Interaction of double layers

Following the treatment of Ottewill and Watanabe [9-11], the total energy K of interaction of double layers can be expressed in terms of the Stern potential to yield an expression for the stability ratio in terms of ij/s, namely. 

In this chapter IV we restrict the treatment to single double layers in equilibrium, postponing electrokinetics to chapter V and interaction of double layers to chapter VI. 

This change of the free energy is equal to the amount of work that has to be per-formed against the forces arising from the interaction of double layers ... 

Although many characteristic features of the interaction of double layers, including a general survey of the conditions of the stability of hydrophobic colloids may be derived from our knowledge of the interaction of two infinitely large flat surfaces, in practical... 

In order to complete the picture of the interaction of double layers, it is still necessary to take account of the finite dimensions and the specific adsorbability of the ions as introduced by Stern (cf, chapter IV, 4b, p. 127) ... 

INTERRELATION OF PROMOTION, ELECTROCHEMICAL PROMOTION AND METAL-SUPPORT INTERACTIONS THE DOUBLE-LAYER MODEL OF CATALYSIS... 

Hence, for two similarly charged surfaces in electrolyte, interactions are determined by both electrostatic doublelayer and van der Waals forces. The consequent phenomena have been described quantitatively by the DLVO theory [6], named after Derjaguin and Landau, and Verwey and Over-beek. The interaction energy, due to combined actions of double-layer and van der Waals forces are schematically given in Fig. 3 as a function of distance D, from which one can see that the interplay of double-layer and van der Waals forces may affect the stability of a particle suspension system. 

A polarizable Interface is represented by a (polarizable) electrode where a potential difference across the double layer is applied externally, i.e., by applying between the electrode and a reference electrode using a potentiostat. At a reversible interface the change in electrostatic potential across the double layer results from a chemical interaction of solutes (potential determining species) with the solid. The characteristics of the two types of double layers are very similar and they differ primarily in the manner in which the potential difference across the interface is established. 

Not only do double layers interact with double layers, the metal of one sphere also interacts with the metal of the second sphere. There is what is called the van der Waals attraction, which is essentially a dispersion interaction that depends on r-6, and the electron overlap repulsion, which varies as r-12. These interactions between the bulk... 

The total interaction between the two metal spheres can therefore be classified into two parts (1) the surface, or double-layer, interaction determined by the Gouy-Chapman potential t f0e"Krand (2) the volume, or bulk, interaction —Ar-6 + Br 12. The interaction between double layers ranges from indifference at large distances to increasing repulsion as the particles approach. The bulk interaction leads to an attraction unless the spheres get too close, when there is a sharp repulsion (Fig. 6.131). The total interaction energy depends on the interplay of the surface (double layer) and volume (bulk) effects and may be represented thus... 

The term tertiary electroviscous effect is applied to the changes in the conformation of poly electrolytes that are caused by //t/ramolecular double-layer interactions. It is customary to extend this definition to include all effects in which the geometry of the system is altered as a result of double-layer interactions. 

Why is it that the force of double-layer interactions for curved surfaces cannot be derived using osmotic pressure arguments as is done in the case of planar double layers ... 

Chapters 11 and 12 in the present edition focus exclusively on the theories of electrical double layers and forces due to double-layer interactions (Chapter 11) and electrokinetic phenomena (Chapter 12). Chapter 11 includes expressions for interacting spherical double layers, and both chapters provide additional examples of applications of the concepts covered. 

The influence of the electric potential of the surface of the drops was shown by Watanabe and Gotoh (W3) for the case of mercury droplets in aqueous solutions. In the case of oil drops in water the electric double layer is in the water phase, which makes possible a real interaction between the double layers of the two drops that approach each other. In the case of water drops in an oil phase, however, the electric double layers are on the inside of the drops, so that the interaction of these layers when two drops approach each other is much smaller [see Sonntag and Klare (S5)], which means that the potential barrier is much smaller or may even be absent, and the attraction by London-van der Waals forces predominates. This at least is a first explanation of why systems in which water is the dispersed phase show much higher interaction rates than systems in which oil is the dispersed phase. 

In the discussion of the different models for the structure of double layer developed up to this point, no specific interactions have been considered. However, specific adsorption is a common phenomena in electrochemistry. Since the interactions implied have to be very short range in nature, the chemisorbed species are strongly bound to the electrode surface with the locus of their centers being the inner Helmholtz plane (IHP, see Fig. 1.10), or compact part of the double layer. 

The crystal structure of [XeF5] AgF4] consists of alternate stacks of double layers of square-pyramidal XeFlj" cations and approximately square-planar AgF anions (site symmetry D2h, Ag-F = 190.2 pm). The XeFj- ion has C4v symmetry with Xe-F(ax) = 185.2, Xe-F(eq) = 182.6 pm, and F(ax)-Xe-F(eq) = 77.7°. Each cation lying on a 4-axis interacts with one bridging F ligand of each of four anions at 263.7 pm, as illustrated below ... 

Newton black films, which are the only ones that can exist in the absence of double layer interactions, can be obtained only if the disj oining pressure has a positive value (otherwise, the film will collapse). The extrema of the disjoining pressure are obtained through the derivation of eq 19 with respect to d... 

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