Dependence on the electrode potential

We consider the transfer of an ion or proton from the solution to the surface of a metal electrode often this is accompanied by a simultaneous discharge of the transferring particle, such as by a fast electron transfer. The particle on the surface may be an adsorbate as in the reaction  

In this case the discharge can be partial that is, the adsorbate can carry a partial charge, as discussed in Chapter 4. Alternatively the particle can be incorporated into the electrode as in the deposition of a metal ion on an electrode of the same composition, or in the formation of an alloy. An example of the latter is the formation of an amalgam such as  

The reverse process is the transfer of a particle from the electrode surface to the solution often the particle on the surface is uncharged or partially charged, and is ionized during the transfer. 

Ion- and proton-transfer reactions are almost always preceded or followed by other reaction steps. We first consider only the charge-transfer step itself. 

Ions and protons are much heavier than electrons. While electrons can easily tunnel through layers of solution 5 to 10 A thick, protons can tunnel only over short distances, up to about 0.5 A, and ions do not tunnel at all at room temperature. The transfer of an ion from the solution to a metal surface can be viewed as the breaking up of the solvation cage and subsequent deposition, the reverse process as the jumping of an ion from the surface into a preformed favorable solvent configuration (see Fig. 9.1). 

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The fact that more than one molecule of water may be displaced for each anion adsorbed, and that the adsorption energy of these water molecules will show a complex dependence on the electrode potential. 

In this relation,

mathematical function, which depends on the electrode potential AU= U- Up, and has, as we will see, a significant meaning for microwave electrochemistry ... 

If a gas bubble adheres to an electrode surface being in contact with an electrolyte solution, the contact angle can be measured as an indicator of the interfacial tension and its change. The respective relationship is cos 6= (y ni - y,m)/ g,s with g, s, m referring to the gas, solution and metal phase respectively. It was initially observed by Mdller, that 6 changes with E [08M61]. Assuming that s and do not depend on the electrode potential a plot of relationship follows ... 

The mechanical friction between the electrode surfaee under investigation and a suitable probe depends on the electrode potential showing a maximum at Ep-. Of various experimental setups reviewed previously [69Boc2] the most recent one is used to measure the frietion between a test eleetrode in wire shape and a cylindrical slider sitting on the wire [69Boel]. Results are interpreted in terms of the repulsion of double layers being present on the wire and the slider [69Boe2]. (Data obtained with this method are labelled F). 

If sound vibrations are applied to an electrode being in contact with a solution, a variable electrode potential component AE is generated. Its amplitude depends on the electrode potential E. It shows a maximum at the Epzc Further details have been provided elsewhere [66Kuk2]. (Data obtained with this method are labelled AE). 

Permanent deformation has also been investigated. The rate of flow of gold wires has been found to depend on the electrode potential with a minimum of the rate at E i.c [51Pfu]. The ereep of a lead eleetrode has been studied [69Lik]. (Data obtained with this method are labelled FL). 

In Eq. (28), the methanol residue is mainly adsorbed CO. As diseussed earlier, other kinds of adsorbed speeies ean also be present on the eleetrode surfaee. The different species and their degree of coverage on the Pt surface depend on the electrode potential and also on the nature and the structure of the electrode surface. For the sake of simplicity, if only two types of adsorbed species, COads and CHOads, are considered, Eq. (28) becomes ... 

Electrochemical reactions differ fundamentally from chemical reactions in that the kinetic parameters are not constant (i.e., they are not rate constants ) but depend on the electrode potential. In the typical case this dependence is described by Eq. (6.33). This dependence has an important consequence At given arbitrary values of the concentrations d c, an equilibrium potential Eq exists in the case of electrochemical reactions which is the potential at which substances A and D are in equilibrium with each other. At this point (Eq) the intermediate B is in common equilibrium with substances A and D. For this equilibrium concentration we obtain from Eqs. (13.9) and (13.11),... 

Depending on the electrode potential, this radical either adds a second electron and a second proton to yield the corresponding secondary alcohol (A), or it dimerizes to the pinacol (B), a dihydric ditertiary alcohol ... 

The surface concentration Cq Ajc in general depends on the electrode potential, and this can affect significantly the form of the i E) curves. In some situations this dependence can be eliminated and the potential dependence of the probability of the elementary reaction act can be studied (called corrected Tafel plots). This is, for example, in the presence of excess concentration of supporting electrolyte when the /i potential is very small and the surface concentration is practically independent of E. However, the current is then rather high and the measurements in a broad potential range are impossible due to diffusion limitations. One of the possibilities to overcome this difficulty consists of the attachment of the reactants to a spacer film adsorbed at the electrode surface. The measurements in a broad potential range give dependences of the type shown in Fig. 34.4. 

When the poisoning reaction is analyzed under potential control, the formation rate is dependent on the electrode potential. The hrst experiments that clearly showed that the poison formation reaction was potential-dependent were performed by Clavilier using pulsed voltammetry [Clavilier, 1987] (Fig. 6.15). In this technique, a short pulse at high potential is superimposed on a normal voltammetric potential... 

These facts indicate that two mechanisms are involved, depending on the electrode potential in the case of a-FePc whereas only one mechanism seems to be involved in the case of /3-FePc. 

Surface reactions that give rise to the electric crurent measmed depend on the electrode potential range and the type of measurements reported. The dominating reactions contributing to the voltammetric data in Fig. 13a-d are chemisorbed CO oxidation, oxidation of methanol to CO2 (on both scans), and chemisorbed CO formation on the reverse mn ... 

Resolving this equation for c at the electrode surface, i.e., at x = 0, Ilkovic assumed the following initial and final conditions c — C for t — 0 and c = c0, the constant value obtained at t > 0, dependent on the electrode potential thus he obtained the expression... 

Heterogeneous chemical reactions in which adsorbed species participate are not pure chemical reactions, as the surface concentrations of these substances depend on the electrode potential (see Section 4.3.3), and thus the reaction rates are also functions of the potential. Formulation of the relationship between the current density in the stationary state and the concentrations of the adsorbing species in solution is very simple for a linear adsorption isotherm. Assume that the adsorbed substance B undergoes an... 

Carbonyl compounds are reduced to alcohols, hydrocarbons or pinacols (cf., for example, Eq. 5.1.8), where the result of the electrode process depends on the electrode potential. 

The modulation of the charge of the adsorbed atom by the vibrations of heavy particles leads to a number of additional effects. In particular, it changes the electron and vibrational wave functions and the electrostatic energy of the adatom. These effects may also influence the transition probability and its dependence on the electrode potential. 

An important question is how this system can work with sugar alcohols and non-reducing sugars. The oxidation is catalysed by the electrode surface, which means that the response is dependent on the electrode potential of the catalytic state rather than the redox potential. 

The Gibbs energy AG°d depends on the electrode potential . This dependence will be different for anions, cations, and neutral species. The simplest possible case is the adsorption and total discharge of an ion according to the equation ... 

The phenomenological treatment assumes that the Gibbs energies of activation Gox and Gred depend on the electrode potential , but that the pre-exponential factor A does not. We expand the energy of activation about the standard equilibrium potential >0o of the redox reaction keeping terms up to first order, we obtain for the anodic reaction ... 

As an example we consider the Au(100) surface of a single crystal Au electrode [3]. This is one of the few surfaces that reconstruct in the vacuum. The perfect surface with its quadratic structure is not thermodynamically stable it rearranges to form a denser lattice with a hexagonal structure (see Fig. 15.3), which has a lower surface energy. In an aqueous solution the surface structure depends on the electrode potential. In sulfuric acid the reconstructed surface is observed at potentials below about 0.36 V vs. SCE, while at higher potentials the reconstruction disappears, and the perfect quadratic structure is ob-... 

The relative position of the electronic level eo to the Fermi level depends on the electrode potential. We perform estimates for the case where there is no drop in the outer potential between the adsorbate and the metal - usually this situation is not far from the pzc. In this case we obtain for an alkali ion eo — Ep — where is the work function of the metal, and I the ionization energy of the alkali atom. For a halide ion eo — Ep = electron affinity of the atom. 

Vibrational spectroscopy techniques are quite suitable for in situ characterization of catalysts. Especially infrared spectroscopy has been used extensively for characterization of the electrode/solution interphases, adsorbed species and their dependence on the electrode potential.33,34 Raman spectroscopy has been used to a lesser extent in characterizing non-precious metal ORR catalysts, most of the studies being related to characterization of the carbon structures.35 A review of the challenges and applications associated with in situ Raman Spectroscopy at metal electrodes has been provided by Pettinger.36... 

It is shown that the rate-limiting step in the photoelectrochemical evolution of hydrogen in an HF electrolyte is linearly dependent on the excess electron concentration at the surface of the p-type silicon electrode. The rate of this step does not depend on the electrode potential and the H+ concentration in the solution, but is sensitive to the surface pretreatment [Sell]. The plateau in the I-V curve, slightly... 

In the case of electrode reactions, the activation energy depends on the electrode potential. We now consider an elementary step in which a charged particle (charge number, zi) transfers across the compact double layer on the electrode interface as shown in Fig. 7-7. In the reaction equilibrium, where the electrochemical potentials of reacting particles are equilibrated between the initial state and the final state (Pk o = Pf( i)), the forward activation energy equals the backward activation energy (P , - Pi = P, i- Pr) P , is the electrochemical potential of the reacting particle at the activated state in equilibrium. 

In the state of band edge level pinning, the electron level of redox particles with the state density of DredoxCe), relative to the electron level rf semiconductor with the state density of Dsc(e), remains unchanged at the electrode interface irrespective of electrode potential. On the other hand, in the state of Fermi level pinning, the electron level of redox particles relative to the electron level of semiconductor electrode depends on the electrode potential in the same way as occurs with metal electrodes (quasi-metallization of semiconductor electrodes). 

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