Structure of the double layer

Two hundred years were required before the molecular structure of the double layer could be included in electrochemical models. The time spent to include the surface structure or the structure of three-dimensional electrodes at a molecular level should be shortened in order to transform electrochemistry into a more predictive science that is able to solve the important technological or biological problems we have, such as the storage and transformation of energy and the operation of the nervous system, that in a large part can be addressed by our work as electrochemists. 

This potential-energy surface will change when the electrode potential is varied consequently the energy of activation will change, too. These changes will depend on the structure of the double layer, so we cannot predict the value of the transfer coefficient a unless we have a detailed model for the distribution of the potential in the double layer. There is, however, no particular reason why a should be close to 1/2. Also, a temperature dependence of the transfer coefficient is not surprising since the structure of the double layer changes with temperature. 

The simplest structure of the double layer is the surface charge in one plane and the counter charge in a similar parallel plane. Then, to a first approximation, the double layer may be visualized as a parallel plate condenser of distance d between the two plates and with its capacitance, C... 

A schematic example is given in Fig. A.4.5. The slope of the electrocapillary curve depends on the nature of the solution or the equilibrium structure of the double layer and on the specific sorbability of dissolved substances. In line with the Gibbs equation (Eq. 4.3), sorbable species depress the interfacial tension. 

The electrical double layer has been dealt with in countless papers and in a number of reviews, including those published in previous volumes of the Modem Aspects of Electrochemistry series/ The experimental double layer data have been reported and commented on in several important works in which various theories of the structure of the double layer have been postulated. Nevertheless, many double layer-related problems have not been solved yet, mainly because certain important parameters describing the interface cannot be measured. This applies to the electric permittivity, dipole moments, surface density, and other physical quantities that are influenced by the electric field at the interface. It is also often difficult to separate the electrostatic and specific interactions of the solvent and the adsorbate with the electrode. To acquire necessary knowledge about the metal/solution interface, different metals, solvents, and adsorbates have been studied. 

We show that the electric field in the metal-solution interphase is very high (e.g., 10 or lO V/cm). The importance of understanding the structure of the metal-solution interphase stems from the fact that the electrodepKJsition processes occur in this very thin region, where there is a very high electric field. Thus, the basic characteristics of the electrodeposition processes are that they proceed in a region of high electric field and that this field can be controlled by an external power source. In Chapter 6 we show how the rate of deposition varies with the potential and structure of the double layer. 

Structure of the double layer, including concentration of different species present in the solution. The pKJtential dependence of additive adsorption and their effects on growth forms are discussed in Chapter fO. 

Before going into this matter of ions, we should not take with us the impression that the solvent molecules are unimportant to the structure of the double layer. On the... 

Equation (39) is known as the Helmholtz-Smoluchowski equation. No assumptions are made in its derivation as to the actual structure of the double layer, only that the Poisson equation applies and that bulk values of rj and e apply within the double layer. It has been shown that this result is valid for values of kR larger than about 100 (i.e., kRs > 100 for spherical particles). 

The structure of the double layer can be altered if there is interaction of concentration gradients, due to chemical reactions or diffusion processes, and the diffuse ionic double layer. These effects may be important in very fast reactions where relaxation techniques are used and high current densities flow through the interface. From the work of Levich, only in very dilute solutions and at electrode potentials far from the pzc are superposition of concentration gradients due to diffuse double layer and diffusion expected [25]. It has been found that, even at high current densities, no difficulties arise in the use of the equilibrium double layer conditions in the analysis of electrode kinetics, as will be discussed in Sect. 3.5. 

In the absence of excess of inert electrolyte, the concentration of an ionic reactant in the pre-electrode plane and the potential at this plane are interconnected and depend on the structure of the double layer. Thus, the apparent electrode reaction order will also be influenced by the double layer. 

Electrically, the electrical double layer may be viewed as a capacitor with the charges separated by a distance of the order of molecular dimensions, The measured capacitance ranges from about two to several hundred microfarads per square centimeter, depending on the structure of the double layer, the potential, and the composition of the electrode materials. 

The magnitude of the ohmic drop at a microelectrode can be evaluated quite readily for case 1 from a knowledge of the specific solution resistance (obtained from conductivity measurements such as in Table 12.1) and the expressions for the voltammetric current for the specific microelectrode employed. Case 2 is also straightforward if the free concentration of ions exceeds that of the electroactive species. However, the situation is somewhat more complicated for the third class. In this case, and in case 2 for fully associated electrolyte, migration as well as diffusion can affect the observed voltammetric signals. In all three cases, the situation may be further complicated by a change in structure of the double layer. However, this is ignored for now, and is considered in the section on very small electrodes. 

These examples show that our knowledge of ion radical chemistry in homogenous soluction is far from complete and that extrapolation of this knowledge to ion radicals produced at electrodes is a risky procedure, especially if one contemplates the additional complexities involved. The composition of the medium in the vicinity of the electrode is not the same as in the bulk of the solution (Sect 5.2), the structure of the double-layer can at its best be the subject of educated guesses, and due allowance must be made for the possibility that reactions may take place between adsorbed intermediates. 

Cation Cationic structure and size will affect the viscosity and conductivity of the liquid and hence will control mass transport of metal ions to the electrode surface. They will also be adsorbed at the electrode surface at the deposition potential and hence the structure of the double layer is dominated by cations. Some studies have shown that changing the cationic component of the ionic liquid changes the structure of deposits from microcrystalline to nanocrystalline [27]. While these changes are undeniable more studies need to be carried out to confirm that it is a double layer effect. If this is in fact the case then the potential exists to use the cationic component in the liquid as a built-in brightener. 

One explanation for the change in deposit morphology with time observed by Sun and others [105-108] could be the structure of the double layer during deposition. 

The structure of the double layer is also affected by the addition of lithium ions. Few studies have been carried out on the structure of the double layer in an ionic... 

In any system whatever containing matter in two phases with different charges, the application of an electric field causes one phase to travel relatively to the other, the negatively charged phase moving to the positive pole, and the positively charged one to the negative pole. This motion is called electrokinetic . The rate of relative motion of the two phases is proportional to the intensity of the applied field it also depends on the size and shape of the objects, on the properties of the fluid, and on the structure of the double layer, particularly on a certain potential, which will be described in more detail presently, called the potential. 

Mixed type of inhibitors are generally represented by organic compounds. Irrespective of the type of inhibitor, the inhibition process involves transport of inhibitor to the metal site followed by interaction of the inhibitor with the surface of the metal, resulting in protection. We now recall the electrical double layer consisting of inner and outer Helmholtz planes and the distribution of anions (A ), cations and water dipoles. This is schematically shown in Figure 1.59. When an inhibitor is added the structure of the double layer is affected, with the inhibitor displacing the adsorbed water molecules on the metal surface and taking their place on the metal surface. 

As pointed out in the introduction, the structure of the double layer between a semiconductor electrode and an elec-... 

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