Double layer theories

The influence of the formation of the electrostatic potential on the adsorbent surface on the retention of a charged analyte could be introduced in an oversimplified form, assuming an ideal partitioning model on a flat surface, where the retention factor is related to the free Gibbs energy as 

In the presence of the double layer the free Gibbs energy of the analyte interaction with the surface will be 

Most of these theories have one significant drawback They are all derived for the flat open adsorbent surface, but HPLC adsorbents are porous materials with average pore size on the level of 100 A for bare material. After chemical modification of the original silica surface, the effective pore diameter decreases and the properties of electric double layer in the confined space of small pores are significantly different from that on the flat surface. 

Detailed and comprehensive discussion of double-layer-based theories of ion-pair and ion-exchange chromatography is given in good review by Stahlberg [136]. 

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Fig. V-5. The repulsive force between crossed cylinders of radius R (1 cm) covered with mica and immersed in propylene carbonate solutions of tetraethylammonium bromide at the indicated concentrations. The dotted lines are from double-layer theory (From Ref. 51).

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... 

In the potential region where nonequilibrium fluctuations are kept stable, subsequent pitting dissolution of the metal is kept to a minimum. In this case, the passive metal apparently can be treated as an ideally polarized electrode. Then, the passive film is thought to repeat more or less stochastically, rupturing and repairing all over the surface. So it can be assumed that the passive film itself (at least at the initial stage of dissolution) behaves just like an adsorption film dynamically formed by adsorbants. This assumption allows us to employ the usual double-layer theory including a diffuse layer and a Helmholtz layer. 

In order to describe the effects of the double layer on the particle motion, the Poisson equation is used. The Poisson equation relates the electrostatic potential field to the charge density in the double layer, and this gives rise to the concepts of zeta-potential and surface of shear. Using extensions of the double-layer theory, Debye and Huckel, Smoluchowski,... 

The role of electrolyte is critical in these nanoscopic interfaces, but is difficult to predict and quantify. For sufficiently large rigid interfacial structures, one can apply the model of electrolyte interaction with a single charged surface in Figure 1(a). The double-layer theories or the recent integral-equation theories have been applied. Reviews of this subject are available in the literature [4,5]. For electrolytes in a nanostructure, the double layers from two surfaces overlap and behave differently from the case of a single surface. Ad-... 

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. " " ... 

Conventional colloid chemistry and elaitrochemistry have always been clo ly related with each other, the keywords electrophoresis, double layer theory, and specific adsorption describing typical asp ts of this relationship. In more ro nt times, new aspects have arisen which again bring colloid chemistry into contact with modem developments in electrcolloidal particles as catalysts for electron transfer reactions and as photocatalysts. In fact, the similarity between the reactions that occur on colloidal particles and on compact electrodes has often been emphasized by calling the small particles microelectrodes . 

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. 

Clearly, then, the chemical and physical properties of liquid interfaces represent a significant interdisciplinary research area for a broad range of investigators, such as those who have contributed to this book. The chapters are organized into three parts. The first deals with the chemical and physical structure of oil-water interfaces and membrane surfaces. Eighteen chapters present discussion of interfacial potentials, ion solvation, electrostatic instabilities in double layers, theory of adsorption, nonlinear optics, interfacial kinetics, microstructure effects, ultramicroelectrode techniques, catalysis, and extraction. 

Unlike the rest of the chapter, here we adopt Gaussian electrostatic units which are typically used in the literature devoted to molecular capacitors and double layer theory. 

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). 

Largely through the painstaking work of Grahame in the 1940s, electrocapillarity effectively established the first experimental basis for the now accepted double layer theory. The basic picture of the electrode/electrolyte interface was thus in place. 

In this chapter, we discuss double layer theory and how it can be incorporated into a geochemical model. We will consider hydrous ferric oxide (FeOOH //IFO), which is one of the most important sorbing minerals at low temperature under oxidizing conditions. Sorption by hydrous ferric oxide has been widely studied and Dzombak and Morel (1990) have compiled an internally consistent database of its complexation reactions. The model we develop, however, is general and can be applied equally well to surface complexation with other metal oxides for which a reaction database is available. 

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