following approximate equation for the repulsive potential  

Now 70 is the surface charge density, such that 70 = Zne, where Zn is the valency of the nth plate in number of charges per unit area, so this expression becomes 

Both theories are based on the calculation of the electrical contribution to the free energy of the region bounded by the macroions. In both theories it is assumed that (a) the motion of the macroions is adiabatically cut off from that of the simple 

If you like, FR(DLVO) = U m (SI) for the Helmholtz free energy of the interaction for two flat plates is our baseline, a point at which everyone can agree. It was the next step in the SI formalism, the calculation of the Gibbs free energy, that sundered the colloid world. It may seem incredible to scientists outside the held that the basic thermodynamic relation 

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The thermodynamic stability of the colloidal gel state has a perfectly natural explanation in terms of the coulombic attraction theory. Just as —> 0 as Xm —> 2a,... 

In aqueous suspension, the stability is discussed in reference to the DLVO (Deryaguin-Landau-Verway-Overbeek) theory. Within this framework, all solid substances have a tendency to coagulate due to their large van der Waals attractive force. The coulombic repulsive force among colloidal particles more or less prevents this tendency. These two opposite tendencies determine the stability of suspensions. What kind of parameters are concerned in the present nonaqueous system, for which little is known about the stability This is an interest in this section. 

Many properties of disperse systems are related to the distribution of charges in the vicinity of the interface due to the adsorption of electrolytes. The adsorption of molecules is driven by the van der Waals attraction, while the driving force for the adsorption of electrolytes is the longer-range electrostatic (Coulomb) interaction. Because of this, the adsorption layers in the latter case are less compact than in the case of molecular adsorption (i.e., they are somewhat extended into the bulk of the solution), and the discontinuity surface acquires noticeable, and sometimes even macroscopic thickness. This diffuse nature of the ionized adsorption layer is responsible for such important features of disperse systems as the appearance of electrokinetic phenomena (see Chapter V) and colloid stability (Chapters VII, VIII). Another peculiar feature of the adsorption phenomena in electrolyte solutions is the competitive nature of the adsorption in addition to the solvent there are at least two types of ions (even three or four, if one considers the dissociation of the solvent) present in the system. Competition between these ions predetermines the structure of the discontinuity surface in such systems -i.e. the formation of spatial charge distribution, which is referred to as the electrical double layer (EDL). The structure and theory of the electrical double layer is described in detail in textbooks on electrochemistry. Below we will primarily focus on those features of the EDL, which are important in colloid... 

Though the theory of Derjaguin-Landau-Verwey-Overbeek (DLVO) [17, 18] was essentially designed for hydrophobic colloids, it is often applied to the analysis of the stability of polyelectrolyte solutions. According to this approach an overlap of the electrical double-layers of two charge-like colloidal spheres in an electrolyte solution always yields a repulsive screened Coulomb interaction, and the van der Waals forces are responsible for the attraction. A number of experiments in the recent decades, however, provide evidence that the effective interparticle potential shows a long-range attraction which cannot be ascribed to the van der Waals forces [15, 88-93], In spite of numerous theoretical attempts to explain this phenomena (for a review see [7, 8, 10, 94,... 

DLVO theory [1-3] describes the stabilization of colloidal dispersions by an interplay of van der Waals and electrostatic forces (as opposed to steric repulsions of colloids by polymeric solubilizers). The theory was developed in the 1940s by Derjaguin and Landau [4] and by Verwey and Overbeek [5]. In DLVO theory, the two determining interactions for the stability of a colloidal system are the attractive van der Waals interactions between the colloidal particles and the repulsive electrostatic Coulomb interactions. When salt is added, the alteration of the electrostatic interactions affects the stability. 

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