Electrical double layer theory

The adhesion between two solid particles has been treated. In addition to van der Waals forces, there can be an important electrostatic contribution due to charging of the particles on separation [76]. The adhesion of hematite particles to stainless steel in aqueous media increased with increasing ionic strength, contrary to intuition for like-charged surfaces, but explainable in terms of electrical double-layer theory [77,78]. Hematite particles appear to form physical bonds with glass surfaces and chemical bonds when adhering to gelatin [79]. 

B. Short Overview Concerning the Electrical Double Layer Theory... 

Studies of theadsorption of surface-active electrolytes at the oil,water interface provide a convenient method for testing electrical double-layer theory and for determining the state of water and ions in the neighborhood of an interface. The change in the surface amount of the large ions modifies the surface charge density. For instance, a surface ionic area of 100 per ion corresponds to 16 pC per square centimeter. " " ... 

Further stability models based on surface area, equilibrium water-content-pressure relationships, and electric double-layer theory can successfully characterize borehole stability problems [1842]. The application of surface area, swelling pressure, and water requirements of solids can be integrated into swelling models and mud process control approaches to improve the design of water-based mud in active or older shales. 

Gur, Y. Ravina, I. Babchin, A. J., On the electrical double layer theory. II. The Poisson-Boltzman equation including hydration forces, J. Colloid Inter. Sci. 64, 333-341... 

Vorotyntsev, M. A., and A. A. Kornyshev, Models for description of collective properties of the metal/electrolyte contact in the electrical double-layer theory, Elektrokhimiya, 20, 3 (1984). 

Some emphasis is given in the first two chapters to show that complex formation equilibria permit to predict quantitatively the extent of adsorption of H+, OH , of metal ions and ligands as a function of pH, solution variables and of surface characteristics. Although the surface chemistry of hydrous oxides is somewhat similar to that of reversible electrodes the charge development and sorption mechanism for oxides and other mineral surfaces are different. Charge development on hydrous oxides often results from coordinative interactions at the oxide surface. The surface coordinative model describes quantitatively how surface charge develops, and permits to incorporate the central features of the Electric Double Layer theory, above all the Gouy-Chapman diffuse double layer model. 

Thus summarizing, we note that at the leading order the asymptotic solution constructed is merely a combination of the locally electro-neutral solution for the bulk of the domain and of the equilibrium solution for the boundary layer, the latter being identical with that given by the equilibrium electric double layer theory (recall (1.32b)). We stress here the equilibrium structure of the boundary layer. The equilibrium within the boundary layer implies constancy of the electrochemical potential pp = lnp + ip across the boundary layer. We shall see in a moment that this feature is preserved at least up to order 0(e2) of present asymptotics as well. This clarifies the contents of the assumption of local equilibrium as applied in the locally electro-neutral descriptions. Recall that by this assumption the electrochemical potential is continuous at the surfaces of discontinuity of the electric potential and ionic concentrations, present in the locally electro-neutral formulations (see the Introduction and Chapters 3, 4). An implication of the relation between the LEN and the local equilibrium assumptions is that the breakdown of the former parallel to that of the corresponding asymptotic procedure, to be described in the following paragraphs, implies the breakdown of the local equilibrium. 

The results of these measurements are in reasonable agreement with predictions based on electric double layer theory, especially at separations greater than 1 Ik. 

Figure 10.4 shows the results of some measurements on aqueous sodium oleate films. The sensitivity of the equilibrium film thickness to added electrolyte reflects qualitatively the expected positive contribution of electric double layer repulsion to the disjoining pressure. However, this sensitivity to added electrolyte is much less than that predicted from electric double layer theory and at high electrolyte concentration an equilibrium film thickness of c. 12 nm is attained which is almost independent of the magnitude of the disjoining pressure. To account for this observation, Deryagin and Titijevskaya have postulated the existence of hydration layers... 

The surface compartment model (SCM)14,15, which is a theory of ion transport focused on ionic process in electrical double layers at membrane protein surfaces, can explain these phenomena. The steady state physical properties of the discrete surface compartments are calculated from electrical double layer theory. 

One item of considerable importance in electrical double layer theory is the potential energy of interaction between two charged surfaces in an electrolyte, V, from which one can derive the force, P, by differentiation. 

One other aspect of nonprimitive electric double layer theories which is particularly relevant to the inner Stern region are the models for the water molecule and the ions. The simplest models for a water molecule and an ion are a hard-sphere point dipole and point charge, respectively. A more realistic model of the hard-sphere water molecule would include quadrupoles and octupoles and also polarizability. However the hard-sphere property is best avoided and replaced, for example, by a Lennard-Jones potential. An alternative to a multipolar water model are three point charge sites associated with the atoms within the water molecule. 

Application of the electric double layer theory to soil minerals at a quantitative level is difficult because soil mineral surfaces at the microscopic scale are not well defined, that is, they are neither perfectly spherical nor flat, as the double layer requires. However, application of the double layer theory at a qualitative level is appropriate because it explains much of the behavior of soil minerals in solution, for example, dispersion, flocculation, soil permeability, and cation and/or anion adsorption. When equilibrium between the counterions at the surface (near the charged surface) and the equilibrium solution is met, the average concentration of the counterions at any... 

G. J. Hills and R. M. Reeves, J. Electroanal. Chem. 42 (1973) 355. 28R. Guidelli and W. Schmickler, Electrochim. Acta 45 (2000) 2317. 29W. Schmickler, Electrical Double-Layers Theory and Simulation, in Encyclopedia of Electrochemistry, Edited by AJ. Bard and M. Stratmann, Wiley-VCH, New York, 2002, Vol. I. 

Charge development on solid surfaces usually results from coordinative interactions at the solid surface. The surface coordinative model describes quantitatively how surface charge develops and permits us to incorporate the central features of the electric double-layer theory. 

The effect of surface charge on sorption (extent of complex formation) can be taken into account by applying a correction factor derived from the electric double-layer theory to the mass law constants for surface reactions. 

Several SCM s have been described in the literature. The more commonly used models include the Constant Capacitance Model (Schindler and Stumm, 1987), the Diffuse Double Layer Model (Stumm et al., 1970) and the Triple Layer Model (Davis et al., 1978 Yates et al, 1974). All are based on electric double layer theory but differ in their geometric description of the oxide-water interface and the treatment of the electrostatic interactions. 

PZC and lEP are important parameters for surface characterization of oxide minerals. The flotation of these minerals is best understood in terms of the electrical double layer theories. Simple oxide minerals such as hematite, goethite, magnetite and corundum float well with cationic collectors above their PZC. Fig. 3.14 shows the flotation of goethite using both anionic and cationic collectors. The PZC of this mineral is pH 6.7. Anionic collectors are effective for goethite below pH 6.7 since the mineral is then positively charged. 

Relationships of the type shown in equation 97 have been obtained for compacted clays (132) and soils (133) and are predicted by simple electrical double layer theory (21). 

The swelling effect results from additional embedding of water molecules into these thin layers. With the increase of the water content, the thickness of the water film increases. If the water is not pure, ion concentration results in a decrease of the film, which may be described by the electric double layer theory. As a consequence of this process, porosity and permeability will change. Swell-ing/shrinking is therefore a strong hydraulic-mechanic-chemical (HMC) coupling phenomenon. 

See, e.g., D. C. Grahame, The electrical double layer and the theory of electrocapillarity, Chem. Rev. 41 441 (1947) C. W. Outhwaite, Modihed Poisson-Boltzmann equatioh in electric double layer theory based on the Bogoliubov-Born-Green-Yvon integral equations, J.C.S. Faraday 7/74 1214 (1978) and the references cited therein. 

---