Charge of the electrode

Another progress in our understanding of the ideally polarizable electrode came from theoretical works showing that the metal side of the interface cannot be considered just as an ideal charged plane. A simple quantum-mechanical approach shows that the distribution of the electron gas depends both on the charge of the electrode and on the metal-solution coupling [12,13]. 

For any quantity/ = f gj, g, a) we have, from the equivalence between changing the position and charging of the electrode... 

An important problem encountered with polymer electrodes is that of overoxidation. It occurs after reversible charging of the electrode at high oxidation potentials and leads to polymer degeneration. The results of thorough studies show that such degenerative mechanisms are promoted by the nucleophilicity of the solvent. Especially the activity of water leads to the formation of quinone-type compounds, to the cleavage of C—C bonds, the liberation of CO2, and the formation of carboxylic acids Hence, there is a clear tendency to avoid both nucleophile solvents... 

At a definite value of the electrode potential E, the charge of the electrode s surface and hence the value of drop to zero. This potential is called the point of zero charge (PZC). The metal surface is positively charged at potentials more positive than the PZC and is negatively charged at potentials more negative than the PZC. The point of zero charge is a characteristic parameter for any electrode-electrolyte interface. The concept of PZC is of exceptional importance in electrochemistry. 

Electrode polarization is associated with a change in EDL charge density at the electrode surface. Other changes in surface state of the electrode are possible, too (e.g., the adsorption or desorption of different components, which also involve a consumption of electric charge). By convention, we describe this set of nonfaradaic processes as charging of the electrode surface. 

A certain potential is applied to the electrode with the potentiostatic equipment, and the variation of current is recorded as a function of time. At the very beginning a large current flows, which is due largely to charging of the electrode s EDL as required by the potential change. The maximum current and the time of EDL charging depend not only on the electrode system and size but also on the parameters of the potentiostat used. When this process has ended, mainly the faradaic component of current remains, which in particular will cause the changes in surface concentrations described in Section 11.2. 

The quantity dyl3 In a2 at the potential of the electrocapillary maximum is of basic importance. As the surface charge of the electrode is here equal to zero, the electrostatic effect of the electrode on the ions ceases. Thus, if no specific ion adsorption occurs, this differential quotient is equal to zero and no surface excess of ions is formed at the electrode. This is especially true for ions of the alkali metals and alkaline earths and, of the anions, fluoride at low concentrations and hydroxide. Sulphate, nitrate and perchlorate ions are very weakly surface active. The remaining ions decrease the surface tension at the maximum on the electrocapillary curve to a greater or lesser degree. 

The diffuse layer is formed, as mentioned above, through the interaction of the electrostatic field produced by the charge of the electrode, or, for specific adsorption, by the charge of the ions in the compact layer. In rigorous formulation of the problem, the theory of the diffuse layer should consider ... 

The model is most vulnerable in the way it accounts for the number of particles that collide with the electrode [50, 115], In the model, the mass transfer of particles to the cathode is considered to be proportional to the mass transfer of ions. This greatly oversimplifies the behavior of particles in the vicinity of an interface. Another difficulty with the model stems from the reduction of the surface-bound ions. Since charge transfer cannot take place across the non-conducting particle-electrolyte interface, reduction is only possible if the ion resides in the inner Helmholtz layer [116]. Therefore, the assumption that a certain fraction of the adsorbed ions has to be reduced, implies that metal has grown around the particle to cover an identical fraction of the surface. Especially for large particles, it is difficult to see how such a particle, embedded over a substantial fraction of its diameter, could return to the plating bath. Moreover, the parameter itr, that determines the position of the codeposition maximum, is an artificial concept. This does not imply that the bend in the polarisation curve that marks the position of itr is illusionary. As will be seen later on, in the case of copper, the bend coincides with the point of zero-charge of the electrode. 

In a CV measurement, the current output always contains two components the Faradaic current, /F, due to the reaction of the redox species and the capacitive charging current, /c, which results from the charging of the electrode double layer and the diffusion layer. (This diffusion layer contains all charged and polar species in the solution and therefore differs from that of the redox species.) While /F changes linearly with vm as determined by diffusion, Ic is directly proportional to v as shown below, where CD is the total electrode capacitance and q the added capacitance charge ... 

Once the values of the charge of the electrode in the presence of adsorbates are obtained, i.e., (<7M)e, one may apply one of the electrocapillaiy equations that will be derived in Section 6.5.3. Specifically, Eq. (6.95) can be integrated to obtain values of... 

On this basis it seems that metal properties do affect the total capacity, C, through the changes in M- Thus, the next question seems quite obvious Would it be possible to measure and then corroborate its contribution to the total capacity of the double layer Unfortunately a direct measurement of CM is not possible because the metal will always form part of the total double layer and therefore only the total capacity can be measured. However, we may still have some weapons left. It is possible to obtain an indirect measurement of in the absence of specific adsorption. The way to proceed is as follows. From Eq. (6.124) we see that CH is independent of the concentration in solution, in contrast to the term Qji which involves the term c0 [see Eq. (6.130)]. However, CM should be independent of the concentration of the solution since it involves only the electrode properties. Thus, it is reasonable to combine the concentration-independent terms and say, for example, that the term CM is included in the CH term.48 Thus, a plot of CH vs. the charge of the electrode, qu, would give an indication of the effect of CM on the interfacial properties. Figure 6.70 shows one of those graphs. Thus, the shape of this graph, the asymmetric parabola, is most probably due to the influence of the properties of the metal in the interfacial properties. 

Section 6.7.6). This means that to determine 5conf, one has to consider in the corresponding calculations the values of [AGJp- and [AG°] 1 igure 6.84(a) shows howSconf varies as a function of the charge of the electrode. 

What conclusions can be obtained from these curves [Fig. 6.84(a-c)] Both the configurational and the libratory entropy of surface water show a strong dependence on the charge or the electrode, showing a maximum at a potential negative to the pzc, just as the experimental results indicate [see Fig. 6.84(d)]. On the other hand, the vibrational entropy of surface water shows a small linear variation with the charge of the electrode. Furthermore, what these three contributions are added according to Eq. (6.166), the result is a curve very similar to that observed experimentally [see Fig.6.84(d)]. 

From this discussion we can see that it is not so simple to determine the value of the lateral interactions of the reference ion. To do so it is necessary to know what type of molecules are surrounding the ion. The type of molecules and their number depend greatly on the state of adsoiption, i.e., how many ions are already adsorbed on the electrode. And this value will depend largely on the chatge of the electrode. Thus the lateral interactions are a function of the charge of the electrode. 

Equation (6.183) or Eq. (6.184) can be identified as the relation between the coverage, the activity in solution of the adsorbed species, and the temperature of the system. Thus, in order to define the system well, only one variable is missing, the charge of the electrode. However this variable is intrinsically expressed in the term AG°. Thus, Eq. (6.183) or Eq. (6.184) represents the isotherm of the system given by the reaction in Eq. (6.179). 

Electrode-solution interface. The tightly adsorbed inner layer (also called the compact, Helmholtz, or Stem layer) may include solvent and any solute molecules. Cations in the inner layer do not completely balance the charge of the electrode. Therefore, excess cations are required in the diffuse part of the double layer for charge balance. 

The chloride ions of the brine solution are attracted to the positive charge of the electrode. Upon contact, they lose electrons to form chlorine molecules, Cl2. Notably, some external source of eneigy is required for this electrode to maintain its positive chaige. 

The Cottrell equation states that the product it,/2 should be a constant K for a diffusion-controlled reaction at a planar electrode. Deviation from this constancy can be caused by a number of situations, including nonplanar diffusion, convection in the cell, slow charging of the electrode during the potential step, and coupled chemical reactions. For each of these cases, the variation of it1/2 when plotted against t is somewhat characteristic. 

Charging of the electrode-electrolyte double-layer capacitance to the new potential... 

Residual currents, also referred to as background currents, are the sum of faradaic and nonfaradaic currents that arise from the solvent/electrolyte blank. Faradaic processes from impurities may be practically eliminated by the careful experimentalist, but the nonfaradaic currents associated with charging of the electrode double layer (Chap. 2) are inherent to the nature of a potential sweep experiment. Equation 23.5 describes the relationship between this charging current icc, the double-layer capacitance Cdl, the electrode area A, and the scan rate v ... 

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