Diffuse electrical double layer

In 1910, Georges Gouy (1854-1926) and independently, in 1913, David L. Chapman (1869-1958) introduced the notion of a diffuse electrical double layer at the surface of electrodes resulting from a thermal motion of ions and their electrostatic interactions with the surface. 

Note that Eqs. (4) and (5) implicitly consider the transfer across the interface as the rate-determining step in the ion transfer processes [51], and neglect other steps involved in the process such as the ion transport across the diffusion boundary layers [55] and across the diffuse electrical double layer [50]. 

Double integration with respect to EA yields the surface excess rB+ however, the calculation requires that the value of this excess be known, along with the value of the first differential 3TB+/3EA for a definite potential. This value can be found, for example, by measuring the interfacial tension, especially at the potential of the electrocapillary maximum. The surface excess is often found for solutions of the alkali metals on the basis of the assumption that, at potentials sufficiently more negative than the zero-charge potential, the electrode double layer has a diffuse character without specific adsorption of any component of the electrolyte. The theory of diffuse electrical double layer is then used to determine TB+ and dTB+/3EA (see Section 4.3.1). 

Similar types of electric double layer may also be formed at the phase boundary between a solid electrolyte and an aqueous electrolyte solution [7]. They are formed because one electrically-charged component of the solid electrolyte is more readily dissolved, for example the fluoride ion in solid LaFs, leading to excess charge in the solid phase, which, as a result of movement of the holes formed, diffuses into the soUd electrolyte. Another possible way a double layer may be formed is by adsorption of electrically-charged components from solution on the phase boundary, or by reactions of such components with some component of the solid electrolyte. For LaFa this could be the reaction of hydroxyl ions with the trivalent lanthanum ion. Characteristically, for the phase boundary between two immiscible electrolyte solutions, where neither solution contains an amphiphilic ion, the electric double layer consists of two diffuse electric double layers, with no compact double layer at the actual phase boundary, in contrast to the metal electrode/ electrolyte solution boundary [4,8, 35] (see fig. 2.1). Then, for the potential... 

According to the Gouy-Chapman theory of the diffuse electric double layer (chapter 3 of [18]), for a uni-univalent electrolyte,... 

The generation of colloidal charges in water.The theory of the diffuse electrical double-layer. The zeta potential. The flocculation of charged colloids. The interaction between two charged surfaces in water. Laboratory project on the use of microelectrophoresis to measure the zeta potential of a colloid. 

Figure 6.2 The diffuse electrical double-layer in aqueous solution next to a flat surface.

Figure 6.7 Diagram of the diffuse electrical double-layer around a small, charged colloid.

Diffusion, of molecular species as well as colloidal particles, plays perhaps a more dominant role in many topics of interest to us. For example, without diffusion of ions we will not have the diffuse electrical double layers next to charged surfaces (discussed in Chapter 11). At the colloidal level, diffusion plays a central role in the transport and collision of particles in colloidal stability (discussed in Chapter 13). There are many more such examples. 

Since the electro-osinotic flow is induced by the interaction of the externally applied electric field with the space charge of the diffuse electric double layers at the channel walls, we shall concentrate in our further analysis on one of these 0 1 2) thick boundary layers, say, for definiteness, at... 

The characteristics of the diffuse electric double layer at a completely polarized interface, such as at a mercury/aqueous electrolyte solution interface are essentially identical with those found at the reversible interface. With the polarizable interface the potential difference is applied by the experimenter, and, together with the electrolyte, specifically adsorbed as well as located in the diffuse double layer, results in a measurable change in interfacial tension and a measurable capacity. 

Figure 4.2 illustrates several features of the diffuse electric double layer. The potential decreases exponentially with increasing distance. This decrease becomes steeper with increasing salt concentration. The concentration of co-ions is drastically increased close to the surface. As a result the total concentration of ions at the surface and thus the osmotic pressure is increased. 

For an electrophysiological experiment you form an electrode from a 5 cm long platinum wire (0.4 mm diameter) by bending it in the shape of a spiral. Calculate the total capacitance of the diffuse electric double layer for aqueous solutions of a monovalent salt at concentrations of 0.1 and 0.001 M. Assume a low surface potential. 

For conducting and completely polarizable surfaces, the capacitance can be measured directly with great precision. In the most simple capacitance measurement, called chronoamperome-try, a potential step AU is applied to an electrode (Fig. 5.10). A current flows due to charging of the diffuse electrical double layer. The current flows until the capacitance is fully charged. By measuring the current as a function of time and integrating the curve with respect to time we get the charge Q. The total capacitance C is easily obtained from C = CA A = Q/AU. 

Figure 7.1 Schematic representation of a diffuse electric double layer...

Calculate the thickness of the diffuse electric double layer for a negatively charged solid surface in contact with the following... 

Surface charge influences the distribution of nearby ions in a polar medium ions of opposite charge (counter-ions) are attracted to the surface while those of like charge (co-ions) are repelled. Together with mixing caused by thermal motion, a diffuse electric double layer is formed. 

Figure 4.2 Illustration of the diffuse electric double layer showing the distributions of counter- and co-ions. Courtesy L.A. Ravina, Zeta-Meter, Inc., Staunton, Va.

Topical application of an ionic polymer forms a diffusion electric double layer on the surface of the skin. We evaluated the effects of topical application of ionic polymers on the recovery rate of the skin barrier after injury. Application of a nonionic polymer did not affect the barrier recovery. Application of sodium salts of anionic polymers accelerated the barrier recovery, while that of cationic polymers delayed it. Topical application of a sodium-exchange resin accelerated the barrier recovery, but application of a calcium-exchange resin had no effect, even when the resins had the same structure. Application of a chloride-exchange resin delayed barrier recovery. Thus, topical application of ionic polymers markedly influenced skin barrier homeostasis (Figure 15.2). 

Shomer, I., Frenkel, H., and Polinger, C. (1991). The existence of a diffuse electric double layer at cellulose fibril surfaces and its role in the swelling mechanism of parenchyma plant cell walls. Carbohydr. Polym. 16 199-210. 

Since these interfaces are usually constructed of charged detergents a diffuse electrical double layer is produced and the interfacial boundary can be characterized by a surface potential. Consequently, electrostatic as well as hydrophilic and hydrophobic interactions of the interfacial system can be designed. In this report we will review our achievements in organizing photosensitized electron transfer reactions in different microenvironments such as bilayer membranes and water-in-oil microemulsions.In addition, a novel solid-liquid interface, provided by colloidal Si02 particles in an aqueous medium will be discussed as a means of controlling photosensitized electron transfer reactions. 

Colloidal Si02 particles in an aqueous suspension provide a solid-liquid interface. The silanol groups on the particle surface are ionized at a pH 6. Consequently, the surface of the particle is negatively charged and a diffuse electrical double layer is produced in the vicinity of the solid interface (17,18). Because of the negative charges on the particles they repel one another and their agglomeration is prevented. The particles can be used to exert electrostatic repulsive and attractive interactions with the components involved in photosensitized reactions. 

The discussion of the relative stability of solutions with inverse micelles and of liquid crystals containing electrolytes may be limited to the enthalpic contributions to the total free energy. The experimentally determined entropy differences between an inverse micellar phase and a lamellar liquid crystalline phase are small (12). The interparticle interaction from the Van der Waals forces is small (5) it is obvious that changes in them owing to added electrolyte may be neglected. The contribution from the compression of the diffuse electric double layer is also small in a nonaqueous medium (II) and their modification owing to added electrolyte may be considered less important. It appears justified to limit the discussion to modifications of the intramicellar forces. 

The earlier concepts of microemulsion stability stressed a negative interfacial tension and the ratio of interfacial tensions towards the water and oil part of the system, but these are insuflBcient to explain stability (13). The interfacial free energy, the repulsive energy from the compression of the diffuse electric double layer, and the rise of entropy in the dispersion process give contributions comparable with the free energy, and hence, a positive interfacial free energy is permitted. 

Polarizahon lowered repulsive osmotic pressure in the overlapped diffuse electrical double layers of the droplets and accelerated demulsihcahon. 

Double Layer Interactions and Interfacial Charge. Schulman et al (42) have proposed that the phase continuity can be controlled readily by interfacial charge. If the concentration of the counterions for the ionic surfactant is higher and the diffuse electrical double layer at the interface is compressed, water-in-oil microemulsions are formed. If the concentration of the counterions is sufficiently decreased to produce a charge at the oil-water interface, the system presumably inverts to an oil-in-water type microemulsion. It was also proposed that for the droplets of spherical shape, the resulting microemulsions are isotropic and exhibit Newtonian flow behavior with one diffused band in X-ray diffraction pattern. Moreover, for droplets of cylindrical shape, the resulting microemulsions are optically anisotropic and non-Newtonian flow behavior with two di-fused bands in X-ray diffraction (9). The concept of molecular interactions at the oil-water interface for the formation of microemulsions was further extended by Prince (49). Prince (50) also discussed the differences in solubilization in micellar and microemulsion systems. 

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