Electrodes diffuse double layer

F r d ic Current. The double layer is a leaky capacitor because Faradaic current flows around it. This leaky nature can be represented by a voltage-dependent resistance placed in parallel and called the charge-transfer resistance. Basically, the electrochemical reaction at the electrode surface consists of four thermodynamically defined states, two each on either side of a transition state. These are (11) (/) oxidized species beyond the diffuse double layer and n electrons in the electrode and (2) oxidized species within the outer Helmholtz plane and n electrons in the electrode, on one side of the transition state and (J) reduced species within the outer Helmholtz plane and (4) reduced species beyond the diffuse double layer, on the other. 

The electrical characteristics, along with the salts, their movement through soil, and the diffuse double layer must be kept in mind when making any soil measurement using electricity or electrodes. 

Soil has electrical characteristics associated with its components, salts, ions in solution, and the diffuse double layer. All, singly or in combination, can affect electrical measurements in soil. Electrodes inserted into soil are used to... 

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. 

The compact double layer extends from the electrode to the plane of the fixed charges at a distance x = Xjj from the electrode. The diffuse double layer extends from the distance Xh to the bulk of the solution. This is shown schematically in Figure 4.9. 

There are, however, differences in the geometry of the two problems. These differences affect the mathematical development. Thus, the central ion puts out a spherically symmetrical field. In contrast, the electrode is like an infinite plane (infinite vis-a-vis the distances at which ion-electrode interactions are considered), and its field displays a planar symmetry. Otherwise, the technique of analysis of the diffuse double layer proceeds along the same lines as in the theoiy of long-range ion-ion interactions (Section 3.3).43... 

Fig. 2.2 Structure of the electric double layer under different conditions of electrode polarization (a) metal positively charged, anions present at the inner Helmholtz plane (chemically interacting with metal) and in the diffuse double layer beyond the outer Helmholtz plane (b) metal negatively charged, inner Helmholtz plane empty, cations in diffuse layer (c) metal positively charged, strong adsorption of anions in inner Helmholtz plane, balancing cations in the diffuse layer...

The electric field which actually affects the charge transfer kinetics is that between the electrode and the plane of closest approach of the solvated electroactive species ( outer Helmholtz plane ), as shown in Fig. 2.2. While the potential drop across this region generally corresponds to the major component of the polarization voltage, a further potential fall occurs in the diffuse double layer which extends from the outer Hemlholtz plane into the bulk of the solution. In addition, when ions are specifically absorbed at the electrode surface (Fig. 2.2c), the potential distribution in the inner part of the double layer is no longer a simple function of the polarization voltage. Under these circumstances, serious deviations from Tafel-like behaviour are common. 

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. 

Another important feature is the relative size of the diffusion layer with respect to the double layer. The diffusion-layer dimensions are proportional to the size of the electrode, and can approach the size of the double layer with electrodes of molecular dimensions [95]. This can also occur in other situations explored with microelectrodes. For example, in solutions of very dilute electrolyte, the diffuse double layer extends several nanometers into solution [62]. Alternatively, very fast cyclic voltammetry results in a very small diffusion layer, which may be of dimensions similar to the double layer [46]. In all these situ-... 

In the electrochemical technique, the electrode provides the source (reduction) or sink (oxidation) for electrons. Variation of the applied potential provides the driving force that enables the redox reaction to occur. Organic depolarizers diffuse toward the electrode surface until they are sufficiently close to the electrode (the double-layer region) to accept electrons from the electrode and then to diffuse away from the electrode surface and to become involved in the bulk solution. 

The addition of the inert electrolyte affords other advantages. The most important point is that the conductivity of the solution increases (and thus the ohmic drop decreases through a decrease of the resistance of the cell, Rccw see Sect. 1.9). Moreover, the diffuse double layer narrows, being formed mainly by the ions of the inert electrolyte (with a sharp potential drop over a very short distance from the electrode surface). This makes the capacitance more reproducible and the Frumkin effects less obtrusive. Activity coefficients of the electroactive species are also less variable (and, therefore, quantities like formal potentials and rate constants), since... 

In an attempt to rationalize the measured capacitance values, and especially the low value for the basal plane (ca. 3pF/cm2), these authors first concluded that space charge within the electrode is the dominant contribution (rather than the compact double layer with ca. 15-20 pF/cm2, or the diffuse double layer with >100 pF/cm2). They then applied the theory of semiconductor electrodes to confirm this and obtained a good agreement by assuming for SAPG a charge carrier density of 6 x 1018/cm3 and a dielectric constant of 3 for GC, they obtained 13 pF/cm2 with the same dielectric constant and 1019 carriers per cubic centimeter. 

The formula (VI-29) is valid for any uni-univalent electrolyte. It is evident from this formula that the sign of the liquid junction potential and also the orientation of the diffusion double layer, in respect to the double layer at the electrodes, depends on the relative magnitude of the anion and cation transference numbers. Should the anion transference number exceed that of cation... 

Gouy length — The width of the diffuse double layer at an electrode depends on a number of factors among which the charge density q on the surface of the metal and the concentration c of electrolyte in the solution are paramount. Roughly speaking, the charge in, and the potential of, the double layer falls off exponentially as one proceeds into the solution from the interface. 

At oxide semiconductor electrode-electrolyte interfaces, with no contribution from surface states, the electrical potential drop exhibits three components the potential drop across the space-charge region, sc, across the Helmholtz layer, diffuse double layer, d, the latter becoming negligible in concentrated electrolytes... 

The chemical system at the surface will be quite complex. There will be strongly bound species at various sites on the metal surface. Where these are ionic, the electric field established at the surface will tend to attract ions of opposite charge from the solution. The first layer has been termed the electrode double layer, while the gegenion distribution in the solution is called the diffuse double layer. A theoretical analysis of the double layer has been made by Gouy and Chapman and adapted to kinetic analysis by Stern. For references, and discussion see paper by D. C. Grahame, J. Chem, Phys, 21, 1054 (1953). 

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