Double excess charge

On the electrode side of the double layer the excess charges are concentrated in the plane of the surface of the electronic conductor. On the electrolyte side of the double layer the charge distribution is quite complex. The potential drop occurs over several atomic dimensions and depends on the specific reactivity and atomic stmcture of the electrode surface and the electrolyte composition. The electrical double layer strongly influences the rate and pathway of electrode reactions. The reader is referred to several excellent discussions of the electrical double layer at the electrode—solution interface (26-28). 

Even in the absence of Faradaic current, ie, in the case of an ideally polarizable electrode, changing the potential of the electrode causes a transient current to flow, charging the double layer. The metal may have an excess charge near its surface to balance the charge of the specifically adsorbed ions. These two planes of charge separated by a small distance are analogous to a capacitor. Thus the electrode is analogous to a double-layer capacitance in parallel with a kinetic resistance. 

According to the model proposed by Verwey and Niessen (1939), an electric double layer is formed at an ITIES, which consists of two ionic space charge regions. As a whole the electric double layer is electrically neutral, so for the excess charge density in the part of the double layer in the aqueous phase, and for the part in the organic phase,... 

Equation (2.33) now defines the double layer in the final model of the structure of the electrolyte near the electrode specifically adsorbed ions and solvent in the IHP, solvated ions forming a plane parallel to the electrode in the OHP and a dilfuse layer of ions having an excess of ions charged opposite to that on the electrode. The excess charge density in the latter region decays exponentially with distance away from the OHP. In addition, the Stern model allows some prediction of the relative importance of the diffuse vs. Helmholtz layers as a function of concentration. Table 2.1 shows... 

Note that both before and after the experiment the sum of the charges on the metal surface and in the adsorbate layer is zero, and hence there is no excess charge in the diffuse part of the double layer. However, after the adsorption has occurred, the electrode surface is no longer at the pzc, since it has taken up charge in the process. 

To obtain the dipole moment we set o = —o% in Eq. (18.14) so that the diffuse double layer is free of excess charge (see Section 4.3). 

Despite these arguments and the conceptual attractiveness of the procedure which is sketched in Fig. 1 convincing evidence for the relevance of a particular gas phase adsorption experiment can only be obtained by direct comparison to electrochemical data The electrode potential and the work function change are two measurable quantities which are particularly useful for such a comparison. In both measurements the variation of the electrostatic potential across the interface can be obtained and compared by properly referencing these two values 171. Together with the ionic excess charge in the double layer, which in the UHV experiment would be expressed in terms of coverage of the ionic species, the macroscopic electrical properties of the interracial capacitor can thus be characterized in both environments. 

An adsorbed layer of water molecules at the interface separates hydrated ions from the solid surface. The interfacial electric double layer can be represented by a condenser model comprising three distinct layers a diffuse charge layer in the ionic solution, a compact layer of adsorbed water molecules, and a diffuse charge layer in the solid as shown in Fig. 5-8. The interfacial excess charge on the... 

Fig. 5-8. An interfadal double layer model (triple-layer model) SS = solid surface OHP = outer Helmholtz plane inner potential tt z excess charge <2h = distance from the solid surface to the closest approach of hydrated ions (Helmluritz layer thickness) C = electric capacity.

Fig. 6-12. Interfacial excess charge in an compact double layer com-prising adsorbed water molecules and hydrated ions = potential of the compact layer (HL).

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... 

The simplest model of the structure of the metal-solution interphase is the Helmholtz compact double-layer model (1879). According to this model, all the excess charge... 

Figure 4.4. a) Helmholtz model of a double layer qy, excess charge density on metal excess charge density in solution, on HP b) linear variation of potential in the double layer with distance from the electrode. 

The current chapter discusses mechanisms of charge transfer reactions in double-stranded DNA (we will not deal with single-stranded DNA, or with individual bases or base-pair structures). We will also focus on interpretation of excess charge behavior in DNA molecules in terms of accepted theoretical models. 

How can this dipole potential be visualized Once again a thought experiment can be performed. The electrode and electrolyte phases are conceptually detached from each other and the double layer turned off. In this process, the excess charges and oriented-dipole layers that characterized the double layer are considered eliminated. 

The surface tension was stated (Section 6.4.5), on general grounds, to be related to the surface excess of species in the interphase. The surface excess in turn represents in some way the structure of the interface. It follows therefore that electrocapillaiy curves must contain many interesting messages about the double layer at the electrode/ electrolyte interface. To understand such messages, one must learn to decode the electrocapillary data. It is necessary to derive quantitative relations among surface tension, excess charge on the metal, cell potential, surface excess, and solution composition. 

Fig. 6.62. The Helmholtz-Perrin parallel-plate model, (a) A layer of ions on the OHP constitutes the entire excess charge in the solution. (b) The electrical equivalent of such a double layer is a parallel-plate condenser, (c) The corresponding variation of potential is a linear one. (Note The solvation sheaths of the ions and electrode are not shown in this diagram nor in subsequent ones.)...

When ions are present in a system that contains an interface, there will be a variation in the ion density near that interface that is described by a profile like that shown in Figure 7.13. The boundary we identify as the surface defines the surface excess charge, as explained in Chapter 7. Suppose that it was possible to separate the two bulk phases at this boundary in the manner shown in Figure 6.8. Then, each of the separated phases would carry an equal and opposite charge. These two charged portions of the interfacial region are called the electrical double layer. 

In the absence of specific adsorption and dipolar contributions, there is no excess charge in the whole double layer when positive and negative ions are equally distributed at the plane of closest approach qM and A02 will be both zero. The corresponding electrode potential is the potential of zero charge (pzc) which can be evaluated from the minimum in the differential capacity—potential curve for a metal electrode in contact with a dilute electrolyte [6]... 

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