Long-range electrical double layer

Another possible approach solving the equilibrium distribution for an electric double layer is offered by integral equation theories [22]. They are based on approximate relationships between different distribution functions. The two most common theories are Percus-Yevick [23] and Hypernetted Chain approximation (HNQ [24], where the former is a good method for short range interactions and the latter is best for long-range interactions. They were both developed around 1960, but are still used. The correlation between two particles can be divided into two parts, one is the direct influence of particle j on particle i and the other originates from the fact that all other particles correlate with particle j and then influence particle i in precisely... 

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,... 

The thermodynamics of adsorption of ionic surfactants is more complicated (in comparison with that of nonionics) because of the presence of long-range electrostatic interactions and, in particular, of an electric double layer (EDL) in the system (Figure 5.1). The electrochemical potential of the ionic species can be expressed in the form ... 

The stress defined by Equation (6) represents the interaction between surfaces due to the macromolecules in solution. To obtain the total stress, contrioutions of long range colloidal forces between the oilayers themselves must be added to (Tp. For phospholipid oilayers, the added stress can be expressed as the sum of a strong exponential repulsion due to hydration forces, a weak power law attraction for the van der Waals force, and exponential repulsion due to electric double layer forces (1-2),... 

In summary, electrochemical promotion may be regarded as catalysis in an electric double layer controlled by current or potential application. The necessary condition to achieve electrochemical promotion is the formation of a double layer at the catalyst/gas interface by the mechanism of ion backspillover from the solid electrolyte support. This may occur over a wide range of conditions. The most important experimental parameters, which favor electrochemical promotion are the following long tpb (porous catalyst), moderate diffusion length (thin catalyst film), and adequate temperature range,... 

In view of the distance over which electrical double layers extend into the solution, interaction between double layers become effective at a separation between the surfaces of at least a few nanometers. Hence, electrical double layer forces can be considered as long-range forces they operate over distances comparable to those over which dispersion forces between particles of colloidal dimensions reach significant magnitudes. 

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